New paper finds Borda count beats STAR, plurality in democratic voting models
Phase transitions in optimal voting rules mapped across rugged landscapes
Joshua Nunley's paper "Democracy on Rugged Landscapes: Phase Transitions in Optimal Voting Rules" (arXiv:2606.02813, submitted to ALIFE 2026) models collective governance as optimization on NK fitness landscapes. In this framework, shared bits represent laws updated by voting, while individual bits remain fixed. A cross-dependency parameter α controls how legislation's effects depend on personal circumstances. The study compares eight standard voting methods—including plurality, Borda count, STAR voting, and cardinal score voting—across landscape ruggedness K from 1 to 20 and α from 0 to 1, with 1,000 runs per configuration.
The results reveal sharp phase transitions in direct democracy: cardinal score voting dominates on smooth landscapes, ordinal scoring with p=0.35 at low-to-moderate ruggedness, Borda count across a wide middle range, and STAR voting at the highest complexity. A two-parameter empirical formula reduces the (K, α) plane to a single complexity axis for visualization. Remarkably, Borda count achieves the highest mean fitness and lowest variance across most of the parameter space. The paper also introduces a representative democracy model with identity weight β and candidate self-interest p_self. Under representation, cardinal score voting dominates most regimes, with plurality emerging as the top method at high β and low-to-moderate p_self.
- Borda count outperforms all other voting methods on both mean fitness and variance across most complexity levels
- Phase transitions in optimal voting rules occur as landscape ruggedness increases
- In representative democracy models, cardinal score voting dominates except at high identity weight where plurality wins
Why It Matters
This research provides a rigorous computational framework for choosing voting rules that maximize collective outcomes in complex policy landscapes.