Game Form Representation for Judgement and Arrovian Aggregation

Judgement aggregation theory provides us by a dilemma since it is plagued by impossibility results. For a certain class of logically interlinked agendas, full independence for all issues leads to Arrovian dictatorship. Since independence restricts the possibility of strategic voting, it is nevertheless a desirable property even if only partially fulfilled. We explore a “Goldilock” zone of issue-wise sequential aggregation rules which offers just enough independence not to constrain the winning coalitions among different issues, but restrict the possibilities of strategic manipulation. Perfect Independence, as we call the associated axiom, characterises a gameform like representation of the aggregation function by a binary tree, where each non-terminal node is associated with an issue on which all voters make simultaneous decisions. Our result is universal insofar as any aggregation rule satisfying independence for sufficiently many issues has a game-form representation. One corollary of the game form representation theorem implies that dictatorial aggregation rules have game-form representations, which can be “democratised” by simply altering the winning coalitions at every node.