Vote swapping in irresolute two-tier voting procedures

We investigate a specific type of group manipulation in two-tier elections, which involves pairs of voters agreeing to exchange their votes. Two-tier elections are modeled as a two-stage choice procedure. In the first stage, voters are distributed into districts, and district preferences result from...

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Bibliographic Details
Published in:Social choice and welfare 2023-08, Vol.61 (2), p.221-262
Main Authors: Dindar, Hayrullah, Lainé, Jean
Format: Article
Language:English
Subjects:
Constitutions
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Elections
Function
Game Theory
International Political Economy
Manipulation
Original Paper
Political majority
Preferences
Public Finance
Quantitative Finance
Social and Behav. Sciences
Social choice
Social Policy
Voter behavior
Voters
Voting
Voting rules
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Summary:We investigate a specific type of group manipulation in two-tier elections, which involves pairs of voters agreeing to exchange their votes. Two-tier elections are modeled as a two-stage choice procedure. In the first stage, voters are distributed into districts, and district preferences result from aggregating voters’ preferences district-wise through some aggregation rule. Final outcomes are obtained in the second stage by applying a social choice function that outputs one or several alternatives from the profile of district preferences. Combining an aggregation rule and a social choice function defines a constitution. Voter preferences, defined as linear orders, are extended to complete binary relations by means of some extension rule. A constitution is swap-proof w.r.t. a given extension rule if one cannot find pairs of voters who, by exchanging their preferences get better off (w.r.t. their extended preference over sets). We consider four specific extension rules: Nehring, Kelly, Fishburn, and Gärdenfors. We establish sufficient conditions for the swap-proofness of a constitution w.r.t. each extension rule. Special attention is paid to majority constitutions, where both the aggregation rule and the social choice function are based on simple majority voting. We show that swap-proofness for majority constitutions pertains to a specific weakening of group strategy-proofness. Moreover, we characterize swap-proof majority constitutions w.r.t. each extension rule. Finally, we show that no constitution based on scoring methods is swap-proof.
ISSN:0176-1714
1432-217X
DOI:10.1007/s00355-022-01445-z