Decoding Distortion: Pushing the Limits of Optimal Collective Decision-Making
Bibliographic record
Abstract
A fundamental question in social choice theory and multi-agent systems is how to aggregate individual agents’ preferences to make a prudent collective decision. A promising line of recent work views elicited preferences as a proxy for underlying cardinal values and aims to optimize objectives based on these values. The restricted expressiveness of the elicited information makes it challenging to optimize cardinal objectives. A pertinent question arises: How close can we get to the optimal cardinal objective with only partial information?Distortion has been introduced as a quantitative measure of the quality of the output of different aggregation rules based on the proximity of their output to the optimal objective. Roughly speaking, distortion measures the worst-case deterioration of an aggregate cardinal objective given the partial elicited (usually ordinal) information. In other words, distortion is the “price” of missing information and acts as a yardstick for answering the above question. This thesis delves into the boundaries of distortion across various social choice scenarios, spanning from rudimentary single-winner voting protocols to realms like matching and participatory budgeting. In Part I we mainly focus on the distortion of single-winner voting rules. This includes investigating the limits of distortion given partial ordinal preferences, capturing the effect of randomization on the distortion, answering computational questions on finding the output with the optimal distortion, and optimizing distortion with uncertainty on the assumption on the cardinal preferences. In Part II we still focus on single-winner voting but consider other elicitation methods. This includes designing a ballot format that captures the intensities in the ordinal preferences and also analyzing the distortion of a well-known voting rule that runs two rounds of elicitation. And finally, in Part III we move beyond voting and show how distortion can be defined in a broader sense. We show the limits of achievable distortion in participatory budgeting and matching problems. We complement these results by designing algorithms that achieve optimal distortion in these settings.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".