Order Independence in Sequential, Issue-by-Issue Voting
Why this work is in the frame
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Bibliographic record
Abstract
We study when the voting outcome is independent of the order of issues put up for vote in a spatial multidimensional voting model. Agents equipped with norm-based preferences that use a norm to measure the distance from their ideal policy vote sequentially and issue by issue via simple majority. If the underlying norm is generated by an inner product—such as the Euclidean norm—then the voting outcome is order independent if and only if the issues are orthogonal. If the underlying norm is a general one, then the outcome is order independent if the basis defining the issues to be voted upon satisfies the following property; for any vector in the basis, any linear combination of the other vectors is Birkhoff–James orthogonal to it. We prove a partial converse in the case of two dimensions; if the underlying basis fails this property, then the voting order matters. Finally, despite existence results for the two-dimensional case and for the general l p case, we show that nonexistence of bases with this property is generic. Funding: The research of A. Gershkov is supported by the Israel Science Foundation [Grant 1118/22]. The research of B. Moldovanu is supported by the German Science Foundation through the Hausdorff Center for Mathematics and The Collaborative Research Center Transregio 224. The research of X. Shi is supported by the Social Sciences and Humanities Research Council of Canada.
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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 | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.002 |
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 it