Aggregation of binary evaluations: a Borda-like approach

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 10:89–99, 1975). In this setting we characterize the “mean rule,” which we derive from properties similar to those Young (J Econ Theory 9:43–52, 1974) used in his characterization of the Borda rule. Complementing our axiomatic approach is a derivation of the mean rule using vector decomposition methods that have their origins in Zwicker (Math Soc Sci 22:187–227, 1991). Additional normative appeal is provided by a form of tension minimization that characterizes the mean rule and suggests contexts wherein its application may be appropriate. Finally, we derive the mean rule from an approach to judgment aggregation recently proposed by Dietrich (Soc Choice Welf 42:873–911, 2014).