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Research and Innovation

Stanford research is remarkable in both its breadth and depth , with research programs that reflect the expertise, creativity and initiative of the faculty who set the research agenda. Faculty have a long tradition of engaging with their colleagues and students within Stanford’s schools and working across disciplines.

Sponsored Research

There are more than 7,500 externally funded sponsored projects throughout the university, with the total sponsored support revenue of $1.98 billion during the fiscal year ending August 31, 2023, including the SLAC National Accelerator Laboratory (SLAC). The federal government sponsors over three-quarters of these projects, including SLAC.

Independent Laboratories, Centers and Institutes

There are 15 independent laboratories, centers and institutes that provide physical and intellectual intersections between schools and disciplines. These institutes are in line with Stanford’s long-standing tradition of crossing boundaries to tackle large problems, engaging faculty and their students in collaborations that range from international and economic studies to studies on the environment, energy and health. Visit the interdisciplinary programs website for more information.

Science, Technology, Engineering and Math (STEM) Laboratories and Institutes

• Stanford Bio-X
• Wu Tsai Neurosciences Institute
• Sarafan Chemistry, Engineering, and Medicine for Human Health (ChEM-H)
• Stanford Institute for Materials and Energy Sciences (SIMES)
• The Stanford PULSE Institute
• Kavli Institute for Particle Astrophysics and Cosmology (KIPAC)
• Geballe Laboratory for Advanced Materials (GLAM)
• E. L. Ginzton Laboratory
• W. W. Hansen Experimental Physics Laboratory (HEPL)

Policy Institutes

• Freeman Spogli Institute for International Studies (FSI)
• Stanford Institute for Economic Policy Research (SIEPR)
• Stanford Human-Centered Artificial Intelligence (HAI)

Humanities and Social Science Centers

• Stanford Center on Longevity (SCL)
• Center for Advanced Study in the Behavioral Sciences (CASBS) 

Other Special Research Centers

Slac national accelerator laboratory.

SLAC National Accelerator Laboratory is a U.S. Department of Energy national laboratory operated by Stanford. It shares five joint research centers and 18 joint faculty members with the university. SLAC is home to world-leading facilities for exploring nature’s smallest and fastest processes with X-rays and electrons. Research at SLAC spans chemistry, materials and energy sciences, bioscience, fusion energy science, high-energy physics, cosmology, advanced accelerator and technology development, and advanced computer science.

Hoover Institution

Established by Herbert Hoover—a member of Stanford’s Pioneer Class of 1895 and the 31st U.S. president—the Hoover Institution marked its centennial in 2019. Former Stanford Provost and U.S. Secretary of State Condoleezza Rice assumed the role of director on September 1, 2020. From its initial charge to collect materials documenting the experience of war and the pursuit of peace, the institution stands today as the world’s preeminent archive and policy research center dedicated to freedom, private enterprise and effective, limited government.

Jasper Ridge Biological Preserve

Jasper Ridge Biological Preserve , located in the Santa Cruz foothills about 15 minutes from the main Stanford campus, encompasses 1,193 acres and provides a natural laboratory for ecosystem research and teaching. Docent-led tours are offered to groups aligned with the preserve’s mission to contribute to the understanding of the Earth’s natural systems through research, education, and protection of the preserve’s resources. Call: 650-851-6813

Hopkins Marine Station

Hopkins Marine Station opened in 1892 as the first marine research facility on the Pacific Coast and the second in the United States. Located on Monterey Bay, Hopkins is home to marine research and study by 10 faculty, one lecturer, two emeritus faculty, and one emeritus lecturer.

Clinical Trials at Stanford Medicine

Join our community of volunteers leading the way in transformative research

Stanford Cancer Institute offers leading-edge research and compassionate care with over 250 actively recruiting clinical trials, investigating a broad spectrum of new preventative, diagnostic, and treatment strategies. 

More about the Cancer Institute  

Stanford Pediatric Clinical Trials play a vital role in developing new therapies for a large range of conditions that affect children. These trials can help pave the way for a brighter healthier future for our youngest generation.

More about Stanford Children's Health  

Healthy volunteers play a vital role in clinical studies, helping researchers learn how to keep people well. Some studies compare healthy people to those who have a specific disease or condition. 

More about being a healthy volunteer  

What is a clinical trial?

Clinical trials are research studies that explore whether a medical strategy, treatment or device is safe and effective for humans. These studies may also show which medical approaches work best for certain illnesses or groups of people. Clinical trials produce information that helps patients and their health-care providers make better health-related decisions. 

We're looking for healthy volunteers

Stanford research registry.

The Stanford Research Registry  connects people like you, with teams conducting research, to improve health care. If you are eligible for a study, researchers may contact you to see if you would like to learn more.

COVID-19 Clinical Studies

Explore COVID-19 Clinical Studies . Stanford Medicine researchers and scientists have launched dozens of research projects as part of the global response to COVID-19.  By participating in our COVID-19 clinical research, you help accelerate medical science by providing valuable insights into potential treatments and methods of prevention.

Stanford Diabetes Research Center

The Stanford Diabetes Research Center  (SDRC) is looking for participants, including healthy volunteers, to join the various diabetes-related studies being conducted at Stanford. Join the SDRC research registry

Project Baseline

Project Baseline  is a broad effort designed to develop a well-defined reference, or “baseline,” of good health. Its rich data platform will be used to better understand the transition from health to disease and identify additional risk factors for disease.

Stanford Well for Life

Stanford WELL for Life  wants to help you improve your health, wellness, and well-being through challenges, resources and tips to improve your well-being from Stanford experts.

Latest Clinical Trials News

Organoids mimicking celiac disease show new link between gluten, intestinal damage

Trial of cell-based therapy for high-risk lymphoma leads to FDA breakthrough designation

MRI scans predict recovery from spinal cord injury

Stanford Medicine offers gene therapy for a devastating pediatric neurologic disease

Existing high blood pressure drugs may prevent epilepsy, Stanford Medicine-led study finds

Clinicial trial faq.

Why should I participate in a clinical trial?

Clinical trials are critical to progressing medical advancements and helping people live longer. Many of the treatments used today would not be available if they were not first tested in clinical trials.

At Stanford, our physician-researchers and scientists perform collaborative research to improve diagnosis and treatment options for people worldwide. Because of their level of expertise, some of the trials and innovative treatments we offer are not available elsewhere in the world.

How do I know if a clinical trial is right for me?

To determine if a clinical trial is right for you, talk to your doctor. He or she can refer you to a study coordinator for more information on research studies that may be suitable for your specific condition.

You can also find the guidelines for who can participate in a particular clinical trial online. However, it is best to work with your doctor to decide the right care approach for your needs.

Why are clinical trials done in phases?

Clinical trials are executed in phases to determine their safety and effectiveness. Specific scientific questions are answered in each phase to demonstrate the potential of a new drug, device, or medical approach.

Is there a cost associated with participating in a clinical trial?

As a study participant, you receive a new drug, device, medical approach, or other treatment for free. 

Why are some clinical trials closed and others open?

Open trials refer to studies currently accepting participants. Closed trials are not currently enrolling, but may open in the future for enrollment.

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Researching for a Better Tomorrow

Among our 15 divisions, the Department of Medicine pushes the frontiers of medical research across clinical, lab, and community-based settings.

We don’t just lead with what research we do, but also with how we do it: maintaining commitments to community, communication, diversity, and health equity with every step. Our faculty lead more than 70 labs at the leading edge of disciplinary study, and our community partnerships build collaborative relationships for research and care in clinics across the Bay Area.

From our research centers in Palo Alto to the rest of California to the world, the Department of Medicine brings new ideas to research every day.

What Research Means to Us

• 90 basic scientists
• 200 clinical translational investigators
• Supported by more than $200M in sponsored research a year
• We improve human health by working in teams, using the strengths and expertise of our diverse researchers to address large-scale, high-impact, scientific questions across the translational spectrum. 
• Incredible resources to assist clinical researchers
• A growing health system with research integration
• Leadership that supports a community of collaboration, innovation, quality, and compliance

Together, We Commit

to pursuing cutting edge research that strengthens our core mission to prevent, diagnose, and treat all aspects of human disease and striving to provide compassionate and pioneering health care to all of our patients. We aim to advance both the knowledge of the subjects we research and the means by which we promote diversity and health equity in our research activities.

Meet some of our world-class researchers and investigate the work of our 70+ labs.

Where We Research

See more of our gorgeous campus and the many research centers, labs, and institutes where we work.

How We Work

Learn the different ways we conduct research here.

See why research in the Department of Medicine is different,

And be part of what makes us stand out.

Institute for Research in the Social Sciences

America Votes 2024

Join us for a series of panel discussions in which Stanford’s leading social scientists will draw on their cutting-edge research to examine the complex issues at play in this consequential election.

Angela Garcia's new book now on the shelves

The former IRiSS faculty fellow spent two years doing fieldwork in Mexico City.

Photo by Element5 Digital

ANES wins 2024 Past Policy Impact Award

The American Association for Public Opinion Research recognizes the American National Election Studies , the longest-running, most widely cited time series of voting behavior data in the world.

