2 research outputs found
Robust Voting Rules from Algorithmic Robust Statistics
Maximum likelihood estimation furnishes powerful insights into voting theory,
and the design of voting rules. However the MLE can usually be badly corrupted
by a single outlying sample. This means that a single voter or a group of
colluding voters can vote strategically and drastically affect the outcome.
Motivated by recent progress in algorithmic robust statistics, we revisit the
fundamental problem of estimating the central ranking in a Mallows model, but
ask for an estimator that is provably robust, unlike the MLE.
Our main result is an efficiently computable estimator that achieves nearly
optimal robustness guarantees. In particular the robustness guarantees are
dimension-independent in the sense that our overall accuracy does not depend on
the number of alternatives being ranked. As an immediate consequence, we show
that while the landmark Gibbard-Satterthwaite theorem tells us a strong
impossiblity result about designing strategy-proof voting rules, there are
quantitatively strong ways to protect against large coalitions if we assume
that the remaining voters voters are honest and their preferences are sampled
from a Mallows model. Our work also makes technical contributions to
algorithmic robust statistics by designing new spectral filtering techniques
that can exploit the intricate combinatorial dependencies in the Mallows model
Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence (AAAI-10) Good Rationalizations of Voting Rules
We explore the relationship between two approaches to rationalizing voting rules: the maximum likelihood estimation (MLE) framework originally suggested by Condorcet and recentl