Combinatorics Seminar: Judgment aggregation, logic, and Fourier analysis on the Hamming cube

Seminar | April 16 | 12-1 p.m. | 939 Evans Hall

 Yan Zhang, San Jose State University

 Department of Mathematics

The classical Arrow's Theorem answers "how can n voters obtain a collective preference on a set of outcomes, if they have to obey certain constraints?" We give an analogue of this theorem in the judgment aggregation framework of List and Pettit, answering "how can n judges obtain a collective judgment on a set of logical propositions, if they have to obey certain constraints?" We introduce the concept of "normal pairs" of functions on the Hamming cube, which we analyze with Fourier analysis and elementary combinatorics. We obtain judgment aggregation results and compare them with existing theorems in the literature. Amusingly, the non-dictatorial classes of functions that arise are precisely the classical logical functions OR, AND, and XOR, meaning that they have yet another special place in the nature of logic.

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