On the Road to Making Science of “Art”: Risk Bias in Market Scoring Rules
Bibliographic record
Abstract
We study market scoring rule (MSR) prediction markets in the presence of risk-averse or risk-seeking agents that have unknown yet bounded risk preferences. It is well known that if agents can be prescreened, then MSRs can be corrected to elicit agents’ beliefs. However, agents cannot always be screened, and instead, an online MSR mechanism is needed. We show that agents’ submitted reports always deviate from their beliefs, unless their beliefs are identical to the current market estimate. This means, in most cases it is impossible for a MSR prediction market to elicit an individual agent’s exact belief. To analyze this issue, we introduce a measure to calculate the deviation between an agent’s reported belief and personal belief. We further derive the necessary and sufficient conditions for a MSR to yield a lower deviation relative to another MSR. We find that the deviation of a MSR prediction market is related to the liquidity provided in the MSR’s corresponding cost-function prediction market. We use the relation between deviation and liquidity to present a systematic approach to help determine the amount of liquidity required for cost-function prediction markets, an activity that up to this point has been described as “art” in the literature.
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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 | 0.034 | 0.205 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.008 |
| Scholarly communication | 0.006 | 0.010 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.004 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".