page_title: Median voter theorem
section_title: Assumptions
hierarchical_section_title: Median voter theorem / Assumptions
caption_attribution_description: English: Example of Multi-Peaked Preferences
context_page_description: The median voter theorem states that "a majority rule voting system will select the outcome most preferred by the median voter". It is associated with public choice economics and statistical political science.
  The median voter theorem rests on two main assumptions, with several others detailed below. The theorem is assuming that voters can place all 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 have one alternative that they favor more than any other. 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.
context_section_description: For the median voter theorem to be successful, there are seven assumptions made, and each includes exceptions for when politicians decide to move away from the median voter:
  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. If each choice is a candidate, and all three start at the median, any slight move captures the entire voting group on that end of the spectrum. No equilibrium exists in this situation, because every candidate has the incentive to move across the ideological spectrum based on the positions of their competitors. 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. In reality, this ignores politician’s ability to change voters’ ideologies to mirror their own. Additionally, career politicians may purposely take positions away from the ideological center in order to gain favor with specific voting bases. 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. In reality, money is one of many variables that contribute to the outcome of elections. The theorem ignores the fact that politicians sometimes take positions with the primary goal of raising money for their campaigns. Political contributions can be used for advertising and campaign trips, and gaining monetary support may require moving away from the median. 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.
  The weak form of the median voter theorem says the median voter always casts his or her vote for the policy that is adopted. If there is a median voter, his or her preferred policy will beat any other alternative in a pairwise vote. (The median voter's ideal point is always a Condorcet winner.) Consequently, once the median voter's preferred outcome is reached, it cannot be defeated by another in a pairwise majoritarian election. The strong form of the median voter theorem says the median voter always gets his or hers most preferred policy.
  The median voter theorem seems to explain some of the things that happen in majoritarian voting systems. First, it may explain why politicians tend to adopt similar platforms and campaign rhetoric. In order to win the majority vote, politicians must tailor their platforms to the median voter. For example, in the United States, the Democratic and Republican candidates typically move their campaign platforms towards the middle during congressional election campaigns. Just as sellers in a free market try to win over their competitors' customers by making slight changes to improve their products, so too do politicians deviate only slightly from their oppone
caption: Example of multi-peaked preferences
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