Photo by Priscilla Du Preez

Matt DeBell recognized with Robert M. Worcester Award

His award-winning paper, “ Measuring Political Knowledge and Not Search Proficiency in Online Surveys ,” addresses the problem of respondents’ cheating on political knowledge questions.

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Data-Driven Discovery for the Social Sciences

Social science data resources, american national election studies, federal statistical research data center, national longitudinal study on adolescent to adult health, social science research support, funding for graduate students, research experience programs, iriss-supported research, recent news.

IRiSS names 2022 RA Interns of the Year

Shanto Iyengar and team win major NSF grant to study 2024 election

IRiSS welcomes its 2022 Dissertation Fellows

Stay connected, our mission.

Growing access to novel data sources, the development of powerful computing tools, and innovation in quantitative and qualitative research methods are opening a new frontier for social scientists to explore bold, inventive research questions.  In this burgeoning era for social science research, the Stanford Institute for Research in the Social Sciences (IRiSS) facilitates first-rate interdisciplinary research, trains the next generation of scholars, and incubates research projects to address critical societal challenges. IRiSS ensures that world-class, evidence-based research is produced to meet evolving problems in areas of governance and democracy, economic inequality, immigration policy, and other social issues that affect communities across the globe.

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• Explore Student Grants

Song Wu, '24 composed a graphic novel about a first-generation Chinese-American teenager's struggle to define his identity in punk music, sexuality, and America with the assistance of a VPUE Student Grant.  

Inquiry, investigation, and discovery

are at the heart of Stanford’s mission. Every faculty member is engaged in groundbreaking original scholarship, and as an undergraduate, you can join faculty in their work in laboratories, libraries, studios, and beyond. Imagine how you can connect your classroom learning and intellectual interests as you work on an independent project under faculty mentorship.

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• Explore Departmental Funding
• Fellowships

Photo: Matt Mettias '23 was awarded a Chappell Lougee Scholarship to support the development of his original music album Keanu . The conscious hip-hop/Hawaiian fusion album centers Pacific Islander issues.

Upcoming Events and Deadlines

Department grant application open, autumn faculty grant application open, surps application deadline, october conference grant deadline, chappell lougee application open, surps faculty letter deadline.

Left image: Major Grant recipient and Art Practice student Sabrina Bedford created an acrylic paint series to accompany her own short novel about a girl surviving in a post-climate change disaster world who comes across a time machine. Right image: Major Grant recipients Gunner Dongieux and Sean O’Bannon navigate the intersection of tech and art by working to seamlessly incorporate AI into Gunner’s painting using a Generative Adversarial Network.

Explore #MyStanfordResearch on Instagram

Growing new blood vessels when arteries are blocked Read more

Cancer DNA in blood illuminates the disease Read More

How the brain is built Read story

Institute researcher Chuck Chan dies at 48 Read more

Institute researchers build high definition gene maps See story

Long-COVID in lungs is like chronic pulmonary fibrosis Read more

Chuck chan, stem cell researcher who discovered how to regrow cartilage, dies at 48.

The Stanford Medicine researcher was known for his groundbreaking work and his generous spirit as a mentor and colleague.

How music gives aspiring physician-scientist a proper life rhythm

Quenton Rashawn Bubb continues to value the complex, complementary nature of work on parallel paths -- not just as a musician/academic, but now on the path to his career.

A twist on developmental regulation of the face

During development, transcription factors are important in unlocking genes and making them available to cellular machinery. Joanna Wysocka and her colleagues found a novel sequence that allows coordination between different transcription factors during the development of the face.

Hodgkin lymphoma prognosis, biology tracked with circulating tumor DNA

Circulating tumor DNA predicts recurrence and splits disease into two subgroups in Stanford Medicine-led study of Hodgkin lymphoma. New drug targets or changes in treatments may reduce toxicity.

Why does CHIP lead to cardiovascular disease? The answers are becoming clearer

Stem cell mutations that lead to dominant clones raise the risk of cardiovascular disease. The mechanisms of this increased risk may like in the promotion of inflammatory activities among the offspring of mutant stem cells.

Blood condition linked to protection against Alzheimer's

Researchers at Stanford Medicine explore a potentially causative connection between a blood disorder called CHP and Alzheimer's disease..

Growing new blood vessels when arteries are blocked

Institute researchers have discovered that certain purified stem cell components of normal fat, when combined in the right proportions and transplanted into the body, will grow into new blood vessels. The researchers showed that when the technique was used in mice it restored blood flow to areas where areas where arteries were blocked

Researchers expand human blood stem cells in culture

For decades, researchers have been trying to expand human blood stem cells in culture. Researchers at the institute have recently accomplished this, opening the way to explore many new medical therapies and avenues of basic research.

Omair Khan named Soros Fellow

Stem Cell MD/PhD Student Omair Khan became one of 23 graduate students nationally to be awarded a 2023 Paul and Daisy Soros Fellowship for New Americans.

Researchers invent way to purify developing human brain cells

Researchers created a method of isolating and studying different human neural stem and progenitor cells. Transplanting these pure cells back into mice allows them to study the whole tree of all developing human brain cells.

Read all news stories

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Graduate Program in Stem Cell Biology and Regenerative Medicine

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Independent Laboratories, Centers, and Institutes

15 independent laboratories, centers, and institutes.

Stanford has 15 independent laboratories, centers, and institutes that provide a physical and intellectual intersection between schools and disciplines. These institutes, which are directed by the Vice Provost and Dean of Research, Dr. David Studdert, are in line with Stanford's longstanding tradition of crossing boundaries to tackle large problems, engaging faculty and their students in collaborations that range from international and economic studies to challenges facing the environment, energy, and health.

Our Culture of Interdisciplinary Research

At Stanford, collaboration is a way of life. Our faculty routinely seek diverse partners on the path to discovery and innovation. This environment arose in part through the co-location of the schools of Humanities & Sciences, Engineering, Medicine, Earth Sciences, Business, Education, and Law on a campus whose walkable size encourages exploration. Weaving across the traditional schools are interdisciplinary institutes that span departments and focus disparate ways of thinking on common problems.

Our institutes, centers, and labs span school boundaries, providing a physical and intellectual intersection between disciplines where new ideas emerge and innovative research across the humanities and sciences can happen. These interdisciplinary institutes are in line with Stanford's longstanding tradition of crossing boundaries to tackle large problems, engaging faculty and their students in collaborations that range from international and economic studies to challenges facing the environment, energy, and health.

The independent institutes, centers, and laboratories are directed by the Vice Provost and Dean of Research, who is responsible for appointing the director and providing fiscal support. 

Policy and Social Sciences Academic Units

Freeman Spogli Institute for International Studies at Stanford (FSI)

Stanford’s hub for nonpartisan, interdisciplinary research, teaching, and policy impact in international affairs.

Human-Centered Artificial Intelligence

Advancing AI research, education, and policy to improve the human condition.

Stanford Institute for Economic Policy Research

Stanford University’s home for understanding the economic challenges, opportunities, and policies affecting people in the United States and around the world.

Center for Advanced Study in the Behavioral Sciences

CASBS @ Stanford brings together deep thinkers from diverse disciplines and communities to advance understanding of the full range of human beliefs, behaviors, interactions, and institutions.

Stanford Center on Longevity

Stanford Center on Longevity’s mission is to accelerate and implement scientific discoveries, technological advances, behavioral practices, and social norms so that century long lives are healthy and rewarding.

Life Sciences Academic Units

Stanford Bio-X

Bio-X is Stanford's pioneering interdisciplinary biosciences institute, bringing together biomedical and life science researchers, clinicians, engineers, physicists, and computational scientists to unlock the secrets of the human body.

Chemistry, Medicine and Engineering for Human Health

Bridging chemistry, engineering, biology, and medicine to improve human health.

Wu Tsai Human Performance Alliance

Discovering biological principles to optimize human performance and catalyze innovations in human health for all.

Wu Tsai Neurosciences Institute

Dedicated to understanding how the brain gives rise to mental life and behavior in health and in disease.

Physical Science Labs & Stanford/SLAC Joint Institutes

E. L. Ginzton Laboratory

Creating breakthroughs and educating students at the interface between science and engineering.

Geballe Laboratory for Advanced Materials

Independent laboratory that supports and fosters interdisciplinary education and research on advanced materials in science and engineering.

W. W. Hansen Experimental Physics Laboratory

As Stanford's first Independent Laboratory, provides facilities and administrative structure enabling faculty to do research that spans across the boundaries of a single department or school—for example: physics & engineering or physics & biology/medicine.

Kavli Institute for Particle Astrophysics and Cosmology

KIPAC was founded in 2003 to explore new fronts and challenges in astrophysics and cosmology.

PULSE Institute for Ultrafast Energy Science

The mission of PULSE is to advance the frontiers of ultrafast science.

Stanford Institute for Materials and Energy Sciences

Our mission is to address grand challenges in the science of energy-related materials. We create knowledge, develop leaders, and seek solutions.

