Testing for Welfare Comparisons when Populations Differ in Size

Abstract

Assessments of social welfare do not usually take into account population sizes. This can lead to serious social evaluation flaws, particularly in contexts in which policies can affect demographic growth. We develop in this paper a little-known though ethically attractive approach to correcting the flaws of traditional welfare analysis, an approach that is population-size sensitive and that is based on critical-level generalized utilitarianism (CLGU). Traditional CLGU is extended by considering arbitrary orders of welfare dominance and ranges of “poverty lines” and values for the “critical level” of how much a life must be minimally worth to contribute to social welfare. Simulation experiments briefly explore the normative relationship between population sizes and critical levels. We apply the methods to household level data to rank Canada’s social welfare across 1976, 1986, 1996 and 2006 and to estimate normatively and statistically robust lower and upper bounds of critical levels over which these rankings can be made. The results show dominance of recent years over earlier ones, except when comparing 1986 and 1996. In general, therefore, we conclude that Canada’s social welfare has increased over the last 35 years in spite (or because) of a substantial increase in population size.