Spatial protection of cooperation by voting-based allocation

The Public Goods Game serves as a classic framework for social dilemmas. Behavioral experiments demonstrate that individuals possess distinct allocation preferences. Existing models typically assume egalitarian allocation. Furthermore, most evolutionary frameworks treat allocation rules as fixed, thereby overlooking the critical process of collective rule selection. Here, we develop an evolutionary game framework that couples individual behavior with voting-based allocation rules. Individuals vote between the egalitarian allocation and the non-egalitarian allocation rule which is modulated by an incentive weight to determine the contribution-based allocation weight of the total payoff. We find that cooperation exhibits a non-monotonic, multi-phase trajectory driven by voting dynamics. At moderate incentive weight, voting induces rule differences at cluster boundaries, giving rise to a self-organized protective layer of contribution-proportional defectors that shields cooperators from exploitation by egalitarian defectors. However, as incentives increase further, this protective layer weakens, transitioning the dynamics to direct competition. We introduce a collective choice mechanism to evolutionary game theory, revealing that the democratic voting mechanism leverages the non-egalitarian allocation rule to shape protective spatial architectures and stabilize cooperation in social dilemmas.