Aggregation of binary evaluations: a Borda-like approach

Abstract

We characterize a rule for aggregating binary evaluations -equivalently, dichotomous weak orders -similar in spirit to the Borda rule from the preference aggregation literature. The binary evaluation framework was introduced as a general approach to aggregation by Wilson (J. Econ. Theory 10 (1975) 63-77). In this setting we characterize the "mean rule," which we derive from properties similar to those Young (J. Econ. Theory 9 (1974) 43-52) used in his characterization of the Borda rule. Complementing our axiomatic approach is a *

Cycles and Intractability in a Large Class of Aggregation Rules

“…See Examples 1 and 2 in this section; Duddy et al (2016) provide detailed proofs and more examples. We say that −…”

“…We introduce the (j, k)-Kemeny rule, a generalization wherein ballots are weak orders with j indifference classes ("j-chotomous" weak orders) and the outcome is a weak order with k indifference classes. Different values of j and k yield rules of interest in social choice theory as special cases, including approval voting, the mean rule and Borda mean rule (see Duddy & Piggins, 2013;Duddy, Piggins, & Zwicker, 2016;Brandl & Peters, 2017), the Borda count voting rule, and plurality voting.…”

An axiomatic characterization of the Borda mean rule

“…Duddy et al. ( 2016 ) study a setting in which every voter holds a binary evaluation of the alternatives or, equivalently, a dichotomous weak order. A binary aggregation function maps the voters’ binary evaluations to an ordered 3-partition of approved, tied, and disapproved alternatives.…”

“…Duddy et al. ( 2016 ) propose the mean rule , which assigns to all alternatives with above-average approval score, assigns 0 to alternatives whose approval score is exactly average, and assigns to all alternatives with below-average approval score. They explain that the mean rule can be used in judgement aggregation for certain agendas, and connect the mean rule with the scoring rules for judgement aggregation introduced by Dietrich ( 2014 ).…”

“…This rule was defined by Duddy et al. ( 2014 ) and further discussed by Duddy et al ( 2016 , Section 5) and Zwicker ( 2018 ). Notice that the Borda mean rule satisfies reversal symmetry.…”