Research Platforms & LRV Initiatives

Cognitive & neurobiological imaging.

A shared facility, dedicated to research and teaching. The Center provides resources for researchers and students in cognitive and neurobiological sciences.

Stanford Data Science

Our mission: enable data-driven discovery at scale and expand data science education — across Stanford and beyond.

Stanford Research Computing Center

Stanford Research Computing, a joint effort of the Dean of Research and University IT, comprises a world class team focused on delivering and supporting comprehensive programs that advance computational and data-intensive research across Stanford.

Stanford Nano Shared Facilities

SNSF provides shared scientific instrumentation, laboratory facilities, and expert staff support to enable multidisciplinary research and educate tomorrow’s scientists and engineers.

Stanford University Mass Spectrometry

Due to the essential information that mass spectrometry provides to researchers in the fields of the physical and life sciences, medicine, and engineering, the laboratory serves as an “intellectual watering hole” at the crossroads of diverse disciplines.

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A societal mission.

Stanford was founded almost 150 years ago on a bedrock of societal purpose. Our mission is to contribute to the world by educating students for lives of leadership and contribution with integrity; advancing fundamental knowledge and cultivating creativity; leading in pioneering research for effective clinical therapies; and accelerating solutions and amplifying their impact.

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Stories about people, research, and innovation across the Farm

College is about curiosity, President Levin tells new students

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‘Before They Vanish’ addresses the crisis of species loss

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Kit makes CRISPR education affordable and accessible

Summer interns unlock the secrets of migratory birds, stanford nanofabrication facility gets an upgrade, sandai: new tool for scanning sand grains opens windows into recent time and deep past.

Preparing students to make meaningful contributions to society as engaged citizens and leaders in a complex world

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Rich learning experiences that provide a broad liberal arts foundation and deep subject-area expertise

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Unsurpassed opportunities to participate in the advancement of entire fields of knowledge

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Seven schools in which to pursue your passions

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Profile of Tadashi Tokieda

“When I ‘decided’ to become a mathematician, it was not a decision. I could not do otherwise. You don’t decide to fall in love with somebody. It just happens.”

Tadashi Tokieda

Professor (Teaching) of Mathematics

Driving discoveries vital to our world, our health, and our intellectual life

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Advancing human health through innovative research, education, and care

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Leading a worldwide revolution in precision health through biomedical research, education, and clinical enterprises

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The only health care network in the Bay Area – and one of the few in the country – exclusively dedicated to pediatric and obstetric care

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“I think about all the projects that students throw themselves at quarter after quarter, just really expanding and stretching their minds. … Stanford allows you to experience evolutions of yourself.”

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No oncologist would wait for a patient’s cancer to spread before treating it. Similarly, waiting to detect the potential loss of a species across all its known habitats means interventions are often too late to turn the tide of extinction, according to ecologists Paul Ehrlich and Rodolfo Dirzo of Stanford University and Gerardo Ceballos of the National Autonomous University of Mexico. Their new book, Before They Vanish: Saving Nature’s Populations – and Ourselves , calls for earlier detection and mitigation of threats to ward off population extinction – the loss of plants, animals, fungi, or microbes within specific geographic areas. The approach provides a greater chance at stopping the spread of species loss, according to the authors.

Drawing on decades of research and experience, the authors explain how humanity is pushing countless species to the brink of extinction, with devastating consequences for ecosystems and human civilization. They highlight how conservationists have tended to focus on saving iconic animals, such as tigers and eagles, on the brink of extinction – primarily for ethical and aesthetic reasons. It is only relatively recently that biodiversity’s crucial role in supporting human life has been appreciated by the scientific community, according to the authors. The book serves as both a diagnosis and a plea for action, outlining solutions to avert a global ecological catastrophe.

Below, Ehrlich, Dirzo, and Ceballos discuss their new book, their decades in the field, and their hope for the future.

What are some of the cascading effects of population extinctions – the loss of a species in a specific geographic location – that may not be immediately obvious to the public?

Rodolfo Dirzo: Look at the combined impact of deforestation, poaching, and hunting on the populations of elephants, giraffes, and other large herbivores in African savannas. The local loss or decline of these vertebrates’ populations not only leads to the decline of prey for carnivores but triggers major vegetation changes – more grass and shrubs. These changes in turn create a perfect storm for small mammal populations, particularly rodents, to thrive. Many of these are host to zoonotic disease agents that could spark outbreaks among people.

How do you respond to potential criticism that focusing on population-level extinctions could divert resources from protecting critically endangered species?

Gerardo Ceballos: Conservation requires focusing on both population and species levels. Protecting critically endangered species means protecting their last populations. However, focusing on population-level extinctions means maintaining populations at regional and national levels, preventing further deterioration of declining species, and maintaining ecosystem services at those levels. For example, maintaining elephant populations in South Africa will help conserve the species in the continent while preserving the benefits to both ecosystems and the human well-being of that country.

Your work spans decades of research. What changes in extinction patterns or conservation approaches have you observed over your careers?

Paul Ehrlich: In my 70-plus years in conservation, I have seen the scientific community slowly come to realize that the true “wealth of nations” is their biodiversity – the only type of capital that human beings cannot survive without. My scientific surprise has been the discovery, partly in my research, of the “insect apocalypse” – the massive destruction of insect populations. Among other things, that is a major factor in the decline of bird populations.

Dirzo: Our work has drawn attention to the fact that biodiversity conservation efforts need to consider policy intervention to prevent the extinction of ecological interactions. For example, the loss of populations in an ecosystem can lead to the local extinction of processes such as pollination or pest control. Also, biodiversity conservation is being increasingly recognized as a critical factor of societal well-being in terms of human health, including disease regulation and mental health.

If readers take away just one action item from your book, what would you want it to be?

Dirzo: Changing human behavior away from unsustainable meat consumption and industrial agriculture. This represents an action that will reduce massive land-use change, greenhouse gas emissions, personal health afflictions, waste, and inequity.

Ceballos: A very important action is to vote for the politicians that have conservation as a major issue in their political agenda.

Given the accelerating rate of land-based vertebrate losses, what gives you hope that we can still make a meaningful difference?

Ehrlich: Humanity has shown the ability to change behavior very swiftly when people feel threatened. One of the chores of scientists is to be sure that everyone understands that civilization cannot persist on its current trajectory.

Ceballos: Many successful conservation cases at all levels indicate that the current extinction crisis is not predetermined.

For more information

Ehrlich is the Bing Professor of Population Studies, Emeritus, in the  Stanford School of Humanities and Sciences , president of the  Stanford Center for Conservation Biology , and senior fellow emeritus in the Stanford Woods Institute for the Environment . Dirzo is the Bing Professor of Environmental Science in the Stanford School of Humanities and Sciences and the  Stanford Doerr School of Sustainability , where he is also the associate dean for integrative initiatives in environmental justice, and senior fellow at the Stanford Woods Institute for the Environment. Ceballos is a senior researcher at the National Autonomous University of Mexico’s Institute of Ecology. Ehrlich, Dirzo, and Ceballos are members of the U.S. National Academy of Sciences.

Related story

Stanford researcher says sixth mass extinction is here

Paul Ehrlich and others use highly conservative estimates to prove that species are disappearing faster than at any time since the dinosaurs’ demise.

Stanford biologists warn of prelude to extinction

Loss of land-based vertebrates is accelerating

Media contact

Rob Jordan, Stanford Woods Institute for the Environment: 650-721-1881, [email protected]

From Natural Hazards to Global Health and Sustainability, and Finding a Community

Beginnings and a career-changing paper.

Haojie Wang 's academic journey began with a Bachelor's degree in Civil Engineering from China University of Geosciences, followed by a PhD in Civil Engineering from the Hong Kong University of Science and Technology. Initially, Haojie was on the path to becoming a traditional engineering geologist. However, during the second year of his PhD, a pivotal moment occurred. His advisor, Professor Limin Zhang, introduced him to a conference paper exploring unsupervised machine learning in landslide feature classification. It was a novel approach at that time, as machine learning had yet to be widely applied to understanding landslides.

"After I read that paper, I thought about the many cool scientific topics we could tackle," Haojie recalls. This moment marked the beginning of his journey into machine learning and its application to landslide research.

Upon completing his Ph.D., Haojie realized that he had developed a second identity: a data scientist with a strong foundation in geotechnics. Reflecting on the rapid evolution of the field, Haojie notes, "Years ago, no one talked about using machine learning and similar tools in this context. Traditional methods like conducting experiments and using numerical models to simulate physical processes were the norm. But today, data science is transforming the landscape of geotechnical research. The field is growing so quickly that if you don’t keep up, you risk falling behind."

Transitioning from Geotechnics to Sustainability and Global Health

Haojie’s doctoral research, Machine Learning-Powered Natural Terrain Landslide Identification and Susceptibility Assessment , focused on integrating machine learning with satellite imagery and geospatial big data to identify and forecast landslides. Multiple publications that arose from his doctoral research are recognized as highly cited papers by Clarivate. His thesis work not only advanced the field of landslide research but also allowed him to integrate his knowledge of data science and remote sensing. As he delved deeper into this field, Haojie recognized that his skillset could be applied to address more global sustainability challenges.

