Strategyproof Randomized Social Choice for Restricted Sets of Utility Functions

2025-08-22

AI Summary

This paper studies the design of social decision schemes (SDSs) that are strategyproof under restricted utility classes—e.g., utilities assigning higher values to optimal alternatives. It introduces *U-strategyproofness*, a novel notion relaxing Gibbard’s theorem by lifting its reliance on complete preference orderings, thereby achieving strong strategyproofness with significantly reduced randomization. Methodologically, the work integrates stochastic social choice theory, utility-constrained modeling, strategic manipulation analysis, and ex post efficiency evaluation. Theoretically, it establishes that highly decisive (almost deterministic) U-strategyproof SDSs exist under specific utility structures; however, U-strategyproofness is incompatible with Condorcet consistency, and fundamental limits arise for decisiveness when preferences approach indifference. The core contribution is a precise characterization of the trade-off among utility structure, strategic robustness, and decisiveness—providing new foundations for designing practical, incentive-compatible social choice mechanisms.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Social decision schemes (SDSs) map the voters' preferences over multiple alternatives to a probability distribution over these alternatives. In a seminal result, Gibbard (1977) has characterized the set of SDSs that are strategyproof with respect to all utility functions and his result implies that all such SDSs are either unfair to the voters or alternatives, or they require a significant amount of randomization. To circumvent this negative result, we propose the notion of $U$-strategyproofness which postulates that only voters with a utility function in a predefined set $U$ cannot manipulate. We then analyze the tradeoff between $U$-strategyproofness and various decisiveness notions that restrict the amount of randomization of SDSs. In particular, we show that if the utility functions in the set $U$ value the best alternative much more than other alternatives, there are $U$-strategyproof SDSs that choose an alternative with probability $1$ whenever all but $k$ voters rank it first. On the negative side, we demonstrate that $U$-strategyproofness is incompatible with Condorcet-consistency if the set $U$ satisfies minimal symmetry conditions. Finally, we show that no ex post efficient and $U$-strategyproof SDS can be significantly more decisive than the uniform random dictatorship if the voters are close to indifferent between their two favorite alternatives.

Problem

• Analyzing tradeoff between strategyproofness and decisiveness in social choice
• Investigating U-strategyproofness for restricted utility function sets
• Exploring compatibility with Condorcet-consistency under symmetry conditions

Innovation

• Introduces U-strategyproofness for predefined utility sets
• Analyzes tradeoff between strategyproofness and decisiveness
• Shows compatibility with decisive SDSs under specific conditions