Dynamics of voting strategies and public good funding

We model an electorate voting on the funding of a public good in a two-party system in an evolutionary game theory framework. Voters adopt one of four strategies: Consensus-makers, Gridlockers, Party 1 Zealots, and Party 2 Zealots, which they may change via imitation. The public good benefits both individuals locally and those in neighbouring regions due to spillover effects. A system of differential equations governs the spatial movement of individuals and shifts in their voting strategies. Local social interactions drive strategy evolution, while migration occurs toward areas of higher utility, which is a function of both social and economic factors. Our results reveal bistability and significant spatial variations. Locally, populations converge to a politically gridlocked state or a mix of consensus-makers and zealots, determining public good provisioning. We find that public good spillovers generate a free-rider effect and poorly funded regions become spatially tied to, and dependent upon, well-funded ones.