Anchor-proofness in Voting
Federico Fioravanti, Zoi Terzopoulou
TL;DR
The paper investigates how sequential presentation creates anchoring in approval ballots and whether voting rules can be robust to this bias. By formalizing a model where voters derive approval via an anchoring mechanism tied to presentation order, it shows that no non-constant approval-based rule is anchor-proof across all profiles, though special restricted domains admit limited invariance. It also analyzes the social planner's capacity to manipulate outcomes, showing zero-information prevents manipulation under weak/total unanimity, while partial information generally enables strategic ordering for common rules like SAV and Nom. The results illuminate fundamental trade-offs between robustness to cognitive biases and the potential for design-driven influence, with implications for participatory budgeting and similar collective-decision contexts. The work motivates extensions to richer ballot types and the exploration of randomized or bias-aware mechanisms to mitigate anchor-driven distortions.
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.