Open AccessOne‐dimensional mechanism design
Author(s) -
Moulin Hervé
Publication year - 2017
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2307
Subject(s) - fair division , mathematical economics , mechanism design , regular polygon , commodity , set (abstract data type) , cover (algebra) , benchmark (surveying) , mathematics , rationing , combinatorics , computer science , economics , mechanical engineering , health care , geometry , geodesy , economic growth , engineering , market economy , programming language , geography
We prove a general possibility result for collective decision problems where individual allocations are one‐dimensional, preferences are single‐peaked (strictly convex), and feasible allocation profiles cover a closed convex set. Special cases include the celebrated median voter theorem (Black 1948, Dummett and Farquharson 1961) and the division of a nondisposable commodity by the uniform rationing rule (Sprumont 1991). We construct a canonical peak‐only rule that equalizes, in the leximin sense, individual gains from an arbitrary benchmark allocation: it is efficient, group‐strategyproof, fair, and (for most problems) continuous. These properties leave room for many other rules, except for symmetric nondisposable division problems.