Mental Math and Life Stories

Imagine you have been offered four options: You could have $10 million, $1 million, another year to live, or a chance to see someone you love. Your mental calculations will have a lot to do with your beliefs about your life. What if you expect to see someone you love tonight anyway? What if you think you have 70 more years to live? Or what if you are certain you have only 30 seconds?

Hamed Hamze (MS ’10), a Repetto-Figueroa Family Graduate Fellow at Caltech, uses math to study how people make decisions. As a graduate student in economics, he models scenarios ranging from the hypothetical one above to real-world social choices such as voting.

While the work feels like play to Hamze, the outcomes matter. Economists combine theory with historical data to help people, businesses, and governments make plans. Sound, theory-driven reasoning ensures economists make the best possible predictions regarding likely responses to different prices, laws, constraints, and opportunities. (See, for example, our story about Caltech Resnick Fellow Hao Zhao.)

Playing with Ideas—and Making an Impact

Hamze’s mother is a mathematics teacher, and he shares her love of the subject. He dropped his first major at Caltech—electrical engineering—when he saw the kind of math involved in economic theory. “At the core, these are brain games,” Hamze says. “I like that. But I also like that these kinds of problems have a flavor of philosophy and psychology.”

Hamze has a knack for spotting mathematical issues that overcomplicate theory. He helped a Caltech economist differentiate critical parts of a problem from extraneous elements that had clouded the simplicity and power of the solution. Then, Hamze realized that the simpler solution could be applied more broadly to resolve an issue raised in a paper by an economist working on a different application.

Returning to the hypothetical choice of a longer life, different amounts of money, or a moment with a loved one. Many economists use a combination of two numbers to predict a likely response to that choice: one number to represent the inherent value of a given option; the other to represent beliefs about that option. However, Hamze agrees with a number of economists who believe this approach misses something, and he has introduced a simple model to make more accurate predictions. This model posits that the inherent value of the options and their associated beliefs changes depending on circumstances. For example, if one has 30 seconds to live, the value of $10 million dollars to that particular individual is zero.


Questions for the Future

Hamze dreams of a future in which he investigates how people make decisions. He is curious to determine whether possessing more options makes one happier or instead leads to regret or second-guessing. Hamze would like to understand the impact of belief in fate, divine will, or luck on the choices people make, and their confidence in those choices. He also would like to ascertain why an equitable division of money or other resources can feel unfair. Experiments show that we value fairness. But they also show that we often overestimate the worth of our own efforts, and end up expecting more than our fair share.

There is likely no end to the questions Hamze may model.

Free to Focus, Thanks to a Graduate Fellowship

Hamze is the first Repetto-Figueroa Family Graduate Fellow in Caltech’s Division of the Humanities and Social Sciences (HSS). Eduardo Repetto (PhD ’98) and Carla Figueroa established two fellowships in 2016 and 2017, one in HSS and one in the Division of Engineering and Applied Science. Figueroa and Repetto, an engineer who works in finance, saw value in gifts that link the two divisions. They boosted their impact through another couple’s generosity, tapping the Gordon and Betty Moore Graduate Fellowship Match.

Such fellowships enable Caltech graduate students to focus deeply on their work and follow their original ideas wherever they lead. Fellowship funding also frees students to explore multiple questions and collaborate with several faculty members, as Hamze does, rather than work on prescribed topics tied to grant-funded research. Those benefits and others make fellowships a high priority in Caltech’s Break Through campaign.

Giving Priorities