Vote Delegation and Misbehavior

TL;DR

This paper compares vote delegation and conventional voting, analyzing how the presence of well-behaving and misbehaving agents affects the likelihood of positive outcomes in liquid democracy.

Contribution

It provides a theoretical comparison of voting methods under different levels of misbehavior, highlighting conditions where each method succeeds or fails.

Findings

High misbehavior leads to failure of both methods.

Intermediate misbehavior favors conventional voting.

Low misbehavior makes delegation more effective.

Abstract

We study vote delegation with "well-behaving" and "misbehaving" agents and compare it with conventional voting. Typical examples for vote delegation are validation or governance tasks on blockchains. There is a majority of well-behaving agents, but they may abstain or delegate their vote to other agents since voting is costly. Misbehaving agents always vote. We compare conventional voting allowing for abstention with vote delegation. Preferences of voters are private information and a positive outcome is achieved if well-behaving agents win. We illustrate that vote delegation leads to quite different outcomes than conventional voting with abstention. In particular, we obtain three insights: First, if the number of misbehaving voters, denoted by f , is high, both voting methods fail to deliver a positive outcome. Second, if f takes an intermediate value, conventional voting delivers a positive outcome, while vote delegation fails with probability one. Third, if f is low, delegation delivers a positive outcome with higher probability than conventional voting. Finally, our results characterize worst-case outcomes that can happen in a liquid democracy.