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This paper explores the reasons why factions within political parties might choose to split and when instead party unity is expected. We develop a theory based on the premise that political factions aim to preserve and cultivate their individual brands. 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 brands, 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---reflecting 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. These damaging splits, we show, only happen 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.