A Model of Relative Deprivation and Reference Group

R. Boudon and K. Kosaka formalized a mathematical model of relative deprivation. The implication derived from the Boudon-Kosaka model (Kosaka 1986) is that proportion of the relatively deprived increases up to a critical point, then decreases as prize density increases. As the marginal rate of return increases, the possible maximum proportion of the relatively deprived also increases. However, in so far as assumptions with regard to reference group, a model seems to take no account of findings of pre-existing empirical studies, such as Merton (1957), and Stouffer et al. (1949a). The present paper attempts to modify the Boudon-Kosaka model and integrate concepts of relative deprivation and reference group theoretically. The modified model will show that, under condition in which players choose reference group based on certain principle of common attribution, the possible maximum values of proportion of the relatively deprived are constant despite changes in the marginal rate of return, R, and a single critical point becomes double where R>1.