Constraint Gain: An Information-Theoretic Foundation for Valuing Negative Scientific Results

Scientific progress depends on learning what doesn’t work, yet negative results are systematically undervalued: unpublished, uncompensated, and excluded from training data. We propose constraint gain, an information-theoretic measure that quantifies the value of negative results based on hypothesis space elimination. Constraint gain equals the mutual information between an experimental outcome and the target location, providing principled valuation for failed experiments.We demonstrate empirically that incorporating negative results into scientific search achieves 25–45% faster discovery compared to positive-only approaches (p < 0.001). We find a decoupling between operational utility and credit assignment: while uniform weighting of negative results performs comparably to constraint-gain weighting for an individual agent’s search, explicit constraint gain computation is necessary to establish fair credit allocation across a research community. In multi-agent simulations, sharing negative results with constraint-gain attribution achieves 39% faster discovery and reduces redundant experimentation from 79% to 28% (p < 10−10). Constraint gain enables this coordination by providing the theoretical foundation for recognizing contributors whose negative results prevent duplicated effort. An illustrative case study of CETP inhibitor failures suggests how constraint gain attribution could have reduced billions of dollars in redundant pharmaceutical development.