Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem (2210.03200v1)

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 byparallel' vs. sequential' execution of agenda formation and preference elicitation, respectively. Under theparallel' version, it is shown that a large class of anonymous and idempotent 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 tightly related to the classic Arrowianindependence of irrelevant alternatives' (IIA) for social welfare functions. In particular, it is shown that using IIA to secure such sequential' version of agenda manipulation-proofness and combining it with a very minimal requirement of distributed responsiveness results in a characterization of theglobal stalemate' social welfare function, the constant function which invariably selects universal social indifference. 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.