How Likely Are Two Voting Rules Different?

Ziqi Yu, Lirong Xia, Qishen Han, Chengkai Zhang

Keywords: Computational Social Choice, Semi-random Analysis.

Abstract:

We characterize the maximum likelihood that two voting rule outcomes are different and that the winner of one voting rule is the loser of another (implying that they are {\em drastically different}) on positional scoring rules, Condorcet winner/loser, Copeland, Ranked Pairs, and STV (Single Transferable Vote) under any fixed number of alternatives.
The most famous problem in this scope is strong Borda's paradox, in which the winner of the plurality rule is the Condorcet loser. Under mild assumptions, we show that the maximum likelihood that different rules are drastically different is $\Theta(1)$ except for a few special cases, demonstrating the difference between these rules.
We also prove that two scoring rules with linear independent scoring vectors have different winners with probability $\Theta(1)$, no matter how similar they are. Our analysis adopts the {\em smoothed social choice framework}~\cite{xia2020smoothed} and can be applied to a variety of statistical models, including the standard impartial culture (IC).

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission127/Authors, auai.org/UAI/2025/Conference/Submission127/Reproducibility_Reviewers

Submission Number: 127