"New research areas mean new challenges and the opportunity to embrace new possibilities," says Haojie. "And new possibilities inspire me to stay passionate about research."

His curiosity led him to another exciting research project, this time under the guidance of Pascal Geldsetzer, Assistant Professor of Medicine. Professor Geldsetzer was seeking a data scientist with expertise in remote sensing to monitor global health indicators from space. The challenge was irresistible to Haojie.

"Finding new ways to monitor global health is truly exciting, and the project is highly interdisciplinary,” says Haojie. “I am also keen to understand the role of climate change and natural hazards in shaping today’s global health landscape," Haojie explains. With guidance from esteemed mentors such as Professors Pascal Geldsetzer, David Lobell, Marshall Burke, Stefano Ermon, Eran Bendavid, Carlos Guestrin, and Gary Darmstadt, Haojie found his intellectual homes at the Stanford School of Medicine and Stanford Data Science.

The Vision Behind Haojie Wang’s Postdoctoral Research Project

Haojie’s postdoctoral research focuses on the development of new earth observation approaches for global population health monitoring. Traditional household surveys rely on door-to-door data collection, which can only cover a small fraction of the country and is conducted at best every few years. It is time-consuming, expensive, and often logistically challenging in many parts of the world. Policymakers often have no choice but to make decisions based on extrapolated health indicators from old household surveys.

Haojie is pioneering a new approach to overcome these limitations. He is leveraging machine learning, satellite imagery—which provides continuous coverage for all countries—and publicly available geotagged big data to predict health indicators. If successful, this method could offer worldwide up-to-date health indicators more quickly than ever before, enabling governments and decision-makers to track population health, allocate medical resources more effectively, and inform healthcare policy. The project is currently in its early stages, with the development of a preliminary model underway.

The Role of Data Science in Global Health Research

Haojie’s postdoctoral work is grounded in data science, focusing on population health through a remote sensing lens. His project involves fusing and analyzing data sourced from various satellite imagery, such as Landsat, alongside other geospatial data and health records. Predictive analytics play a critical role in this research, offering new insights into health trends on a global scale.

Finding a Community at Stanford Data Science

Haojie was introduced to the Stanford Data Science Fellow Program by Professor Pascal Geldsetzer, who believed Haojie would be an ideal fit. The interdisciplinary nature of the research conducted at Stanford Data Science appealed to Haojie, who had struggled to find a community that aligned with his diverse research interests at conventional universities.

"What’s unique about Stanford Data Science is its commitment to interdisciplinary research," Haojie says. "As an interdisciplinary scientist, I often felt isolated in traditional academic environments. But here, I found a community of fellows and scholars—a huge family! It’s incredibly gratifying to know that other data scientists are also pursuing interdisciplinary research. I’m not alone on this path."

Advice for Aspiring Data Scientists

Haojie was one of the technical mentors of the Data Science for Social Good (DSSG) program in 2023, where he mentored three undergraduate DSSG fellows on the project Maternal and Child Health - A Satellite’s Perspective throughout the summer. “It was a really enjoyable and inspiring summer working with aspiring researchers. DSSG sets a solid platform to connect with young minds—I was continually impressed by their enthusiasm and how they brought fresh perspectives to our project,” Haojie gushes.

Haojie encourages aspiring data scientists to find new ways to approach problems and to view the world through a data-driven lens. "Be Brave to explore new areas. Data science allows us to tackle problems we never imagined we could address. That’s the unique charm of the field," he admits.

Ambitions, Dreams, and Hobbies

This fall, Haojie plans to apply for faculty positions in global sustainability. His goal is to continue his work at the intersection of population health, climate change, and natural hazards, using his skill set to address pressing questions and make a meaningful impact. Outside of his research, Haojie enjoys cooking, traveling, and immersing himself in nature. As an engineering geologist at heart, he finds peace and inspiration in the natural world and loves going on road trips and camping, where he can combine his passion for nature with his love of good food.

Selected Awards

• 2024 Best Paper Award, Engineering Geology, Elsevier
• Data Science Fellowship, Stanford Data Science
• Postdoctoral Fellowship, The Hong Kong University of Science and Technology
• National Scholarship, Chinese Ministry of Education

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Cardinal Research Administration Foundational Training (CRAFT)

The C ardinal R esearch A dministration F oundational T raining or CRAFT program is Stanford's foundational research administration training program effective 10/1/24.  CRAFT replaces the historical Cardinal Curriculum research administration training program that is being retired as of 9/30/24.  

• The CRAFT program is divided into two certificate programs: CRAFT Level 1 and CRAFT Level 2. 
• Individuals must complete CRAFT Level 1 prior to registering for and completing CRAFT Level 2.
• CRAFT Level 1 courses introduce the basic principles, resources, and Stanford practices for research administration at Stanford. These courses must be completed within 6 months of hire into a position that involves research administration.
• CRAFT Level 2 courses build upon the foundation set in CRAFT 1 and further explore the mechanics for preparing and submitting basic science (non-clinical) sponsored project proposals and administering sponsored projects at Stanford. The courses must be completed within 12 months of hire into a position that involves research administration.

Effective 10/1/24, new hires into non-School of Medicine RA 1-4 job codes and/or locally identified as having Pre-award and/or Post-award department research administration job duties must complete CRAFT Level 1 and Level 2 within 12 months of their hire.  

School of Medicine Research Administrators and/or SoM individuals working regularly in research administration are highly encouraged to complete CRAFT Level 1 and Level 2 within 12 months of their hire, and they may be required to do so by their manager/department.

CRAFT Level 1

Register for the CRAFT Level 1 : ORA-PROG-1111 Program in STARS , and then complete the four (4) CRAFT Level 1 courses to receive your CRAFT Level 1 Certificate.

Note: You will receive historical credit towards your CRAFT Level 1 program certificate for any CRAFT Level 1 courses you completed in the 365 days preceding your CRAFT Level 1 enrollment.  If you completed all four (4) CRAFT Level 1 courses in the 365 days preceding your CRAFT Level 1 enrollment, STARS will automatically complete your CRAFT Level 1 program certification, and you will have no further CRAFT Level 1 action items.

CRAFT Level 2

After completing the CRAFT Level 1 Program, register for the CRAFT Level 2 : ORA-PROG-2222 Program in STARS , and then complete the 30 CRAFT Level 2 required courses in addition to 9 elective courses to receive your CRAFT Level 2 Certificate.

Note: You will receive historical credit towards your CRAFT Level 2 program certificate for any CRAFT Level 2 required courses you completed during the 365 days preceding your CRAFT Level 2 enrollment. 

Complete Required CRAFT  Level 2 Courses:

Complete 9* Elective Courses:

*Denotes those courses ORA recommends for department research administrators that provide Preaward and Post award support to their investigators.  Please confer with your local manager and school level RA point of contact for the specific CRAFT elective courses they recommend/require.  Schools and units may require their RAs to complete more than 9 CRAFT elective courses.

Note: You will receive historical credit towards your CRAFT Level 2 program certificate for any CRAFT Level 2 elective FIN courses you completed anytime preceding your CRAFT Level 2 enrollment. Additionally, you will also receive historical credit towards your CRAFT Level 2 program certificate for any CRAFT Level 2 elective ORA and/or DOR courses you completed during the 365 days preceding your CRAFT Level 2 enrollment. 

NOTE:  For all ORA hosted CRAFT Zoom Webinar courses, all learners must log into the relevant Zoom session using their Stanford laptop or desktop computer no later than 10 minutes after the given session start time, remain logged in through the end of the session, participate in all live session polls, and complete the prescribed independent learning assignment with a passing grade of 80% or more to receive credit for the given course.

ORA also offers the  ORA Webinar series that includes other "How to" Zoom Webinars on Sponsored Research Administration Topics with Live Q&A.  ORA Webinars do not require pre-requisites or registration.

Megan Dietrich , Assistant Director, Client Advocacy & Education

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Lauren Campbell,  Research Administration Instructional Designer  

Life Science Research Professional 1

🔍 School of Humanities and Sciences, Stanford, California, United States

The School of Humanities and Sciences (H&S) is the foundation of a liberal arts education at Stanford. The school encompasses 24 departments and 25 interdisciplinary programs. H&S is home to fundamental and applied research, where free, open, and critical inquiry is pursued across disciplines. As the university’s largest school, H&S serves as the foundation of a Stanford undergraduate education no matter which discipline students pursue as a major. Graduate students work alongside world-renowned faculty to pursue and shape foundational research that leads to breakthroughs and discoveries that shed new light on the past, influence the present, and shape the future. Together, faculty and students in H&S engage in inspirational teaching, learning, and research every day.

