Aggregating Credences into Beliefs: Agenda Conditions for Impossibility Results
Minkyung Wang, Chisu Kim

TL;DR
This paper explores the logical conditions under which impossibility theorems in belief aggregation occur, identifying specific agenda properties that lead to oligarchies, triviality, or impossibility results.
Contribution
It generalizes previous impossibility results using an agenda-theoretic approach, pinpointing exact logical conditions for belief aggregation impossibilities.
Findings
Path-connectedness and even-negatability lead to oligarchy results.
Negation-connectedness results in triviality when adding anonymity.
Blockedness causes impossibility when adding completeness and consistency.
Abstract
Binarizing belief aggregation addresses how to rationally aggregate individual probabilistic beliefs into collective binary beliefs. Similar to the development of judgment aggregation theory, formulating axiomatic requirements, proving impossibility theorems, and identifying exact agenda conditions of impossibility theorems are natural and important research topics in binarizing belief aggregation. Building on our previous research on impossibility theorems, we use an agenda-theoretic approach to generalize the results and to determine the necessary and sufficient level of logical interconnection between the issues in an agenda for the impossibility theorems to arise. We demonstrate that (1) path-connectedness and even-negatability constitute the exact agenda condition for the oligarchy result stating that binarizing belief aggregation satisfying proposition-wise independence and…
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