Anchor-proofness in Voting

2026-02-04

AI Summary

This study investigates how cognitive anchoring bias affects collective decision-making under approval voting, with a focus on whether a social planner can alter election outcomes by manipulating the order in which alternatives are presented. Under the behavioral assumption that voters approve only those alternatives perceived as superior to previously encountered options, the paper formally introduces the notion of “anchor-proof” voting rules for the first time. Employing tools from game theory, social choice theory, and a model of sequence-dependent approval behavior, the authors provide an axiomatic analysis of such rules. Their findings demonstrate that voting rules satisfying anchor-proofness are exceedingly rare and structurally constrained, revealing a fundamental tension between behavioral biases and mechanism design. Moreover, the study shows that without accurate knowledge of voters’ true preferences, a planner cannot effectively manipulate the outcome.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Humans and AI: Voting

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

This work contributes to a foundational question in economic theory: how do individual-level cognitive biases interact with collective choice mechanisms? We study a setting where voters hold intrinsic preference rankings over a set of alternatives but cast approval ballots to determine the collective outcome. The ballots are shaped by an anchoring bias: alternatives are presented sequentially by a social planner, and a voter approves an alternative if and only if it is acceptable and strictly preferred to all alternatives previously encountered. We first analyze which approval-based voting rules are anchor-proof, in the sense that they always select the same winner regardless of the presentation order. We show that this requirement is extremely demanding: only very restrictive rules satisfy it. We then turn to the potential influence of the social planner. On the upside, when the planner has no information about the voters'intrinsic preferences, she cannot manipulate the outcome.

Problem

• anchor-proofness
• voting
• anchoring bias
• approval voting
• preference ordering

Innovation

• anchor-proofness
• anchoring bias
• approval voting
• preference elicitation
• mechanism design