Center for Applied Mathematics Colloquium

Sid BanerjeeCornell University
The Mathematics (and Ethics) of Fair Resource Allocation

Friday, March 8, 2024 - 3:45pm
Rhodes 655

In many settings, a finite supply of some public resource is allocated among people over time, without using money: a computing cluster among researchers, food among food-banks, medical supplies between hospitals, funding between non-profit projects, fellowships among admitted students, etc. The underlying aim is often to try and be ‘fair’ in these allocations…but what exactly do we mean?Understanding fairness in sequential decision-making is one of the most urgent (but also, intellectually beautiful) topics today, with deep connections to control theory, economics, optimization, and normative philosophy. I will demonstrate this using two case studies: one where we know the exact numerical utility each agent gets from being allocated; and one where we do not, but still want some rules as to which agents should have priority over others, and why. Through these examples, I will try to convince you of one big idea: as applied mathematicians, our main task should be to characterize trade-offs between fairness and efficiency in different settings, as a guide to policy-makers to help determine what is socially relevant. Luckily, doing so turns out to be very intellectually rewarding -- I will try and describe surprising connections between our problems and a host of other topics -- physics, information theory, combinatorics, computational complexity, and many more!

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