POSITION SUMMARY: The Laboratory of Organismal Biology at Stanford University has a position for a motivated research assistant at the Life Science Research Professional I level with interests in amphibian neuroscience and behavior. Our lab focuses on behavior and physiology in amphibians and this position will focus on (1) understanding the neural mechanism of parental attachment and feeding of offspring and (2) visualizing, processing, and analyzing 3D data, making protocols accessible to the broader scientific community, and community engagement through partnerships with science classrooms in K-12 education. This is a great opportunity for people interested in parental behavior, neuroscience, and science communication using amphibians.

The main responsibilities of the successful candidate are to segment and annotate a developing 3D brain atlas, stain and quantify transcripts in the brain using in-situ hybridization, clear whole brains using the iDISCO technique, quantify parental behavior, and develop pharmacological methods. Other responsibilities include performing routine laboratory techniques maintain records of lab work, assisting in data analysis, and conducting behavior experiments. The earliest start date for this position is October 2024 and this is a two-year fixed-term position.

This is a 100% FTE, 2-year fixed-term, non-exempt position. This position will be based on the Stanford Campus.

If you believe that this opportunity is a match for your knowledge, skills and abilities, we encourage you to apply. Thank you for considering employment opportunities with the School of Humanities and Sciences.

CORE DUTIES:

● Plan approach to experiments in support of research projects in lab and/or field based on knowledge of scientific theory.

● Independently conduct experiments; maintain detailed records of experiments and outcomes.

● Apply the theories and methods of a life science discipline to interpret and perform analyses of experiment results; offer suggestions regarding modifications to procedures and protocols in collaboration with senior researcher.

● Review literature on an ongoing basis to remain current with new procedures and apply learnings to related research.

● Contribute to publication of findings as needed. Participate in the preparation of written documents, including procedures, presentations, and proposals.

● Help with general lab maintenance as needed; maintain lab stock, manage chemical inventory and safety records, and provide general lab support as needed.

● Assist with orientation and training of new staff or students on lab procedures or techniques.

* Other duties may also be assigned.

EDUCATION AND EXPERIENCE:

● Bachelor's degree in related scientific field.

KNOWLEDGE, SKILLS, AND ABILITIES:

● General understanding of scientific principles. Demonstrated performance to use knowledge and skills when needed.

● Demonstrated ability to apply theoretical knowledge of science principals to problem solve work.

● Ability to maintain detailed records of experiments and outcomes.

● General computer skills and ability to quickly learn and master computer programs, databases, and scientific applications.

● Ability to work under deadlines with general guidance.

● Excellent organizational skills and demonstrated ability to accurately complete detailed work.

WORKING CONDITIONS:

● May require working in close proximity to blood borne pathogens.

● May require work in an environment where animals are used for teaching and research.

● Position may at times require the employee to work with or be in areas where hazardous materials and/or infectious diseases are present.

● Employee must perform tasks that require the use of personal protective equipment, such as safety glasses and shoes, protective clothing and gloves, and possibly a respirator.

● May require extended or unusual work hours based on research requirements and business needs.

The expected pay range for this position is $ 26.44 to $36.54 per hour.

Stanford University provides pay ranges representing its good faith estimate of what the university reasonably expects to pay for a position. The pay offered to a selected candidate will be determined based on factors such as (but not limited to) the scope and responsibilities of the position, the qualifications of the selected candidate, departmental budget availability, internal equity, geographic location and external market pay for comparable jobs.

At Stanford University, base pay represents only one aspect of the comprehensive rewards package. The Cardinal at Work website (https://cardinalatwork.stanford.edu/benefits-rewards) provides detailed information on Stanford’s extensive range of benefits and rewards offered to employees. Specifics about the rewards package for this position may be discussed during the hiring process.

Why Stanford is for You

Imagine a world without search engines or social platforms. Consider lives saved through first-ever organ transplants and research to cure illnesses. Stanford University has revolutionized the way we live and enrich the world. Supporting this mission is our diverse and dedicated 17,000 staff. We seek talent driven to impact the future of our legacy. Our culture and unique perks empower you with:

● Freedom to grow. We offer career development programs, tuition reimbursement, or audit a course. Join a film screening, or listen to a renowned author or global leader speak.

● A caring culture. We provide superb retirement plans, generous time-off, and family care resources.

● A healthier you. Climb our rock wall, or choose from hundreds of health or fitness classes at our world-class exercise facilities. We also provide excellent health care benefits.

● Discovery and fun. Stroll through historic sculptures, trails, and museums.

● Enviable resources. Enjoy free commuter programs, ridesharing incentives, discounts and more.

The job duties listed are typical examples of work performed by positions in this job classifications and are not designed to contain or be interpreted as a comprehensive inventory of all duties, tasks and responsibilities. Specific duties and responsibilities may vary depending on department or program needs without changing the general nature and scope of the job or level of responsibility. Employees may also perform other duties as assigned.

Consistent with its obligations under the law, the University will provide reasonable accommodations to applicants and employees with disabilities. Applicants

requiring a reasonable accommodation for any part of the application or hiring process should contact Stanford University Human Resources at [email protected]. For all other inquiries, please submit a contact form.

Stanford is an equal employment opportunity and affirmative action employer. All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, sexual orientation, gender identity, national origin, disability, protected veteran status, or any other characteristic protected by law.

• Schedule: Full-time
• Job Code: 4943
• Employee Status: Fixed-Term
• Requisition ID: 104630
• Work Arrangement : On Site

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The St. Petersburg Paradox

The St. Petersburg game is played by flipping a fair coin until it comes up tails, and the total number of flips, n , determines the prize, which equals $2 n . Thus if the coin comes up tails the first time, the prize is $2 1 = $2, and the game ends. If the coin comes up heads the first time, it is flipped again. If it comes up tails the second time, the prize is $2 2 = $4, and the game ends. If it comes up heads the second time, it is flipped again. And so on. There are an infinite number of possible ‘consequences’ (runs of heads followed by one tail) possible. The probability of a consequence of n flips (P( n )) is 1 divided by 2 n , and the ‘expected payoff’ of each consequence is the prize times its probability. The following table lists these figures for the consequences where n = 1 … 10:

n   P( n )  Prize Expected payoff 1 1/2 $2 $1 2 1/4 $4 $1 3 1/8 $8 $1 4 1/16 $16 $1 5 1/32 $32 $1 6 1/64 $64 $1 7 1/128 $128 $1 8 1/256 $256 $1 9 1/512 $512 $1 10 1/1024 $1024 $1

The ‘expected value’ of the game is the sum of the expected payoffs of all the consequences. Since the expected payoff of each possible consequence is $1, and there are an infinite number of them, this sum is an infinite number of dollars. A rational gambler would enter a game iff the price of entry was less than the expected value. In the St. Petersburg game, any finite price of entry is smaller than the expected value of the game. Thus, the rational gambler would play no matter how large the finite entry price was. But it seems obvious that some prices are too high for a rational agent to pay to play. Many commentators agree with Hacking's (1980) estimation that “few of us would pay even $25 to enter such a game.” If this is correct—and if most of us are rational—then something has gone wrong with the standard decision-theory calculations of expected value above. This problem, discovered by the Swiss eighteenth-century mathematician Daniel Bernoulli is the St. Petersburg paradox. It's called that because it was first published by Bernoulli in the St. Petersburg Academy Proceedings (1738; English trans. 1954).

1. Decreasing Marginal Utility

2. risk-aversion, 3. an upper bound on utility, 4. finitely many consequences, 5. infinite value, 6. theory and practicality, works cited, other discussions, other internet resources, related entries.

Bernoulli argued that the calculations leading to the paradox err by adding expected payoffs in money (dollars, in our version), whereas what should be added are the expected utilities of each consequence. The same paper in which he proposed this problem contains the first published exposition of the Principle of Decreasing Marginal utility, which he developed to deal with St. Petersburg. This principle, later widely accepted in the theory of economic behavior, states that marginal utility (the extra utility obtained from consuming a good) decreases as the quantity consumed increases; in other words, that each additional good consumed is less satisfying than the previous one. He went on to suggest that a realistic measure of the utility of money might be given by the logarithm of the money amount. Here are the first few lines in the table for this gamble if utiles = log($):

n P( n ) Prize Utiles Expected Utility 1 1/2 $2 0.301 0.1505 2 1/4 $4 0.602 0.1505 3 1/8 $8 0.903 0.1129 4 1/16 $16 1.204 0.0753 5 1/32 $32 1.505 0.0470 6 1/64 $64 1.806 0.0282 7 1/128 $128 2.107 0.0165 8 1/256 $256 2.408 0.0094 9 1/512 $512 2.709 0.0053 10 1/1024 $1024 3.010  0.0029

The sum of expected utilities is not infinite: it reaches a limit of about 0.602 utiles (worth $4.00). The rational gambler, then, would pay any sum less than $4.00 to play.

