Reinstating Combinatorial Protections for Manipulation and Bribery in Single-Peaked and Nearly Single-Peaked Electorates

TL;DR

This paper explores how allowing voters to submit partial preferences in single-peaked electorates can restore computational complexity barriers against manipulation and bribery, which are otherwise easier in complete preferences.

Contribution

It demonstrates that partial preferences, such as top-truncated ballots, can reintroduce NP-hardness in manipulation and bribery problems for single-peaked electorates.

Findings

NP-hardness of manipulation and bribery is restored with top-truncated ballots.

Complexity increases from P to NP-complete in single-peaked settings.

Partial preferences can serve as a protective measure against election manipulation.

Abstract

Understanding when and how computational complexity can be used to protect elections against different manipulative actions has been a highly active research area over the past two decades. A recent body of work, however, has shown that many of the NP-hardness shields, previously obtained, vanish when the electorate has single-peaked or nearly single-peaked preferences. In light of these results, we investigate whether it is possible to reimpose NP-hardness shields for such electorates by allowing the voters to specify partial preferences instead of insisting they cast complete ballots. In particular, we show that in single-peaked and nearly single-peaked electorates, if voters are allowed to submit top-truncated ballots, then the complexity of manipulation and bribery for many voting rules increases from being in P to being NP-complete.