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Kota Saito
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Resources/RA and SURF Opportunity

Student Resources

RA/SURF:

I am seeking a highly motivated Research Assistant. My research uses mathematics and computer science to study human choice. The work in this position is much closer in style to mathematics (e.g., combinatorics, geometry, optimization, probability) than to a typical econ RA job.

Methodologically, we use tools from discrete geometry (the theory of polytopes) and flow theory. The work involves describing and analyzing high-dimensional polytopes, studying their vertices and facets, and using flow representations to capture constraints on choice probabilities. We do not limit our tools: we will use any mathematics that is useful to analyze consumers' choice. A short video overview of the project and its background is available here:

Project Description:

In economics, observable data typically take the form of stochastic choice, such as individual choice frequencies (e.g., an individual chooses one item 30% of the time and another item the rest of the time) or market-share data for a population (e.g., the market share of Toyota SUVs is 40%, Honda 20%, etc.). The standard framework for interpreting such data is the random utility model (RUM), which posits a probability distribution over linear orders on the set of alternatives. Each linear order represents the preference relation of a (latent) consumer type in the population.

One important question in economics is to understand meaning of RUM in terms of observable stochastic choice data. Such a result is called a characterization of RUM. Classical characterization results for RUM in terms of observable stochastic choice data apply only to complete datasets, in which choice frequencies are observed for all menus of all alternatives. Extending these characterizations to incomplete datasets has been an open problem since the 1980s across economics, mathematical psychology, and discrete mathematics.

My project will extend these characterizations, explore applications to empirical literature in Economics, study systematic deviations from RUM, and apply the same methodology to deterministic individual choice to propose a new measure of irrationality.

The followings are responsibilities:

  • (a) Regular collaboration: Meet about twice per week with me and coauthors. Progress also requires steady work between meetings. That said, I understand that you are students with coursework and other responsibilities. I respect your time, and we can find a mutually agreeable schedule.
  • (b) Mathematical analysis: Formulate and test conjectures; develop proofs and counterexamples; read and synthesize related literature. Many tasks look like advanced problem-set or research-style questions in discrete math / analysis / probability, rather than data cleaning or routine coding.
  • (c) Programming: Implement algorithms, run simulations, and organize computational experiments as needed. This will mainly support the theoretical work (e.g., exploring examples, stress-testing conjectures, or visualizing high-dimensional objects).

Required Background/Skills/Courses:

There are two main requirements: Exceptional mathematical ability and Commitment

(1) Exceptional mathematical ability: Successful RAs in my group (e.g., Alec Sandroni and Yuexin Liao) have been among the very best math students in their cohort, often excelling in advanced courses early on. You should demonstrate strong proficiency-typically evidenced by high grades (A or A+) in courses such as Ma 108 or Ma 110, or notable performance in mathematics competitions. No prior knowledge of economics is required; what matters most is that you enjoy hard, proof-based mathematics and are willing to learn whatever economics is needed along the way.

(2) Commitment: My work is highly theoretical and time-intensive. This is not a casual, part-time role; it involves sustained engagement with significant open problems in economics. If the collaboration is successful, the goal is to coauthor a research paper together. (In theoretical work, author lists are typically small---you will not be one of many.)

(3) This is not required, but the position is ideal for students who aspire to become independent researchers. (in Economics, OR, CS, or Mathematics). The role offers substantial research experience and the potential for a detailed recommendation letter for graduate schools based on your contributions. We may not always get a publishable result, but I can guarantee meaningful research experience. For example, Alec joined in his first year, helped solve a difficult part of our paper, coauthored it, presented at major conferences (London, Kyoto, Paris), and the paper is now accepted—exactly the kind of training that prepares you for serious research in any field.

How to Apply:

If you are interested, please follow these steps:

  • (a) Read the Paper: Carefully read the paper I co-authored with Alec. The paper is now accepted in American Economic Review, one of the leading journals in economics. Assess whether you can understand the material. My presentation video posted above would be useful. If you find it too challenging or outside your area of interest, it may be worth exploring other RA opportunities.
  • (b) Solve the Quiz: Complete the provided quiz. All past successful RAs were able to solve it.
  • (c) Email Me: Send me an email with your CV and the solution to the quiz. Your CV should include details about your math and computer science coursework and your achievement in math competition along with your grades.

SURF positions are available only to Caltech students. I am happy to supervise motivated students from outside Caltech, but I am unable to provide funding because I cannot receive Caltech financial support for them.

Former RAs and current coauthors:

Alec Sandroni has worked with me on multiple SURF projects over four years, starting from his freshman year (he is now a graduate student at MIT). He participated in every stage of developing the paper that is now accepted: generating ideas, completing rigorous proofs, finalizing the manuscript, presenting it at international conferences, and handling submission and revision.

Yuexin Liao joined our team in her third year through SURF, when she transferred to Caltech. Within a year, we were already close to completing several projects together. She quickly learned the necessary economics and, drawing on her exceptional abilities in mathematics and computer science, contributed at a very high level to the research.

Let me know if you have any questions by email.