Eliciting Kemeny Rankings

TL;DR

This paper models the elicitation of Kemeny rankings as a Dueling Bandits problem, proposing algorithms with theoretical bounds and adaptive sampling strategies to efficiently approximate the ranking based on pairwise comparisons.

Contribution

It introduces a novel formulation of preference elicitation as a Dueling Bandits problem and develops algorithms with sample complexity bounds for PAC solutions.

Findings

Algorithms with approximation bounds for Kemeny rankings.

Adaptive sampling methods improve efficiency in preference elicitation.

Comparative analysis on synthetic data demonstrates effectiveness.

Abstract

We formulate the problem of eliciting agents' preferences with the goal of finding a Kemeny ranking as a Dueling Bandits problem. Here the bandits' arms correspond to alternatives that need to be ranked and the feedback corresponds to a pairwise comparison between alternatives by a randomly sampled agent. We consider both sampling with and without replacement, i.e., the possibility to ask the same agent about some comparison multiple times or not. We find approximation bounds for Kemeny rankings dependant on confidence intervals over estimated winning probabilities of arms. Based on these we state algorithms to find Probably Approximately Correct (PAC) solutions and elaborate on their sample complexity for sampling with or without replacement. Furthermore, if all agents' preferences are strict rankings over the alternatives, we provide means to prune confidence intervals and thereby guide a more efficient elicitation. We formulate several adaptive sampling methods that use look-aheads to estimate how much confidence intervals (and thus approximation guarantees) might be tightened. All described methods are compared on synthetic data.