Hirschman and Widder introduced a class of Pólya frequency functions given by linear combinations one-sided exponential functions. The members this are probability densities, the is closed under convolution but not pointwise multiplication. We show that, generically, polynomial function such density only if homothety, also identify subclass for which each positive-integer power function. furthe...

In his The Rhetoric of Reaction, Albert Hirschman (1991) argues that each major advance in the development of citizenship in Western democracies has provoked three common forms of reactionary rhetoric by opponents of reform which, in turn, have been met by their three “progressive counterparts” advanced by advocates of reform. In this short note, we apply Hirschman’s taxonomies of rhetoric to t...

The Laakso–Taagepera index (Laakso and Taagepera, 1979) has become the most commonly used measure to specify the ‘effective’ number of political parties in a party system where parties vary substantially in their vote and/or seat shares. It is well known that the Laakso–Taagepera index is the inverse of the even more widely used Herfindahl–Hirschman index of concentration (Hirschman, 1945; Herf...