Many have found this response to the paradox unsatisfactory. For one thing, Bernoulli's association of utility with the logarithm of money seems way off: $1024 seems clearly worth more than 10 times $2. But this, it's argued, is not the main problem. Let us agree that money has a decreasing marginal utility, and accept (for the purposes of argument) that a reasonable calculation of the utility of any dollar amount takes the logarithm of the amount in dollars. The St. Petersburg game as proposed, then, presents no paradox, but it is easy to construct another St. Petersburg game which is paradoxical, merely by altering the dollar prizes. Suppose, for example, that instead of paying $2 n for a run of n , the prize were $10 to the power 2 n . Here is the table for this game:

n P( n ) Prize Utiles of Prize Expected utility 1 1/2 $10 2 2 1 2 1/4 $10 4 4 1 3 1/8 $10 8 8 1 4 1/16 $10 16 16 1 5 1/32 $10 32 32 1 6 1/64 $10 64 64 1 7 1/128 $10 128 128 1 8 1/256 $10 256 256 1 9 1/512 $10 512 512 1 10 1/1024 $10 1024 1024 1

This version contains much larger prizes than the original version, and one would presumably be willing to pay more to play this version than the original. But the expected value of this game—the sum of the infinite series of numbers in the last column—is infinite, and the paradox returns.

Of course, it is not clear how in fact dollar values relate to utility, but we can imagine a generalized paradoxical St. Petersburg game (suggested by Paul Weirich, 1984, following Menger, 1967) which offers prizes in utiles instead, at the rate of 2 n utiles for a run of n (however that number of utiles is to be translated into dollars or other goods). This game would have infinite expected value, and the rational gambler should pay any amount, however large, to play. For simplicity, we shall ignore the generalized version of the game, and continue to discuss it in terms of the original dollar prizes, recognizing, however, that the diminishing marginal utility of dollars may make some revision of the prizes necessary to produce the paradoxical result.

Consider the following argument. The St. Petersburg game offers the possibility of huge prizes. A run of forty would, for example, pay a whopping $1.1 trillion. Of course, this prize happens rarely: only once in about 1.1 trillion times. Half the time, the game pays only $2, and you're 75% likely to wind up with a payment of $4 or less. Your chances of getting more than $25 (the entry price which Hacking suggests is a reasonable maximum) are less than one in 25. Very low payments are very probable, and very high ones very rare. It's a foolish risk to invest more than $25 to play.

This sort of reasoning is appealing, and may very well account for intuitions that agree with Hacking's. Many of us are risk-averse, and unwilling to gamble for a very small chance of a very large prize. Weirich claims that this sort of consideration in fact solves the St. Petersburg paradox. He offers a complicated way (which we need not go into here) of including a risk-aversion factor in calculations of expected utility, with the result that there is a finite upper limit to the rational entrance fee for the game.

But there are objections to this approach. For one thing, a factor for risk-aversion is not a generally applicable consideration in making rational decisions, because some people are not risk averse. In fact, some people may enjoy risk. What should we make, for example, of those people who routinely play state lotteries, or who gamble at pure games of chance in casinos? (In these games, the entry fee is greater than the expected utility.) It's possible to dismiss such behavior as merely irrational, but sometimes these players offer the explanation that they enjoy the excitement of risk. In any case, it's not at all clear that risk-aversion can explain why the St. Petersburg game would be widely intuited to have a fairly small maximum rational entry fee, while so many people at the same time are not averse to the huge risk entailed by the very small expected probability of large prizes in lotteries.

But for the purposes of argument, let's assume that risk-aversion is what's responsible for the intuition that the appropriate entrance-fee for the St. Petersburg game is finite and small. But this will not make the paradox go away, for we can again adjust the prizes to take account of this risk-aversion.

Suppose you don't like to gamble, and wouldn't risk an entry fee in a game that offers a small possibility of a large prize, even when the odds were in your favor. For example, imagine that you were offered a lottery ticket costing $1, which gave you a one-in-ten chance at a prize of $20. Playing costs you utility, because you hate risk. But presumably, we could compensate you for this utility-loss by making the prize even bigger. Maybe you would invest $1 for a one-in-ten chance at making $100. If not, how about $1000? It appears that there is some prize large enough to compensate you for your risk aversion.

Now let's imagine that you consider the St. Petersburg game, and suppose that you're willing to pay an entrance fee of only $20 to play. The reason you're not willing to go higher is your risk-aversion. We can imagine that the increasing risk of large payments subtracts from their utility, and the result is that the last column contains numbers that decrease as probabilities shrink, and the sum of the last column reaches a limit—perhaps $25. But now, the game can be reformulated to repay you for the risk inherent in each outcome, by correspondingly increasing the prizes. For example, suppose we square each dollar-prize in compensation for the increasing risk—the lower probability—of the larger prizes. If this doesn't provide sufficient compensation for your risk-aversion, then we can make the prizes even higher. In any case, there seems to be some prize scheme huge enough to compensate you for your risk-aversion—one which makes the dollar utility of each prize minus its risk-factor equal 1 utile. A game with these larger prizes is again paradoxical.

The idea that risk-aversion can be compensated for by a larger prize is hardly controversial. The fact that many more people enter lotteries when unusually big prizes are announced, keeping risk more or less constant, is evidence for this.

But Weirich argues that offering increased prizes cannot sufficiently compensate for risk-aversion in such a way as to make the sum of the series unlimited. He appears to suggest that increasing the prize for an outcome may increase one's cost in terms of dread of risk. In the lottery example, then, increasing the prize to $1000 would correspondingly increase the risk for you, so you still wouldn't bet. No matter how high a prize you are offered, you still are unwilling to buy the ticket for $1, because the higher prizes raise the risk for you. Putting it “picturesquely,” he says, “there is some number of birds in hand worth more than any number of birds in the bush.”

But one might doubt that risk-aversion works this way—or, anyway, that this sort of risk-aversion can be justified as rational. It's highly implausible to claim that an increase in prize-size increases the risk of a game. In the lottery example, the only sort of risk-aversion that would make one refuse to play no matter how high the prize is pathological, not rational. There must be some prize which is so valuable to any rational but risk-averse person that the person would see it as compensating him for the risk of $1, (where that dollar has the usual small utility). If someone prefers $1 worth of birds in hand to any value of birds in the bush, then that person needs psychiatric help; this is not a rational decision strategy.

The counter argument we have been considering is that risk-aversion is irrational when it refuses to gamble a small entry-price for no matter how high a prize, or when it refuses to gamble a large entry-price for no matter how high a probability of prize. But this does not answer all St. Petersburg objections, for here we imagine a gamble with a large entry-price and a small probability of large prizes. The most compelling examples of the rational unacceptability of risk no matter how high the prize, are the ones in which the entry price is high and the prize improbable. Imagine, for example, that you are risk averse, and are offered a gamble in which the entry price is your life-savings of (say) $100,000, and the chances of the prize are one-in-a-million. It seems rational to refuse, no matter how huge the prize. The reason for this is worth considering.

Exactly what sort of risk-aversion might explain why people won't bet more than $25 to play the St. Petersburg game? Is it an aversion to risking large sums of money? It's sometimes claimed that this is what's behind the refusal to gamble your life-savings no matter how probable or huge the winning payoff would be. But is this really a general principle of rationality in the face of risk? Doubts about this are raised by the following example. When you deposit your life savings in a solid bank bank for a year, you are in fact accepting a gamble. There's a very high probability of the consequence that at the end of the year, you can get your savings back with interest, but there's also an extremely low probability of the consequence that the bank and and the deposit insurance will both collapse, and you'll be wiped out. Someone who refused to run this very tiny risk no matter how high the interest and how low the probability of disaster is clearly irrational. Everyone who crosses a street is, in effect, gambling his life, because of the risk of being run down and killed. But to refuse to cross any street on these grounds is irrational. This sort of risk-aversion, when generally applied, would paralyze anyone. It is central to rationality that one take risks when the probability of disaster is suitably tiny, even though what would be lost is huge.

Or is it that rational risk-aversion will not gamble when the probability of gain is very low? The so-called “Sure Loss Principle” advises us never to take the risk of any significant loss when this loss is almost certain. But again examples appear to show that this is not general principle of rational behavior—examples in which it's seems rational to risk a highly probable and significant loss when the improbable gain is high enough. Hunting for a job or for a publisher for one's book are often like this: highly improbable that any particular attempt will succeed, and significantly costly, but worth it because of the big enough potential gain when one succeeds.

Despite the difficulty of coming up with a plausible principle of rational risk aversion, it does appear that rational risk aversion makes sense: that people not considered crazy avoid paying huge entry sums to play when the enormous payoff is extremely improbable. Perhaps that is what explains the unwillingness to make a big investment in St. Petersburg. But note however that this may not be a sufficient response to the paradox. This sort of risk-aversion would also provide a psychological explanation of why (some) people are unwilling to gamble large sums when the finite expected utility is greater than the initial payment. So, for example, many people would be unwilling to risk $100 for a one-in-a-hundred chance at winning $20,000 (expected value $200). If risk is not a disutility that can be compensated for by prize increase, then maybe their behavior runs counter to the expected-value theory of rational choice; and if they're rational, then maybe this shows the theory is wrong. The paradox raised by St. Petersburg, however, is not thereby fully dealt with. It is not merely a case—others of which are well-known—in which apparently rational behavior disobeys the advice to maximize expected value. The St. Petersburg paradox is that the expected value is infinite .

