# Median voter theorem

One possible model; here, if parties A and B want to catch the median voters, they should move towards the center. The red and blue areas represent the voters that A and B expect they have already captured.

The median voter theorem states that "a majority rule voting system will select the outcome most preferred by the median voter".[1]

The median voter theorem makes two key assumptions. First, the theorem assumes that voters can place all election alternatives along a one-dimensional political spectrum.[2] 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.[3] 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.

## Explanations

To appreciate the logic of the median voter model, consider a setting where three individuals, Al, Bob, and Charlie, are to choose a restaurant for lunch. Al prefers a restaurant where lunch costs $5, Bob favors somewhat better fare at a restaurant serving$10 lunches, and Charlie wants a gourmet restaurant where lunch will cost around $20. Bob can be said to be the median voter, because there are exactly the same number of people who prefer a more expensive restaurant than Bob as there are who prefer a less expensive restaurant than Bob: here one each. For convenience assume that, given any two options, each member of the lunch group prefers restaurants with prices closer to their preferred restaurant to those that are farther from it. Now consider some majority decisions over alternative restaurants: Options Pattern of votes Result$20 vs. $5 A: 5 B: 5 C: 20 5$10 vs. $20 A: 10 B: 10 C: 20 10$10 vs. $5 A: 5 B: 10 C: 10 10 The weak form of the median voter theorem says the median voter always casts his or her vote for the policy that is adopted. Note that Bob always votes in favor of the outcome that wins the election. Note also that Bob's preferred$10 restaurant will defeat any other. 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 most preferred policy.[4]

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.[2] For example, in the United States, the Democratic and Republican candidates typically move their campaign platforms towards the middle during congessional 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 opponent's platform so as to gain votes.[2]

Second, the median voter theorem reflects that radical candidates or parties rarely get elected. For example, a politician or party which is an extreme liberal at the very left end of the political spectrum will usually not get nearly as many votes as a more moderate party. Finally, the theorem may explain why two major political parties tend to emerge in majoritarian voting systems (Duverger's law). In the United States there are countless political parties, but only two established major parties play a part in almost every major election: the Democratic and Republican parties. According to the median voter theorem third parties will rarely, if ever, win elections for the same reason why extreme candidates do not tend to win. The major parties tend to co-opt the platforms of the minor parties in order to secure more votes.[1] In many other long-established democratic countries there are several parties who each get a substantial share of the vote, although most of these have some form of proportional representation.

## History

In his 1929 paper titled Stability in Competition, Harold Hotelling notes in passing that political candidates' platforms seem to converge during majoritarian elections.[2] Hotelling compared political elections to businesses in the private sector. He postulated that just as there is often not much difference between the products of different competing companies, so, too, there is not a stark contrast between electoral platforms of different parties. This is because politicians, just like salesmen with consumers, seek to capture the majority of voters. Duncan Black, in his 1948 paper titled On the Rationale of Group Decision-making, provided a formal analysis of majority voting that made the theorem and its assumptions explicit.[5] Black wrote that he saw a large gap in economic theory concerning how voting determines the outcome of decisions, including political decisions. Black's paper thus triggered research on how economics can explain voting systems. In 1957 with his paper titled An Economic Theory of Political Action in Democracy, Anthony Downs expounded upon the median voter theorem.[6]

## Accuracy

Several important economic studies strongly support the median voter theorem. For example, Holcombe analyzes the Bowen equilibrium level of education expenditures for 257 Michigan school districts and finds that the actual expenditures are only about 3% away from the estimated district average.[7]

The theorem also explains the rise in government redistribution programs over the past few decades. Thomas Husted and Lawrence W. Kenny examined growth of redistribution programs especially between the years of 1950 and 1988.[8] Tom Rice also writes that voters with the median income will take advantage of their status as deciders by electing politicians who will tax those who are earning more than the median voter, and then redistribute the money, including to those who are at the median.[9] More specifically, Rice demonstrates that if a systematic closing of the gap between the median and mean income levels in the United States could be shown, more credibility could be given to the median voter theorem. Until the mid-1960s, Rice says that the gap between median and mean income levels tightened. Three main forces served to tighten this gap. First, the strength of the Democratic Party in the United States Congress in the decades leading up to the 1960s, as Democrats are more disposed to redistribution of wealth. Second, increased turnout at the polls, just as Husted and Kenny postulated, tightened the gap because an increase in voters means more individuals of lower income are voting. Finally, since unemployment, which causes median income families to fall below the median income[citation needed], was relatively low compared to after the 1960s, this tightened the gap.

## Limitations

The median voter theorem has several limitations. Keith Krehbiel postulates that there are many factors which prevent the political process from reaching maximum efficiency.[10] Just as transaction costs prevent efficiency in market exchanges, the limitations of the majoritarian voting process stop it from reaching optimality. With the median voter theorem in particular, Krehbiel argues that voters' inability to directly amend legislation acts against the theorem. Sometimes, as Krehbiel writes, the policies being voted on are too complex to be placed within a one-dimensional continuum. Buchanan and Tollison also note that this is a problem for the median voter theorem, which assumes that decisions can be made on a one-dimensional field.[11] If voters are considering more than one issue simultaneously, the median voter theorem is inapplicable. This may happen if, for example, voters may vote on a referendum regarding education spending and police spending simultaneously.

