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Ordinally Efficient and Reliable Social Choice: The Pluri-Borda Rule

Klaus Nehring (University of California, Davis)

Ordinally efficient choice correspondences are characterized as maximing a weighted average over comparison alternatives of the number of agents preferrring an alternative over any comparison alternative. The Borda rule is the classical example, assign equal weight to all comparison alternatives. However, the Borda rule suffers from severe problems of unreliability, as it is highly and implausibly sensitive to the inclusion of Pareto inferior and of minor variants (“clones”) in the feasible set.

Reliability can be ensured, however, by an appropriate choice of weights that depends on the profile of preferences. This is achieved, for example, by weighting alternatives in proportion their "plurality’, i.e. frequency as top choices, and induces the "Plurality-weighted Borda rule", or “Pluri-Borda rule” for short. While this weighting rule is not claimed to the ideal one, it has many attractive properties and comes with a transparent axiomatic characterization.

We summarize the analysis of the paper with an Arrowian possibility result, according to which the Pluri-Borda rule is able to jointly satisfy ordinal efficiency and reliability axioms on social choice, unlike any (familiar) rule in the literature.



Klaus Nehring
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