Optimal Majority Rules and Quantitative Condorcet Properties of Setwise Kemeny Voting Schemes
Bibliographic record
Abstract
The Kemeny problem consists of computing consensus rankings of an election with respect to the Kemeny voting rule, admits important applications in biology and computational social choice [1, 2, 4, 6]. The problem was generalized recently via an interesting setwise approach by Gilbert et al. [9, 10] where not only pairwise comparisons but also the discordance between the winners of subsets of three candidates are also taken into account. We elaborate an exhaustive list of quantified axiomatic properties such as the Condorcet and Smith criteria, the 5/6-majority rule, and the Unanimity property of the 3-wise Kemeny rule. Since the 3-wise Kemeny problem is NP-hard, our results also provide some of the first useful search space reduction techniques by determining the relative orders of pairs of alternatives. Our works suggest similar interesting properties of higher setwise Kemeny voting schemes which justify the more expensive computational cost than the classical Kemeny scheme. We also establish optimal quantitative extensions of the Unanimity property and the well-known 3/4-majority rule of Betzler et al. [4] for the classical Kemeny problem.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".