Anchor-proofness in Voting

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.