Spectra Seminar at UCR

Monday, 4-5pm in Skye 284

Speaker:

Chris Grossack (University of California, Riverside)

Title:

Your Nobel Prize in Economics

Abstract:

Say you want to hold an election with 3 candidates, Alyss, Bob, and Cam. Every voter ranks the candidates, and then you use some strategy to turn the individual voter rankings into a “collective ranking” of the candidates (you could use a majority rule, or an electoral college, or something even more convoluted). It turns out that some strategies can result in a paradoxical state of affairs, where (according to the collective ranking) the people prefer Alyss to Bob, prefer Bob to Cam, and somehow prefer Cam to Alyss! In a situation like this, it’s impossible to say who “won” the election, so it’s natural to want a “collective ranking” system where such paradoxical outcomes never happen. Unfortunately, the ONLY voting system which is never paradoxical is a dictatorship! That is, the “collective ranking” is actually just the ranking of some fixed voter. In 1972 this theorem won Kenneth Arrow the nobel prize in economics (though he proved the theorem in his 1950 PhD thesis)!

In this talk, we’ll introduce the subject of Boolean Fourier Analysis, a central tool in computer science, and use the techniques we learn in order to prove Arrow’s impossibility theorem for ourselves.