In presidential primaries, proportional campaign resource allocation to states with respect to their delegate numbers is a desirable concept. To study proportionality, we introduce a novel model for n-player multi-battle dynamic contests. We show that when players maximize their expected number of delegates there is a subgame perfect equilibrium in which players allocate their resources proportionally. However for at least 4 number of states and at least 2 delegates, when players maximize their probability of winning, there is always a distribution of delegates over the states such that population proportionality is not satisfied.
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- Presidential elections, dynamic contests, presedential primaries, population proportionality, multi-battle contests