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Stochastically Dominant Peer Prediction
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Introduces SD-truthfulness for peer prediction (score distribution under truth-telling first-order stochastically dominates any deviation), shows rounding reductions enforce it, and proposes the enforced agreement mechanism, which is SD-truthful for binary self-predicting signals and has highest sensitivity among known SD-truthful mechanisms.
Problem
Classic peer prediction mechanisms guarantee truthfulness only for expected scores, which assumes agents have linear utility in score; non-linear payments and non-linear agent utilities break truthfulness, and existing mechanisms are not stochastically dominant truthful without strong assumptions.
Approach
Define SD-truthfulness (score distribution under truth-telling first-order stochastically dominates any deviation), so truth-telling is optimal for any increasing utility. Achieve it via direct and partition rounding of truthful mechanisms into binary lotteries, and propose enforced agreement, which forces a pre-set marginal distribution of reports before applying output agreement to retain high s
Key results
- EA is SD-truthful for binary self-predicting signals for any enforcement, and in the binary setting it achieves the highest sensitivity among known SD-truthful mechanisms except when the prior is nearly uniform.
- Partition rounding multiplies sensitivity by sqrt(K) relative to direct rounding, while direct rounding loses about sqrt(n) in sensitivity for OA.
- Even EA-uniform (prior-free) outperforms PTS-partition-round in most settings; in budget experiments, SD-truthful mechanisms with threshold payments beat truthful mechanisms with linear payments at higher target effort.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace direct rounding with partition rounding (ablation) | truthful bounded-score mechanisms · multi-task peer prediction | sensitivity: exactly $\sqrt{K}$ times | Helped |
| apply direct rounding instead of retaining the original averaged scores (ablation) | Output Agreement (OA) · multi-task peer prediction | sensitivity: $\sqrt{n}$ | Hurt |
| enforce the signal prior (ablation) | Enforced Agreement (EA) · J1, binary signals | sensitivity | Helped |
| use uniform enforcement rather than requiring prior knowledge (ablation) | Enforced Agreement (EA) · J1, binary signals | sensitivity | Helped |
| use EA-uniform instead of PTS-partition-round | SD-truthful mechanisms · J1, binary signals with a biased prior | sensitivity | Helped |
| use PTS-partition-round when the signal prior is nearly uniform | Peer Truth Serum (PTS) · binary signals with prior near 0.5 | sensitivity | Helped |
| use EA rather than other SD-truthful mechanisms | SD-truthful mechanisms · binary signals, except when the signal prior is nearly uniform | sensitivity | Helped |
| use CA-partition-round or MA-partition-round rather than higher-sensitivity alternatives | Correlated Agreement (CA) and Matching Agreement (MA) · general signal settings | sensitivity | Hurt |
| pair an SD-truthful mechanism with threshold payments instead of using a truthful mechanism with linear payments | peer prediction mechanisms · J1 effort elicitation | budgetary efficiency | Helped |
| use EA with signal-prior enforcement | SD-truthful mechanisms with threshold payments · J1 effort elicitation | total payment | Helped |
| use EA with a non-binary signal space | Enforced Agreement (EA) · non-binary signals | stochastic-dominance truthfulness | Hurt |
Surprising findings
- EA is not SD-truthful for signal spaces larger than two, even when signals are self-predicting; SD-truthfulness requires uniformly self-predicting signals for three signals.
- CA with the original implementation is not SD-truthful, even though it is truthful when the joint distribution is known.
Limitations
- EA is only SD-truthful for binary signals; for larger signal spaces it is only truthful when the information structure is known.
- Partition rounding and direct rounding substantially reduce sensitivity compared with the original mechanisms.
- SD-truthfulness does not guarantee truthfulness under tournament (rank-order) rewards.
Experimental setup
Datasets: compound appropriateness crowdsourced labels (Dawid-Skene estimated information structure, J1) tweet sentiment annotations with 300 tweets, 4 signals (J2)
Benchmarks: sensitivity under varying prior and number of tasks on J1 and J2 budgetary efficiency under threshold and linear payments
Metrics: sensitivity total payment (budgetary efficiency)
Baselines: Output Agreement Peer Truth Serum Correlated Agreement Matching Agreement linear payment truthful mechanisms
Builds on: output agreement peer truth serum correlated agreement matching agreement
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