Strategy-Proof Judgment Aggregation

Abstract

In the theory of judgment aggregation on logically connected propositions, an important question remains open: Which aggregation rules are manipulable and which are strategyproof? We de…ne manipulability and strategy-proofness in judgment aggregation, characterize all strategy-proof aggregation rules, and prove an impossibility theorem similar to the Gibbard-Satterthwaite theorem. Among other escape-routes from the impossibility, we discuss weakening strategy-proofness itself. Comparing two prominent aggregation rules, we show that conclusion-based voting is strategy-proof, but generates incomplete judgments, while premise-based voting is only strategy-proof for "reason-oriented" individuals. Surprisingly, for "outcome-oriented"individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy.

Approximate Judgement Aggregation

“…The independence criterion is sometimes criticized as being unjustified normatively in most real-life scenarios 15 . The impossibility results of judgement aggregation can also be seen as 'empirical' argument against independence since they show that it contradicts the more natural assumption of consistency.…”

“…In [15] Dietrich and List define the notion of manipulability of an aggregation mechanism 16 and proved that any aggregation mechanism that does not satisfy independence is manipulable. In this paper they further prove that this manipulability property is equivalent to a more game-theoretic property of strategy-proofness under some assumptions on players' preferences.…”

“…Another argument might be than there are scenarios in which you need to define the aggregation method and only at a later stage choose from the 14 In successive works we relax this assumption and prove similar results for more general distributions. 15 Chapman( [8]) and Mongin([34]) attack this criterion and claim it removes the discipline of reason from social choice since it disregards the intra-issue dependencies which is the essence of the problem. According to this criterion the aggregation of 'complex' issues is done without regarding the reasons of the voters for their opinions and hence lacks the information for good aggregation.…”

Majority voting on restricted domains

“…Anonymity requires equal treatment of all individuals, and acceptance/rejection neutrality prevents the aggregation function from favouring the acceptance of a proposition over its rejection or vice versa; that is, if the individuals accepting a given proposition in one pro…le are the same as those rejecting it in another, then the proposition must be collectively accepted in the …rst pro…le if and only if it is collectively rejected in the second. 8 Let D 2 be the set of all pro…les (A 1 ; :::; A n ) of consistent individual judgment sets where at most two of the A i 's are distinct.…”

“…Giving up propositionwise aggregation, possibility results were obtained, for example, by using sequential rules (List [23]) and fusion operators (Pigozzi [33]). Voter manipulation in the judgment-aggregation model was analysed in Dietrich and List [8]. But so far the only domain-restriction condition known to guarantee consistent majority judgments is List's unidimensional alignment ( [21], [22]), a global non-product domain condition based on orders of individuals.…”