The Role of Selectivity in Hierarchical Social Systems

We consider a selection process and a hierarchical institution in a dynamic model as in Harrington [3], where agents are "climbing the pyramid" in a rank-order contest based on the "up or out" policy. Agents are ranked according to the quality of their performances in a particular environment that they face in groups, and a fraction of the highest ranked agents are promoted. The size of this fraction characterizes the selectivity of the process, and we distinguish between local and global selectivity. We study the role of the degree of local and global selectivity in the dynamic process where agents' types differ in their expected performances. Surprisingly, we find that an increase in the selectivity of the process can be detrimental to the agents with the highest expected performances. In fact, it does not matter how small the expected performance of a particular type of agent is. If the degree of selectivity is high enough, that type of agent will survive. However, if the selectivity decreases, the only survivor is the agent with the highest expected performance.Social hierarchy, Selection, Selectivity, Promotion

An Unexpected Role of Local Selectivity in Social Promotion

A selection process and a hierarchical promotion system in a dynamic model are considered as in Harrington (1998) and Garcia-Martinez (2010), where agents are "climbing the pyramid" in a rank-order contest based on the "up or out" policy. The population at any level of the hierarchy is matched in groups of n agents, and each group faces a particular environment. Agents are ranked according to the quality of their performances in each particular environment. The top k performing agents from each group are promoted. The fraction (k/n) characterizes the local selectivity of the process. The role of the degree of local selectivity in the dynamic process where agents' types differ in their expected performances is studied. For low selectivity, the selection process is not strong enough to overcome the inertia of the initial population. If selectivity increases, only the best-performing type of agent will survive. If the selectivity is increased far enough, the worst-performing type also survives, and the proportion for which they account at equilibrium increases as selectivity increases. Therefore, surprisingly, no matter how low the expected success rate of a type is, if the selection process has a high enough level of selectivity, agents of that type survive in the long run: Too much selectivity is always harmful to the best-performing type.Social hierarchy; Selection; Selectivity; Promotion