The Smoothed Possibility of Social Choice

06/11/2020
by   Lirong Xia, et al.
0

We develop a framework to leverage the elegant "worst average-case" idea in smoothed complexity analysis to social choice, motivated by modern applications of social choice powered by AI and ML. Using our framework, we characterize the smoothed likelihood of some fundamental paradoxes and impossibility theorems as the number of agents increases. For Condrocet's paradox, we prove that the smoothed likelihood of the paradox either vanishes at an exponential rate, or does not vanish at all. For the folklore impossibility on the non-existence of voting rules that satisfy anonymity and neutrality, we characterize the rate for the impossibility to vanish, to be either polynomially fast or exponentially fast. We also propose a novel easy-to-compute tie-breaking mechanism that optimally preserves anonymity and neutrality for even number of alternatives in natural settings. Our results illustrate the smoothed possibility of social choice—even though the paradox and the impossibility theorem hold in the worst case, they may not be a big concern in practice in certain natural settings.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/25/2020

The Smoothed Complexity of Computing Kemeny and Slater Rankings

The computational complexity of winner determination under common voting...
research
05/11/2021

The Smoothed Likelihood of Doctrinal Paradox

When aggregating logically interconnected judgments from n agents, the r...
research
07/14/2023

Beyond the worst case: Distortion in impartial culture electorates

Distortion is a well-established notion for quantifying the loss of soci...
research
10/02/2018

Relating Metric Distortion and Fairness of Social Choice Rules

One way of evaluating social choice (voting) rules is through a utilitar...
research
10/15/2022

Beyond the Worst Case: Semi-Random Complexity Analysis of Winner Determination

The computational complexity of winner determination is a classical and ...
research
04/09/2018

Balancedness of Social Choice Correspondences

A social choice correspondence satisfies balancedness if, for every pair...

Please sign up or login with your details

Forgot password? Click here to reset