We present a dynamic model to analyze how political parties evolve. In the model, two factions can belong to the same party or not. When together, factions can decide to split. A split sets in motion the evolution of factions’ individual brand, which can be positive or negative. When apart, factions can decide to merge. By merging, factions reap a benefit from being together, but need to divide party resources according to their relative strength.
We characterize when splits and mergers are stable–which reflect fragmented and non-fragmented party systems, respectively–and when instead cycles emerge in equilibrium. Factions may want to split even if by doing so they hurt their brand. This damaging splits, we show, only happens when factions re-merge in the future: by merging, the splinter faction might gain either by becoming the bigger fish in a smaller pond or the smaller fish in a bigger pond.