Identifying strong voter support : Condorcet and Smith revisited
Bibliographic record
Abstract
The conditions of strong Condorcet winner consistency and strong Condorcet loser consistency are, in essence, universally accepted as attractive criteria to evaluate the performance of social choice functions. However, there are many situations in which these conditions are silent because such winners and losers may not exist. Hence, weakening these desiderata in order to extend the domain of profiles where they apply is an appealing task. Yet, the often-proposed and accepted weak counterparts of these properties suffer from the shortcoming that a weak Condorcet winner can be a weak Condorcet loser at the same time. We propose new notions of Condorcet-type winners and losers that are between these two extremes: they share the intuitive appeal of strong Condorcet winner consistency and strong Condorcet loser consistency and avoid the contradictory recommendations that would derive from the double identification of candidates as being weak Condorcet winners and losers at the same time. We provide a thorough examination of the extent to which some important reference properties are satisfied by social choice functions that are consistent with our new proposals. In addition, we revisit the concept of Smith sets (Smith, 1973) and examine a possible modification. As is the case for our intermediate Condorcet winners and losers, these notions are intended to generalize Condorcet's ideas. Using our reference properties again, we discuss the social choice functions that are consistent with the selection of candidates from these sets. By contrasting the consequences of using the suggestions inspired by Smith with those that are implied by the intermediate Condorcet consistency conditions that we propose, we hope to shed new light on the possibilities of extending Condorcet's principles to a larger set of circumstances.
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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 | 0.054 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.003 | 0.006 |
| Scholarly communication | 0.005 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 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".