Fisher (1930), Haldane (1932), and others discussed short and long term fitness relationships of the biological basis of social behaviour. Hamilton (1964a, b) proposed the inequality b/c > 1/r (b and c are marginal benefit and cost parameters, respectively, r is an appropriate kinship coefficient) as an essential concomitant of the evolution of altruism. Virtually all current kin selection models take the marginal benefit and cost parameters as primitive concepts and combine them in various ways to determine population fitness values. We offer an intrinsic `fitness function' approach to modelling the theory of kin selection. The components of the model involve: (a) the delineation of the basic group structure specifying individual relationships; (b) the specification of local fitness functions that depend on group composition; (c) the determination of average fitness functions for the different phenotypes with respect to the population at large. We then derive a pair of benefit and cost functions, which are functions of the group composition and the numbers of altruist and selfish phenotypes. In this new framework the quantitative validity of the Hamilton criterion for the evolution of altruism are assessed and reinterpreted.