distances from P to any data points located at M is likewise minimised when P and M coincide. Thus the sum of distances from the data points to P is minimised when P coincides with M . Hotelling's law The more informal assertion – the median voter model – is related to Harold Hotelling's 'principle of minimum differentiation', also known as 'Hotelling's law'. It states that politicians gravitate toward the position occupied by the median voter, or more generally toward the position favored by the electoral system. It was first put forward (as an observation, without any claim to rigor) by Hotelling in 1929. Hotelling saw the behavior of politicians through the eyes of an economist. He was struck by the fact that shops selling a particular good often congregate in the same part of a town, and saw this as analogous the convergence of political parties. In both cases it may be a rational policy for maximizing market share. As with any characterization of human motivation it depends on psychological factors which are not easily predictable, and is subject to many exceptions. It is also contingent on the voting system: politicians will not converge to the median voter unless the electoral process does so. Uses of the median voter theorem The theorem is valuable for the light it sheds on the optimality (and the limits to the optimality) of certain voting systems. Valerio Dotti points out broader areas of application: The Median Voter Theorem proved extremely popular in the Political Economy literature. The main reason is that it can be adopted to derive testable implications about the relationship between some characteristics of the voting population and the policy outcome, abstracting from other features of the political process. He adds that... The median voter result has been applied to an incredible variety of questions. Examples are the analysis of the relationship between income inequality and size of governmental intervention in redistributive policies (Meltzer and Richard, 1981), the study of the determinants of immigration policies (Razin and Sadka, 1999), of the extent of taxation on different tyes of income (Bassetto and Benhabib, 2006), and many more. See also Arrow's impossibility theorem McKelvey–Schofield chaos theorem Median mechanism Ranked voting References Further reading Dasgupta, Partha and Eric Maskin, "On the Robustness of Majority Rule", Journal of the European Economic Association, 2008. External link The Median Voter Model Political science theories Public choice theory