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 (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 derivation of the mean rule using vector decomposition methods that have their origins in Zwicker (Math. Soc. Sci. 22 (1991) 187-227). Finally, we derive the mean rule from an approach to judgment aggregation recently proposed by Dietrich (Soc. Choice. Welf. 42 (2014) 873-911)