Institutional arrangements may be imposed exogenously, but they are often chosen by institutional agents. One arrangement that is found in a variety of institutional settings is seniority, the practice of connecting privileges and benefits to experience. Institutional age becomes a measure of political power (legislative seniority), privilege (elders in pastoralist societies), or extraordinary benefits (the position of senior generations in pension schemes). But why would self-governing agents select such an arrangement? And to what perturbations are such arrangements robust? In the political science literature, a seminal paper by McKelvey and Riezman is the starting point for our analysis. We propose a more general model. In a divide-the-dollar extensive form game, we show that under specified conditions the legislator with the median number of previous terms served will be pivotal. At the preliminary institutional choice stage of the game, she will set the cut-off criterion that partitions agents into “juniors” and “seniors” at her seniority level, even if she can offer a more fully ordinal schedule. Consequently, in this categorical seniority system selected in equilibrium, the most junior senior legislator has median number of previous terms of service.