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881. AGENDA MANIPULATION-PROOFNESS, STALEMATES, AND THE WORTH OF REDUNDANT ELICITATION IN PREFERENCE AGGREGATION. Exposing the Bright Side of Arrow's Theorem

Working Paper n. 881 - Maggio 2022

Stefano Vannucci

DEPS, USiena

Abstract

This paper provides a general framework to explore the possibility of agenda manipulation-proof and proper consensus-based preference aggregation rules, so powerfully called in doubt by a disputable if widely shared understanding of Arrow’s ‘general possibility theorem’. We consider two alternative versions of agenda manipulation-proofness for social welfare functions, that are distinguished by ‘parallel’ vs. ‘sequential’ execution of agenda formation and preference elicitation, respectively. Under the ‘parallel’ version, it is shown that a large class of anonymous and idem-potent social welfare functions that satisfy both agenda manipulation-proofness and strategy-proofness on a natural domain of single-peaked ‘meta-preferences’ induced by arbitrary total preference preorders are indeed available. It is only under the second, ‘sequential’ version that agenda manipulation-proofness on the same natural domain of single-peaked ‘meta-preferences’ is in fact shown to be equivalent to the classic Arrowian ‘independence of irrelevant alternatives’ for social welfare functions. In particular, it is shown that combining such ‘sequential’ version of agenda manipulation-proofness with a very minimal requirement of distributed responsiveness results in a characterization of the ‘global stalemate’ social welfare function, the constant function which invariably selects universal social indi¤erence. It is also argued that, altogether, the foregoing results provide new significant insights concerning the actual content and the constructive implications of Arrow’s ‘general possibility theorem’ from a mechanism-design perspective.

Keywords

Agenda manipulation, strategy-proofness, social welfare functions, aggregation, median join-semilattices.

Jel Codes

D71