# Weighted Voting Via No-Regret Learning

## TL;DR

This paper proposes a no-regret learning framework to assign dynamic weights to voters in voting systems, aiming to improve decision quality by emphasizing historically reliable voters.

## Contribution

It introduces a formal framework for weighted voting based on no-regret learning, providing new possibility and impossibility results for such schemes under various conditions.

## Key findings

- Existence of weighting schemes depends on voting rule properties.
- Deterministic and randomized schemes have different feasibility conditions.
- Certain social choice axioms restrict the design of effective weighting schemes.

## Abstract

Voting systems typically treat all voters equally. We argue that perhaps they should not: Voters who have supported good choices in the past should be given higher weight than voters who have supported bad ones. To develop a formal framework for desirable weighting schemes, we draw on no-regret learning. Specifically, given a voting rule, we wish to design a weighting scheme such that applying the voting rule, with voters weighted by the scheme, leads to choices that are almost as good as those endorsed by the best voter in hindsight. We derive possibility and impossibility results for the existence of such weighting schemes, depending on whether the voting rule and the weighting scheme are deterministic or randomized, as well as on the social choice axioms satisfied by the voting rule.