Paradoxes in Sequential Voting

TL;DR

This paper investigates paradoxical outcomes in sequential voting with complete information, revealing that strategic voting can lead to rejecting Condorcet winners or electing Pareto dominated options, even with few voters and alternatives.

Contribution

It provides a comprehensive analysis of strategic voting paradoxes in various voting mechanisms with complete information, highlighting conditions leading to undesirable outcomes.

Findings

Condorcet winners can be rejected due to strategic voting.

Condorcet losers may be elected in certain voting procedures.

Paradoxical outcomes occur with as few as four alternatives and small voter groups.

Abstract

We analyse strategic, complete information, sequential voting with ordinal preferences over the alternatives. We consider several voting mechanisms: plurality voting and approval voting with deterministic or uniform tie-breaking rules. We show that strategic voting in these voting procedures may lead to a very undesirable outcome: Condorcet winning alternative might be rejected, Condorcet losing alternative might be elected, and Pareto dominated alternative might be elected. These undesirable phenomena occur already with four alternatives and a small number of voters. For the case of three alternatives we present positive and negative results.