The Condorcet set: majority voting over interconnected propositions
Bibliographic record
Abstract
Judgement aggregation is a model of social choice in which the space of social alternatives is the set of consistent evaluations (‘views’) on a family of logically interconnected propositions, or yes/no issues. However, simply complying with the majority opinion in each issue often yields a logically inconsistent collective view. Thus, we consider the Condorcet set: the set of logically consistent views which agree with the majority on a maximal subset of issues. The elements of this set turn out to be exactly those that can be obtained through sequential majority voting, according to which issues are sequentially decided by simple majority unless earlier choices logically force the opposite decision. We investigate the size and structure of the Condorcet set for several important classes of judgement aggregation problems. While the Condorcet set verifies a version of McKelvey's (1979) celebrated ‘chaos theorem’ in a number of contexts, in others it is shown to be very regular and well-behaved.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.011 | 0.051 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.004 | 0.009 |
| Scholarly communication | 0.008 | 0.013 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".