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

TL;DR

This paper explores agenda manipulation-proofness in preference aggregation, proposing frameworks that relate to Arrow's theorem, and identifies conditions under which certain social welfare functions are resistant to manipulation or lead to stalemates.

Contribution

It introduces two versions of agenda manipulation-proofness, characterizes social welfare functions under these notions, and links them to Arrow's IIA, offering new insights into Arrow's theorem from a mechanism-design perspective.

Findings

Parallel agenda manipulation-proof social welfare functions exist.

Sequential version relates manipulation-proofness to Arrow's IIA.

Constant social welfare function emerges as a stalemate under certain conditions.

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 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 Arrowian `independence 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 the `global 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.