In presidential primaries in the U.S., proportional campaign resource allocation to states with respect to their delegate numbers is a desirable concept. To study such population proportionality, we introduce a novel model for
\(n\)-player multi-battle dynamic contests. In this general model, we show that proportional resource allocation is supported as a subgame perfect equilibrium when players maximize their expected number of delegates. However, when candidates maximize their probability of winning with at least 4 states and 2 delegates, there is always a distribution of delegates over the states such that population proportionality is not satisfied.
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