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arxiv: 1907.09111 · v1 · pith:F4NPVVJOnew · submitted 2019-07-22 · 💻 cs.AI · cs.MA

Aggregating Probabilistic Judgments

Magdalena Ivanovska , Marija Slavkovik This is my paper

Pith reviewed 2026-05-24 18:28 UTC · model grok-4.3

classification 💻 cs.AI cs.MA
keywords judgment aggregationprobabilistic judgmentsaggregation functionslogical consistencyimpossibility resultsopinion poolingmulti-agent systems
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The pith

Boolean judgment aggregation methods can be generalized to pool probabilistic judgments on logically related issues.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper modifies the standard Boolean judgment aggregation framework so that it accepts probabilistic judgments rather than true-or-false ones. It then constructs new aggregation functions by extending the classical Boolean versions to this probabilistic domain. The authors examine which standard properties the new functions satisfy and identify impossibility results that persist after the generalization. A sympathetic reader would care because many practical opinions arrive as probabilities yet still involve logical connections between statements that must be respected during pooling.

Core claim

We first modify the Boolean judgment aggregation framework in the way that allows handling probabilistic judgments and then define probabilistic aggregation functions obtained by generalization of the classical ones. In addition, we discuss essential desirable properties for the aggregation functions and explore impossibility results.

What carries the argument

The modified probabilistic judgment aggregation framework obtained by lifting the Boolean structure while preserving logical consistency on related issues.

If this is right

  • Impossibility results known for Boolean judgment aggregation continue to hold after the generalization to probabilities.
  • Desirable properties such as anonymity or neutrality can be verified for the new probabilistic aggregation functions.
  • The generalized functions produce outputs that respect logical relations whenever the input judgments are consistent.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach supplies a systematic way to combine uncertain beliefs held by multiple agents in AI systems.
  • Similar lifting techniques might apply to other non-classical logics beyond probabilities.
  • Empirical tests on actual collections of probabilistic forecasts could show where the inherited properties succeed or break.

Load-bearing premise

The core structure and properties of Boolean judgment aggregation can be directly lifted to a probabilistic setting while preserving logical consistency on related issues.

What would settle it

A collection of probabilistic judgments on logically dependent propositions where every generalized aggregation function produces an output that violates the logical constraints between the issues.

read the original abstract

In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way that allows handling probabilistic judgments and then define probabilistic aggregation functions obtained by generalization of the classical ones. In addition, we discuss essential desirable properties for the aggregation functions and explore impossibility results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript modifies the Boolean judgment aggregation framework to accommodate probabilistic judgments on logically related issues and defines probabilistic aggregation functions obtained by generalizing classical ones. It further discusses essential desirable properties of these functions and explores associated impossibility results.

Significance. If the generalizations preserve the intended logical consistency properties and the impossibility results are rigorously established, the work would provide a useful bridge between classical judgment aggregation and probabilistic opinion pooling. This could support applications in multi-agent AI systems and epistemic logic, with the impossibility results offering concrete limitations on what can be achieved under logical constraints.

minor comments (2)
  1. [Abstract] The abstract states that the Boolean framework is modified 'in the way that allows handling probabilistic judgments' but does not indicate the precise technical device (e.g., replacement of {0,1} valuations by [0,1] probabilities subject to coherence constraints) used in the modification step; a short clarifying sentence would improve readability.
  2. [Abstract] No concrete example of a probabilistic judgment profile or an explicit definition of a generalized aggregation function (e.g., a probabilistic majority or premise-based rule) appears in the abstract; including one brief illustrative case would help readers assess the generalization.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of our manuscript on adapting judgment aggregation to probabilistic opinions. The recommendation for minor revision is noted. No specific major comments were raised in the report, so we have no points requiring direct rebuttal or revision at this stage. We remain available to address any additional feedback.

Circularity Check

0 steps flagged

No significant circularity; direct theoretical generalization

full rationale

The paper frames its contribution as a modification of the Boolean judgment aggregation framework followed by generalization of classical aggregation functions to the probabilistic case, with discussion of properties and impossibility results. No equations, fitted quantities, or load-bearing self-citations appear in the provided abstract or description. The derivation is presented as a formal extension rather than any reduction of outputs to inputs by construction, making the work self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard mathematical logic and the existing Boolean judgment aggregation framework; no free parameters, ad-hoc axioms, or invented entities are indicated in the abstract.

axioms (1)
  • domain assumption Standard properties of Boolean judgment aggregation can be meaningfully extended to probabilistic judgments while preserving logical relations.
    Invoked when the abstract states the framework is modified to allow probabilistic judgments.

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discussion (0)

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