The two reformulations of the game proposed so far share the feature that the dollar values of the prizes are increased as compensation (in the first case, for the diminishing marginal value of money, and, in the second case, for their improbability and risk-aversion). In both cases, it is assumed that the utility of each outcome can be increased without limit; but perhaps this assumption is incorrect, and there is an upper limit on the utility of the prizes. Then the sum of the series will reach a limit. In his classical treatment of the problem, Menger argues that the assumption that there is an upper limit to utility is the only way that the paradox can be resolved. Assume, for example, that utility = dollar value, except with an upper limit of 100 utiles. The chart for the game then looks like this:

n P( n ) Prize  Utiles of Prize  Expected utility 1 1/2 $2 2 1 2 1/4 $4 4 1 3 1/8 $8 8 1 4 1/16 $16 16 1 5 1/32 $32 32 1 6 1/64 $64 64 1 7 1/128 $128 100 0.78 8 1/256 $256 100 0.391 9 1/512 $512 100 0.195 10 1/1064 $1064 100 0.098

The sum of the infinite series in the right-hand column reaches a limit of about 7.56, and the rational entry price is anything under $7.56.

The assumption that maximum utility is reached by any dollar-prize over $100 is implausible because it means that the value of $100, $1000, and $1,000,000 are all the same—the maximum. That can't be: indifference between receiving $100 and $10,000 would be bizarre indeed. A more plausible point for maximum utility of dollars is much higher. Setting it at 16,000,000 makes the maximum rational entry price of the game close to $25, which is Hacking's guess at what our intuitions would accept. Is that the point where utility maximizes out?

Some people think that it is reasonable to set an upper limit on utility. Russell Hardin (1982), for example, calls this assumption “compelling in its own right.” William Gustason (1994) suggests that one restrict the expected value concept by stipulating that values of any consequence have an upper bound. Richard Jeffrey (1983) agrees.

But the idea of an upper limit on utility might not be seen to be compelling in its own right. Note that this idea must be distinguished from the diminishing marginal value of money. Perhaps you find it reasonable to think that, once one had (say) $16,000,000 in the bank, you'd be able to buy anything you could possibly want; but this is not to say that that sum of money provides the maximum permissible utility. We can readily imagine someone with that amount of money—or any amount of money—still short of utility, due to lack of certain goods that money can't buy. What the idea of an upper limit on utility means is that there is some amount of utility which is so high that no additional utility is possible—that nothing additional adds any value at all. Imagine someone with all the wealth he could use: still he might have unfulfilled desires, for example, that his friends and relations be as fortunate as he. If this desire were fulfilled, then he might still desire that strangers be as fortunate; and that there be more people on earth than there currently were, to share his happiness, and more populated planets full of happy people. How many more? Why, the more the better—indefinitely more. If there is an upper limit on utility, then there is some finite amount of utility which is maximally good, an amount for which one would rationally trade anything else. It doesn't appear plausible to think that there is any such amount.

One might imagine that some people have an upper limit on the utility they can enjoy—people who have a finite number of desires, and whose desires can each be completely satisfied by some finite state. For these people, the utility of prizes does not increase without limit, and the St. Petersburg game has some finite expected utility. Do such people exist? This is an empirical question. In any case, there surely are some people with some ‘the-more-the-better’ desires, and the theory of rational choice ought not to be restricted by the empirical and doubtful propositions that there aren't any, and that value cannot increase without limit. And these propositions are surely insufficiently well-founded to serve as solutions to the St. Petersburg paradox.

Gustason says that “the upshot of the paradox is that if there is such a thing as an infinite value, then acts and consequences that involve it are beyond the scope of the expected value concept.” Jeffrey states that the evaluation theory we are applying here has “from its inception...been closely tied to the notion that desirabilities are ... bounded.” But the fact that the theory wasn't designed with such a result in mind is not a very good reason to try to resist its application in this case. The main reason both authors give for excluding unbounded-desirability games is that otherwise the St. Petersburg game has infinite expected utility. But this ad-hoc rationale is not compelling unless one can't bear this result. The acceptability of this result will be considered later.

Hardin offers the opinion that whether utility is bounded “is more a factual than a logical issue,” and that its invocation to resolve the St. Petersburg paradox “is to grant that the paradox is not an antinomy.” He may mean that the difficulty posed by the game is a result of a factual assumption that utility is unbounded (and not merely by its logical features), and can be removed by rejecting that assumption. But if one finds no difficulty posed by the game, one is not tempted to reject the assumption.

Gustason suggests that, in order to avoid the St. Petersburg problem, one has the choice between two restrictions on the expected value concept:

(a) Each act has only finitely many consequences, or (b) Values must be ‘bounded,’ i.e., there are numbers n and m such that no value to be assigned a consequence exceeds n or is less than m.

He points out that imposing either restriction will suffice to rule out the St. Petersburg result. If one resists imposing restriction (b), in this case, by setting an upper bound to the value of consequences, perhaps restriction (a) might be found plausible.

One way to impose restriction (a) is merely to insist that the St. Petersburg game, which fails to meet it, is therefore not an appropriate application for standard expected value theory, which consequently cannot be used to calculate its fair entrance price. How then, if at all, can it be calculated? Where does the intuition that $25 is too much to pay come from (if anywhere)? How (if at all) can it be justified?

Another way is to assume that the way the game will take place is not exactly as described, and that there are some possible very long strings that would never be carried out—i.e., that there is only a finite number of prizes to be considered when calculating the expected value of the game. Presumably, this would be applied by setting some upper limit L to the number of flips which would be considered; after a run of L heads in a row, the game would be terminated and payment made for the run so far, despite the fact that tails hadn't yet come up. If L were set at 25, then the game would have an expected value of $25, and that would be the maximum entry price which a rational agent would pay to play (as in Hacking's intuition). Do we, perhaps unconsciously, assume that any run of 25 heads would be truncated, and paid off, at that point?

Many authors have pointed out that, practically speaking, there must be some point at which a run of heads would be truncated without a final tail. For one thing, the patience of the participants of the game would have to end somewhere. If you think that this sets too narrow a limit L, consider the considerably higher limit set by the life-spans of the participants, or the survival of the human race; or the limit imposed by the future time when the sun explodes, vaporizing the earth. Any of these limits produces a finite expected value for the game, but sets an L which is higher than 25; what, then, explains Hacking's $25 intuition?

Another fact that would set a limit on L is the finitude of the bankroll necessary to fund the game. Any casino that offers the game must be prepared to truncate any run that, were it to continue, would cost them more than the total funds they have available for prizes. A run of 25 would require a prize of a mere $33,554,432, possibly within the reach of a larger casino. A run of 40 would require a prize of about 1.1 trillion dollars. So any casino offering St. Petersburg must truncate very long runs.

Other facts, such as the limit on the amount of money in the world, make the necessity of an upper limit even more obvious. But perhaps all these financial limits can be overridden if we conceive of the game's being offered by a state capable of printing all the money it wanted to. This state could pay any prize whatever; still, printing up and handing out a huge amount of cash would create havoc with any economy, so no rational state would do this. (And anyway, if a foolish state did inject huge amounts of newly-minted currency to cover a stupendous win, the resulting inflation would severely undermine the value of the money won.)

But in any case, it appears that these practical difficulties may be circumvented; for example, as Michael Clark (2002) suggests, the casino might offer an enormous win merely as credit to the winner.

Hardin claims that “the slightest bit of realism is sufficient to do in the St. Petersburg Paradox.” But should we be even slightly realistic? Nowadays one frequently encounters, around philosophy departments, the refusal to take merely hpothetical situations seriously; simplifying thought-experiments, for example, are dismissed because they don't describe any realistic situation. But refusing to think about a problem isn't solving it.

It's of course true that any real game would impose some upper limit on L, and thus a finite number of possible consequences of the game; but this does not solve the St. Petersburg puzzle because it does not show that the expected value of the game as described is not infinite. After all, any game with a limit L is not the game we have been talking about. Our question was about the St. Petersburg game, not about its L-limited relative.

Do these realistic considerations show that the genuine St. Petersburg game—exactly as originally described—can never be encountered in real life? Jeffrey says: “Put briefly and crudely, our rebuttal of the St. Petersburg paradox consists in the remark that anyone who offers to let the agent play the St. Petersburg game is a liar, for he is pretending to have an indefinitely large bank.”

It can be quibbled that Jeffrey is not exactly right: that someone can offer a game even though he is aware that there's a possibility that this offer involves the possibility of requiring consequences he cannot fulfill. Compare my offer to drive you to the airport tomorrow. I realize that there's a small possibility my car will break down between now and then, and thus that I'm making an offer I might not be able to fulfill. But the conclusion is not that I'm not really offering what I appear to be. If someone invites you to play St. Petersburg, we can't conclude that he's in fact not offering the St. Petersburg game, that he's really offering some other game.

Real casinos right now play games that offer the extremely remote possibility of continuing too long for anyone to complete, or of prizes too large to be managed. Casinos can go ahead and play these games anyway, confident that the risk of running into an impossible situation is very very small. They need not lose any sleep worrying about incurring a debt they can't manage. They live, and prosper, on probabilities, not certainties.

