Abstract
In their foundational work, List and Pettit formalized the judgment aggregation framework and showed that the preference aggregation framework from social choice theory can be mapped into it, arguing that the reverse was not possible. We show that a natural extension of a graph-theoretic representation of the preference aggregation framework indeed allows us to embed also the judgment aggregation framework. Moreover, we show that many concepts from the two original frameworks match up under the new one, show that it is possible to detect “logical consistency” with graph-theoretical properties, and give a new nuanced comparison between the doctrinal paradox and the Condorcet paradox.
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Notes
Notice that a cycle is not necessarily a Condorcet cycle, except when only 3 preferences are given as in the historical example made by Condorcet himself. Indeed a Condorcet winner can exits even if there is a cycle.
List and Pettit encode judgments using sets of propositions while we use a functions to preserve coherence with the rest of the paper. The two encodings are equally expressive.
Notice that this has different meaning on atomic and compound propositions. Indeed while for the atomic ones the values of all other propositions are fixed if and only if we are comparing vertices with Humming distance 1, for compound propositions this is not necessarily true.
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Acknowledgements
We wish to thank Yoshiki Nakajima for his initial exploration of this work with the first two authors and the two anonymous referees for their very insightful comments which helped to improve the paper.
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Marengo, L., Settepanella, S. & Zhang, Y.X. Towards a unified aggregation framework for preferences and judgments. Evolut Inst Econ Rev 18, 21–44 (2021). https://doi.org/10.1007/s40844-021-00200-w
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DOI: https://doi.org/10.1007/s40844-021-00200-w