The Canegrati's formulae are obtained by the resolution of a maximisation problem in a probabilistic voting model (Persson and Tabellini (2000)) characterised by the presence of single-minded groups (Mulligan and Sala-i-Martin (1999)). The first formula describes the way politicians set Indirect Taxation and states that marginal tax rates are lower for those goods consumed most by more single-minded groups. The second formula describes the way politicians set direct taxation and states that marginal tax rates are, again, lower for those groups which have an higher preference for leisure. Finally, the third formula represents a variant of the second, this time considering clusters of groups which differ not only for preference for leisure but also for wage rates.
The parameter that mostly contributes to explain the power of a group is the probability density function (usually assumed as uniform, probit, logit), which captures the degree of homogeneity of political preferences within a specific group.