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 ∗Financial support from the Spanish Ministry of Science and Innovation through MICINN/FEDER grant ECO2010-21624, the NUI Galway Millennium Fund and the Irish Research Council co-funding from the European Commission is gratefully acknowledged. Conal Duddy conducted this research while visiting the Centre for Philosophy of Natural and Social Science at the London School of Economics. He is grateful for their hospitality. Thanks to Felix Brandt, Franz Dietrich, Nicholas Houy, Marcus Pivato and the participants at PET 13 for their helpful comments. This joint project began after we attended a workshop on New Developments in Judgement Aggregation and Voting Theory, held in Freudenstadt, September 2011. The workshop was organised by Clemens Puppe and Klaus Nehring. We are extremely grateful to them for organizing this workshop, and for providing financial support. †J.E. Cairnes School of Business and Economics and the Whitaker Institute, National University of Ireland Galway, Ireland. Email: [email protected] ‡J.E. Cairnes School of Business and Economics and the Whitaker Institute, National University of Ireland Galway, University Road, Galway, Ireland. Email: [email protected] §Department of Mathematics, Union College, Schenectady, NY 12308, USA. Email: [email protected]