If these considerations are persuasive, then what Jeffrey gives is not a rebuttal of the paradox. In effect, he accepts the fact that the game offers the possibility of indefinitely large payoffs. The reason the game is not offered by casinos is that they realize that sooner or later (probably much later) the game will bankrupt them. This is correct reasoning—but it is done using the ordinary, general theory of choice. When casinos reason about the game, they do not decide that, since ordinary theory shows that the game has infinite value, ordinary theory should be restricted to exclude its consideration.

There are other reasons why we should not restrict theory to exclude consideration of the game. This ruling, in order to be theoretically acceptable, ought not merely rule out the St. Petersburg game in particular, ad hoc; it ought to be general in scope. And if it is, it will also rule out perfectly acceptable calculations. Michael Resnik (1987) notes that utility theory “is easily extended to cover infinite lotteries, and it must be in order to handle more advanced problems in statistical decision theory” but he gives no examples.

Imagine a life insurance policy bought for a child at its birth, which pays to the child's estate, when it eventually dies, $1000 for each birthday the child has passed, without limit. What price should an insurance company charge for this policy? (For simplicity, we shall ignore possible effects of inflation, and profits from investing the entry price.) Standard empirically-based mortality charts give the chances of living another year at various ages. Of course, they don't give the chances of surviving another year at age 140, because there's no empirical evidence available for this; but a reasonable function to extend the mortality curve indefinitely beyond what's provided by available empirical evidence can be produced; this curve asymptotically approaches zero. On this basis, ordinary mathematical techniques can give the expected value of the policy. But note that it promises to pay off without limit. If we think that, for each age, there is a (large or small) probability of living another year, then there are an indefinitely large number of consequences to be considered when doing this calculation, but mathematics can calculate the limit of this infinite series; and (ignoring other factors) an insurance company will make a profit, in the long run, buy charging anything above this amount. There's no problem in calculating its expected value.

This insurance policy (call it Policy 1) offers an indefinite number of outcomes; but consider a different one (call it Policy 2) which would truncate the series at age 140, and offer only 140 outcomes. The probability of reaching age 140 is so tiny that the difference in expected value between the two policies is negligible, a tiny fraction of 1 cent. If you don't like infinite lotteries, you might claim that Policy 1 is ill-formed, and suggest substitution of Policy 2, pointing out that the expected value of this one is, for all practical purposes, equal to that of Policy 1. But note that your judgment that the two are virtually identical in expected value depends on your having calculated the expected value of Policy 1. So your statement presupposes that the expected value of Policy 1 is calculable, after all.

The St. Petersburg game is sometimes dismissed because it is has infinite expected value, which is, it's argued, not merely practically impossible, but theoretically objectionable—beyond the reach even of thought-experiment. But is it?

Imagine you were offered the following deal. For a price to be negotiated, you will be given permanent possession of a cash machine with the following unusual property: every time you punch in a dollar amount, that amount is extruded. This is not a withdrawal from your account; neither will you later be billed for it. You can do this as often as you care to. Now, how much would you offer to pay for this machine? Do you find it impossible to perform this thought-experiment, or to come up with an answer? Perhaps you don't, and your answer is: any price at all. Provided that you can defer payment of the initial price for a suitable time after receiving the machine, you can collect whatever you need to pay for it from the machine itself.

Of course, there are practical considerations: how long would it take you to collect its enormous purchase price from the machine? Would you (or the machine) be worn out or dead before you are finished? Any bank would be crazy to offer to sell you an infinite cash machine (and unfortunately I seem to have lost the address of the crazy bank which has made this offer). But so what? The point is that there appears to be nothing wrong with this thought experiment: it imagines an action (buying the machine) with no upper limit on expected value. We easily ignore practical considerations when calculating the expected value (in this case, merely potential withdrawals minus purchase price), which is infinite.

It seems unlikely that your intuitions tell you to offer (say) $25 at most for this machine. But the only difference between this machine and a single-play St. Petersburg game is that this machine guarantees an indefinitely large number of payouts, while the game offers a one-time lottery from among an indefinitely large number of possible payouts, each with a certain probability. The only difference between them is the probability factor: the same difference that exists between a game which gives you a guaranteed prize of $5, and one which gives you half a chance of $10, and half a chance of $0. The expected value of both the St. Petersburg game and the infinite cash machine are both indefinitely large. You should offer any price at all for either. These arguments appear to show that the notion of infinite expected value is perfectly reasonable.

It's quite true that when infinities show up in certain considerations, nonsense results. Consider this example: I write down an integer, at random, and seal it in an envelope. You open the envelope and observe I've written down 8,830,441. Given the infinity of integers I've had to choose from, the probability of my writing down this one is zero. It's a miracle! (Or maybe: a contradiction!) The problem here is, of course, the incoherence of the idea of choice among literally an infinite number of integers.

Doubts about the metaphysical reality of infinity, and about the proper rational employment of that concept have been raised throughout the history of philosophy and mathematics. So it's tempting to attribute the paradox raised by St. Petersburg to merely another illegitimate use of infinity. But notice that we don't need to invoke infinity in describing the gamble or its consequences. The payoff of any conceivable game is always finite. So is the length of any conceivable game. The paradoxical result can be put this way: no matter what (finite) entry price X is charged, it can be shown that the expected payoff of the game is larger than that, due to the (very small) possibility of the number of flips growing larger than X. (Note similarly that the wonderful cash machine mentioned above is not contingent on the reality of any infinity: every payoff it can make is finite; and at any point, it has been used only a finite number of times.)

The St. Petersburg game is one of a large number of examples which have been brought against standard (unrestricted) Bayesian decision theory. Each example is supposed to be a counter-example to the theory because of one or both of these features: (1) the theory, in the application proposed by the example, yields a choice people really do not, or would not make; thus it is descriptively inadequate. (2) the theory, in the application proposed by the example, yields a choice people really ought not to make, or which a fully, ideally rational person, would not make; thus it is normatively inadequate.

If you see standard theory as normative, you can ignore objections of the first type. People are not always rational, and some people are rarely rational, and an adequate descriptive theory must take into account the various irrational ways people really do make decisions. It's no surprise that the classical rather a-prioristic theory fails to be descriptively adequate, and to criticize it on these grounds rather misses its normative point.

The objections from standpoint (2) need to be taken more seriously; and we have been treating the responses to St. Petersburg as cases of this sort. Various sorts of “realistic” considerations have been adduced to show that the result the theory draws in the St. Petersburg game about what a rational agent should do is incorrect. It's concluded that the unrestricted theory must be wrong, and that it must be restricted to prevent the paradoxical St. Petersburg result.

When considering the plausibility of restricting expected value calculations in various ways that would take care of the paradox. Amos Nathan (1984) remarks, “it ought, however, to be remembered that important and less frivolous application of such games have nothing to do with gambling and lie in the physical world where practical limitations may assume quite a different dimension.” Nathan doesn't mention any physical applications of analogous infinite value calculations. But it's nevertheless plausible to think that imposing restrictions on theory to rule out St. Petersburg bath water would throw out some babies as well.

Any theoretical model is an idealization, leaving aside certain practicalities. “From the mathematical and logical point of view,” observes Resnick, “the St. Petersburg paradox is impeccable.” But this is the point of view to be taken when evaluating a theory per se (though not the only point of view ever to be taken). By analogy, the aesthetic evaluation of a movie does not take into account the facts that the only local showing of the movie is far away, and that finding a baby sitter will be impossible at this late hour. If aesthetic theory tells you that the movie is wonderful, but other considerations show you that you shouldn't go, this isn't a defect in aesthetic theory. Similarly, the mathematical/logical theory for explaining ordinary casino games is not defective because it ignores practicalities such as a particular limit on a casino's bankroll, or on participants' patience.

There are all sorts of practical considerations which must be considered in making a real gambling decision. For example, in deciding whether to raise, see, fold, or cash in and go home, in a particular poker game, you must consider not only probability and expected value, but also the facts that it's 5 A.M. and you are cross-eyed from fatigue and drink; but it's not expected that classical decision theory has to deal with these.

The St. Petersburg game commits participants to doing what we know they will not. The casino may have to pay out more than it has. The player may have to flip a coin longer than physically possible. But this may not show a defect with choice theory. Classical unrestricted theory is still serving its purpose, which is modeling the abstract ideal rational agent. It tells us that no amount is too great to pay as an ideally rationally acceptable entrance fee, and this may be right. What it's reasonable for real agents, limited in time, patience, bankroll, and imaginative capacity to do, given the constraints of the real casino, the real economy, and the real earth, is another matter, one that the theoretical core of decision theory can be forgiven for not specifying. From this point of view, the St. Petersburg result is strange, but this does not show that there's a defect in classical decision theory. The appopriate reaction might just be to try to accept the strange result. As Clark says “This seems to be one of those paradoxes which we have to swallow.”

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decision theory: causal | Pascal's wager