Complexity of Terminating Preference Elicitation

TL;DR

This paper explores the computational complexity of terminating preference elicitation, strategic manipulation, and winner prediction in voting systems, revealing that strategy and granularity significantly impact computational difficulty.

Contribution

It demonstrates how the complexity of preference elicitation and manipulation varies with different strategies and levels of preference granularity, providing new insights into election computational issues.

Findings

Eliciting preferences from one agent at a time can be computationally more efficient.

Manipulation complexity depends on the extent of preference change allowed.

Certain voting rules are computationally hard to analyze for winner probability prediction.

Abstract

Complexity theory is a useful tool to study computational issues surrounding the elicitation of preferences, as well as the strategic manipulation of elections aggregating together preferences of multiple agents. We study here the complexity of determining when we can terminate eliciting preferences, and prove that the complexity depends on the elicitation strategy. We show, for instance, that it may be better from a computational perspective to elicit all preferences from one agent at a time than to elicit individual preferences from multiple agents. We also study the connection between the strategic manipulation of an election and preference elicitation. We show that what we can manipulate affects the computational complexity of manipulation. In particular, we prove that there are voting rules which are easy to manipulate if we can change all of an agent's vote, but computationally intractable if we can change only some of their preferences. This suggests that, as with preference elicitation, a fine-grained view of manipulation may be informative. Finally, we study the connection between predicting the winner of an election and preference elicitation. Based on this connection, we identify a voting rule where it is computationally difficult to decide the probability of a candidate winning given a probability distribution over the votes.