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Position: Scarce Resource Allocations That Rely On Machine Learning Should Be Randomized
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Position paper arguing that scarce-resource allocations relying on machine learning should be randomized, using Broome's weighted-lottery theory of claims, and proposing weighted, partial, variance-based, and outlier-based lottery procedures evaluated via simulations and Swiss Unemployment/Census data.
Problem
Deterministic top-k or threshold allocations based on ML predictions can violate individuals' claims to scarce resources and compound systemic exclusion and patterned inequality under uncertainty.
Approach
Grounds randomization in Broome's theory of claims: a weighted lottery proportional to claim strength (BF-fairness), with partial lotteries near the decision boundary, bootstrap-variance-based weighting, and conformal-prediction-based outlier lotteries, trading small utility losses for large reductions in systemic exclusion rate.
Key results
- On Swiss Unemployment with random forest at k/n=0.25, variance-based randomization gives 64.1% utility vs 64.3% for top-k while randomizing 32.2% of resources over 15% of people.
- Partial BF lottery with k'=0.5k and n'=k yields an expected utility difference under 0.05 in simulations while substantially reducing systemic exclusion rate (over 20% reduction with m>2 decision-makers for a 2% utility drop).
- Outlier-based randomization randomizes about 2% of resources over 20% of people with utility loss slightly larger than decision-boundary randomization.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the variance-based lottery instead of randomizing near the decision boundary | Swiss Unemployment, random forest · Swiss Unemployment (k/n=0.25) | utility: 63.7% -> 64.1% | Helped |
| Use the variance-based lottery instead of randomizing near the decision boundary | Census Income, random forest · Census Income (k/n=0.25) | utility: 81.6% -> 84.5% | Helped |
| Randomize using prediction variance rather than deterministic top-k selection | Swiss Unemployment, random forest · Swiss Unemployment (k/n=0.25) | utility: 64.4% -> 64.1% | Hurt |
| Randomize near the decision boundary rather than deterministic top-k selection | Swiss Unemployment, decision tree · Swiss Unemployment (k/n=0.25) | utility: 62.9% -> 58.9% | Hurt |
| Randomize using outlier detection rather than deterministic top-k selection | Census Income, logistic regression · Census Income (k/n=0.25) | utility: 86.1% -> 78.5% | Hurt |
| Use randomized allocations rather than top-k deterministic allocation | Proposed allocation methods · Swiss Unemployment | systemic exclusion rate | Helped |
| Use a partial weighted lottery with k'=0.5·k and n'=k instead of top-k selection (ablation) | Partial BF lottery · Normally distributed claims | expected utility: < 0.05 | Hurt |
| Use partial BF randomization with a 2% expected-utility difference (ablation) | Partial BF lottery · Normally distributed claims; m>2 decision-makers | systemic exclusion rate: greater than a 20% reduction in SER | Helped |
| Increase the partial BF randomization rate (ablation) | Partial BF lottery · Normally distributed claims; k/n=0.25 | expected utility | Hurt |
| Randomize using prediction variance rather than the decision-boundary method at the same randomization rates | Swiss Unemployment · Swiss Unemployment (k/n=0.25) | utility: 62.9% vs 62.8%; 64.1% vs 63.7%; 61.5% vs 58.9% | Mixed |
Surprising findings
- Apparent utility tradeoff may be illusory because under uncertainty deterministic selection over-represents prediction certainty.
- For decision trees on Census data at k/n=0.10, variance-based randomization was not applicable (0% randomization rate).
Limitations
- Argument is restricted to settings with comparative claims; authors explicitly exclude domains like criminal justice.
- Claim strength is assumed measurable and equal to utility/probability, and the calculation of claims is uncertain.
- Experiments are simulations plus two datasets with simple model classes and mostly small utility differences.
Experimental setup
Datasets: Swiss Unemployment (2003) New Adult Census Income
Benchmarks: Swiss Unemployment (2003) Census Income
Metrics: utility (precision among selected) expected utility systemic exclusion rate randomization rate
Baselines: deterministic top-k selection decision-boundary randomization unweighted lottery
Builds on: Broome's theory of claims conformal prediction predictive multiplicity
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