Abstract
This paper introduces a new class of judgment aggregation rules, to be called ‘scoring rules’ after their famous counterparts in preference aggregation theory. A scoring rule generates the collective judgment set which reaches the highest total ‘score’ across the individuals, subject to the judgment set having to be rational. Depending on how we define ‘scores’, we obtain several (old and new) solutions to the judgment aggregation problem, such as distance-based aggregation, premise- and conclusion-based aggregation, truth-tracking rules, and a generalization of the Borda rule to judgment aggregation theory. Scoring rules are shown to generalize the classical scoring rules of preference aggregation theory.
Highlights
The judgment aggregation problem consists in merging many individuals’ yes/no judgments on some interconnected propositions into collective yes/no judgments on these propositions
Any set scoring σ gives rise to an aggregation rule Fσ, the set scoring rule w.r.t. σ, which for each profile (J1, . . . , Jn) ∈ J n selects the collective judgment set(s) C in J having maximal sum-total score across individuals: Fσ ( J1, . . . , Jn) = argmaxC∈J σJi (C)
I hope to have convinced the reader that scoring rules, and more generally set scoring rules, form interesting positive solutions to the judgment aggregation problem
Summary
The judgment aggregation problem consists in merging many individuals’ yes/no judgments on some interconnected propositions into collective yes/no judgments on these propositions. The classical example, born in legal theory, is that three jurors in a court trial disagree on which of the following three propositions are true: the defendant has broken the contract ( p); the contract is legally valid (q); the defendant is liable (r ). According to a universally accepted legal doctrine, r (the ‘conclusion’) is true if and only if p and q (the two ‘premises’) are both true. R is logically equivalent to p ∧ q. The simplest rule to aggregate the jurors’ judgments—namely propositionwise majority voting—may generate logically inconsistent collective judgments, as
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