Strategyproof and efficient preference aggregation with Kemeny-based criteria

Suppose a group of agents submit strict linear orderings over a set of alternatives. An aggregation rule is a function mapping this information into a unique social ordering. In a recent paper, Bossert and Sprumont (2014) introduced betweenness-based notions of efficiency and strategyproofness for aggregation rules and identified three broad classes of rules which satisfy them. The current paper suggests that such betweenness-based requirements may at times be too weak and introduces stronger concepts based on Kemeny distances, namely K-efficiency and K-strategyproofness. When there are three alternatives, all Condorcet–Kemeny rules are both K-efficient and K-strategyproof for a large subdomain of profiles. Moreover, all status-quo rules are K-strategyproof, though not K-efficient. When the number of alternatives exceeds three none of the rules discussed by Bossert and Sprumont satisfies K-strategyproofness, while just Condorcet–Kemenyrules satisfy K-efficiency. The existence of a nondictatorial and onto K-strategyproof rule is an open question.