Median voter theorem
A different argument due to Anthony Downs and Harold Hotelling is only loosely-related to Black's median voter theorem, but is often confused with it.
However, Donald Saari constructs an example in two dimensions where the Borda count (but not the Condorcet winner) correctly identifies the candidate closest to the center (as determined by the geometric median).
The simplest example consists of a distribution limited to 3 points not lying in a straight line, such as 1, 2 and 3 in the second diagram.
Whenever a discrete distribution has a median M in all directions, the data points not located at M must come in balanced pairs (A,A ' ) on either side of M with the property that A – M – A ' is a straight line (ie.
Thus the sum of distances from the data points to P is minimized when P coincides with M. A related observation was discussed by Harold Hotelling as his 'principle of minimum differentiation', also known as 'Hotelling's law'.
Most importantly, politicians must win primary elections, which often include challengers or competitors, to be chosen as major-party nominees.
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.
Examples are the analysis of the relationship between income inequality and size of governmental intervention in redistributive policies (Meltzer and Richard, 1981),[16] the study of the determinants of immigration policies (Razin and Sadka, 1999),[17] of the extent of taxation on different types of income (Bassetto and Benhabib, 2006),[18] and many more.In the United States Senate, each state is allocated two seats.
According to the Median Voter Theorem, the voting patterns of two senators representing the same state should be identical, regardless of party affiliation.
The data she collected showed that as a result of these changes, transfer payments to these populations increased even though the overall electorate (which had already included these groups) remained unchanged.
[20] Chattopadhyay and Duflo (2004) examined another political change in India, which mandated that women lead one-third of village councils.
According to the Median Voter Theorem, this policy should not have affected the composition of public goods supplied by local governments, as a female candidate still needs to be elected by a majority vote.
However, empirical data showed that in villages where a woman was elected, the distribution of public goods shifted toward those preferred by women.
It is important to note, however, that while the composition of public goods changed when a woman led the village council, this does not necessarily imply an improvement or decline in overall social welfare.
[21] Similar findings were reported by Miller (2008), who analyzed the impact of granting women the right to vote across the United States in 1920.
This change resulted in a significant increase in healthcare spending and a consequent reduction in child mortality rates by 8%–15%.
[22] Lee, Moretti, and Butler (2004) investigated whether voters influence politicians' positions or merely choose from existing policy stances.
For instance, an increase in Democratic voters in a given area does not push a Republican candidate’s stance further to the left, and vice versa.
[23] Gerber and Lewis (2015) analyzed voting data from a series of referendums in California to estimate the preferences of the median voter.
They found that elected officials are constrained by the preferences of the median voter in homogeneous regions but less so in heterogeneous ones.
[25] Referendum data from Switzerland was used by Stadelmann, Portmann, and Eichenberger (2012) to examine the degree to which legislators' votes align with the preferences of the median voter in their districts.