A larger problem for the median voter theorem, however, is the incentives structure for government representatives. Downs, in A Theory of Bureaucracy, writes that people's decisions are motivated by self-interest, an idea deeply rooted in the writings of Adam Smith.[12] This holds for the government system as well, because it is composed of individuals who are self-interested. One cannot guarantee the degree to which a government representative will be committed to the public good, but it is certain that, to some degree, they will be committed to their own set of goals. These goals can include a desire to serve the public interest, but most often they include the desire for power, income, and prestige. To continue obtaining these things, then, officials must secure re-election. When representatives are constantly focused on becoming re-elected, this distorts the mandate they receive from their constituents: representatives will translate the wishes of their constituents into benefits for themselves.[12] They will tend to vote for short-term policies that they hope will get them reelected.[1]

## References

1. ^ a b c Holcombe, Randall G. (2006). Public Sector Economics, Upper Saddle River: Pearson Prentice Hall, p. 155.
2. ^ a b c d Hotelling, Harold (1929). "Stability in Competition". The Economic Journal 39: 41–57. doi:10.2307/2224214.
3. ^ Downs, Anthony (1957). "An Economic Theory of Political Action in a Democracy". Journal of Political Economy 65: 135–150. doi:10.1086/257897.
4. ^ Congleton, Roger (2002). The Median Voter Model. In * C. K. *Rowley (Ed.); F. Schneider (Ed.) (2003). The Encyclopedia of Public Choice. Kluwer Academic Press. ISBN 978-0-7923-8607-0.
5. ^ Black, Duncan (1948). "On the Rationale of Group Decision-making". Journal of Political Economy 56: 23–34. doi:10.1086/256633.
6. ^ Downs, Anthony (1957). An Economic Theory of Democracy. Harper Collins.
7. ^ Holcombe, Randall G. (1980). "An Empirical Test of the Median Voter Model". Economic Inquiry 18: 260–275. doi:10.1111/j.1465-7295.1980.tb00574.x.
8. ^ Husted, Thomas A. and Lawrence W. Kenny (1997). "The Effect of the Expansion of the Voting Franchise on the Size of Government Model". Journal of Political Economy 105: 54–82. doi:10.1086/262065.
9. ^ Rice, Tom W. (1985). "An Examination of the Median Voter Hypothesis". The Western Political Quarterly 38: 211–223. doi:10.1177/106591298503800204.
10. ^ Krehbiel, Keith (2004). "Legislative Organization". Journal of Economic Perspectives 18: 113–128. doi:10.1257/089533004773563467.
11. ^ Buchanan, James M.; Tollison, Robert D. (1984). The Theory of Public Choice.
12. ^ a b Downs, Anthony (1965). "A Theory of Bureaucracy". American Economic Review 55: 439–446.
• Mas-Colell, Andreu, Michael D. Whinston, and Jerry R. Green (1995). Microeconomic Theory. Oxford University Press. ISBN 978-0-19-507340-9.
• Buchanan, James M. and Robert D. Tollison (1984). The Theory of Public Choice—II, Ann Arbor: University of Michigan Press.
• Clinton, Joshua D. (2006). “Representation in Congress: Constituents and the Roll Calls in the 106th House”, The Journal of Politics, 68(2): 397-409.
• Congleton, Roger (2002). The Median Voter Model. In * C. K. *Rowley (Ed.); F. Schneider (Ed.) (2003). The Encyclopedia of Public Choice. Kluwer Academic Press. ISBN 978-0-7923-8607-0.
• Downs, Anthony (1957). “An Economic Theory of Political Action in a Democracy”, Journal of Political Economy, 65(2): 135-150.
• Holcombe, Randall G. (1980). “An Empirical Test of the Median Voter Model”, Economic Inquiry, 18(2): 260-275.
• Holcombe, Randall G. and Russell S. Sobel (1995). “Publicness of State Legislative Activities”, Public Choice, 83: 47-58.
• Husted, Thomas A. and Lawrence W. Kenny (1997). “The Effect of the Expansion of the Voting Franchise on the Size of Government”, Journal of Political Economy, 105(1): 54-82.
• Krehbiel, Keith (2004). “Legislative Organization”, The Journal of Economic Perspectives, 18(1):113-128.
• McKelvey, Richard D. (1976). “Intransitives in Multidimensional Voting Models and Some Implications for Agenda Control”, Journal of Economic Theory, 12: 472-482.
• Rice, Tom W. (1985). “An Examination of the Median Voter Hypothesis”, The Western Political Quarterly, 38(2): 211-223.
• Romer, Thomas and Howard Rosenthal (1979). “The Elusive Median Voter”, Journal of Public Economics, 12(143-170).
• Sobel, Russell S. and Randall G. Holcombe (2001). “Unanimious Voting Rule”, Public Choice, 106: 233-242.