Median voter theory

The median voter theorem states that "a majority rule voting system will select the outcome most preferred by the median voter".

The median voter theorem rests on two main assumptions, with several others detailed below. First, the theorem assumes that voters can place all election alternatives along a one-dimensional political spectrum. It seems plausible that voters could do this if they can clearly place political candidates on a left-to-right continuum, but this is often not the case as each party will have its own policy on each of many different issues. Similarly, in the case of a referendum, the alternatives on offer may cover more than one issue. Second, the theorem assumes that voters' preferences are single-peaked, which means that voters choose the alternative closest to their own view. This assumption predicts that the further away the outcome is from the voter's most preferred outcome, the less likely the voter is to select that alternative. It also assumes that voters always vote, regardless of how far the alternatives are from their own views. The median voter theorem implies that voters have an incentive to vote for their true preferences. Finally, the median voter theorem applies best to a majoritarian election system.

For the median voter theorem to be successful, there is a total of seven assumptions that are made. As mentioned above, (1) the first assumption is that there is single-dimensional voting. Put simply, this means that there is only one issue that is being voted on at a time. Additionally, it is assumed that (2) voters' preferences are single-peaked, which is just the notion that people's preferences are a spectrum of utility, with the strongest preference at the maximum (see figures to the right). This assumption is critical because it prevents a phenomenon called "cycling" which is detailed below. The third assumption (3) is that voters are only choosing between two options. This is important because when there are more than two choices for voters, the median voter may not have voted for the most popular option. For example, in a population of 100 people voting between A, B, and C imagine 33 people vote for A, 33 people vote for B, and 34 people vote for C. Assuming A, B, and C lie on a spectrum (i.e. a scale from liberal to neutral to conservative) the median voter would have voted for B even though choice C was the most popular. The fourth assumption (4) is that there is no ideology or influence with regards to the voting options. Essentially, this means that politicians only care about maximizing votes, not necessarily sticking true to their beliefs. The fifth assumption (5) is that there is no selective voting and all eligible voters for an election will turn out to vote. The sixth assumption (6) says that money and lobbying have no effect on elections because introducing these incentives can dramatically change voting patterns. The final assumption (7) is the notion that all parties of elections have full information. This means that voters have knowledge on the issues, candidates have knowledge on the issues, and candidates have knowledge on voter preferences.

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