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Social Choice Foundations for Simulation-Augmented Generation
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Formalizes inference-time routing for simulation-augmented generation (SAGE) via mPJR+ proportional representation, gives a faster SEAR implementation and population-transfer bounds, and shows on Remesh and Reddit AITA that predictive route-then-simulate beats k-means and random selection.
Problem
Simulation-augmented generation needs to query only a few simulated individuals at inference time while still proportionally representing the viewpoints of a large target population.
Approach
Adapts the proportional clustering axiom mPJR+ and the spatial expanding approval rule (SEAR) to route k of n simulations per prompt, shows simulating and routing approximately commute under factorized rewards, and learns a cheap predictor of simulation response embeddings so only k simulations are queried.
Key results
- Predictive Route-then-Simulate with SEAR achieves higher mPJR+ satisfaction than k-means and random routing for all k in {3,...,10} on both domains.
- Oracle Simulate-then-Route achieves 100% mPJR+ satisfaction, while all routing methods degrade as k grows.
- Improved SEAR implementation runs in O(mn log n) time versus prior O(k^2 n^4); population transfer needs sample size roughly 9x10^3 for n_H=8 billion, k=10, delta=0.05, eps=0.03.
Surprising findings
- k-means and random selection pick outliers that leave the dense majority underrepresented, causing mPJR+ violations even when the minority group is below the proportionality threshold.
- Performance of all routing methods degrades as k increases, since representing smaller groups is more sensitive to prediction error.
Limitations
- Evaluation limited to two datasets; generalization to other domains and populations untested.
- Empirical evaluation uses simulation pool as proxy for humans because no human reward functions are available.
- Choice of k left open and must be tailored to application; fidelity gap effect not systematically measured.
Experimental setup
Datasets: Remesh U.S. campus protests 2024 session (n=310) humanual-opinion (Reddit AITA, 992 posts, 4567 users)
Benchmarks: Remesh humanual-opinion (Reddit AITA)
Metrics: mPJR+ satisfaction rate
Baselines: Simulate-then-Route (oracle) k-means Random
Builds on: SEAR mPJR+ expanding approvals rule modular pluralism HumanLM
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