Every Bit Helps: Achieving the Optimal Distortion with a Few Queries
Why this work is in the frame
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Bibliographic record
Abstract
A fundamental task in multi-agent systems is to match n agents to n alternatives (e.g., resources or tasks). This is often done by eliciting agents' ordinal rankings over the alternatives rather than their exact numerical utilities. While this simplifies elicitation, the incomplete information leads to inefficiency, captured by a worst-case measure called distortion. Recent work shows that making just a few cardinal utility queries per agent can significantly improve the distortion, with Amanatidis et al. (2024) achieving O(√n) distortion with two queries per agent. We generalize their result by achieving O(n^(1/λ)) distortion with λ queries per agent, for any constant λ, which is optimal up to a constant factor given a previous lower bound by Amanatidis et al. (2022). We extend this finding to the general social choice problem of selecting one of m alternatives based on n agents' preferences, achieving O((min{n, m})^(1/λ)) distortion with λ queries per agent, for any constant λ, which is also optimal given prior results. Thus, our work settles open questions regarding the optimal distortion achievable with a fixed number of cardinal value queries in both settings.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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 it