Individual welfare and the group size paradox

How does an increase in group size affect individual welfare in the presence of Olson’s group size paradox? Under the standard approaches to modeling the group size paradox, individual welfare declines as the size of the group expands. However, this may not be true if we apply the group size paradox to politics. In particular, if a smaller group attempts to extract a fixed income transfer from a larger group, the welfare of individuals in the larger group is increasing monotonically in the size of their group under a standard contest success function. Even though the probability of the transfer taking place is rising monotonically in the size of the group, the expected transfer per member shrinks because more members share the burden of financing the transfer. A similar result is obtained if the transfer is modeled as a fixed entitlement to be received by each member of the smaller group. By contrast, if the transfer imposes a fixed cost per member of the larger group, the result that individual welfare in the larger group is falling monotonically in its own group size is restored.