# Talk:Median voter theorem

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## Confusing image

I think the image is confusing. What does y-axis mean (what kind of value)? Must point M exactly coincide with the peak? Is it important that the graph is so symmetrical?
What does "already won" mean? (I think some "gray" voters will vote for A or B too) --Y2y 11:12, 12 March 2007 (UTC) Y2y 11:59, 12 March 2007 (UTC)

The main issue with the image is that there are no "hard" values for the graph. The 'M' stands for median and by its very nature must be at the peak of the curve, which by its very nature must be symmetrical. The Y-axis is somewhat arbitrary and the X-axis represents increments of people, and goes from 0% to 50% towards the M.
"Already won" signifies the voters who have made up their minds, or decided to vote for a certain candidate who endorsed their opinion on the issue. The idea is that there are some people who will be extremists and others who are more middle of the road - say the issue at hand is the eradication of all apple trees. Some people will right away be for it (those maybe allergic to apples?) while others will right away be against it. Those are the starting points, the edges of the skirt of the graph. Others might need more convincing to make a decision. In such an idealized representation, one would think that the people with the most extreme views are very small in number, and that most people are indifferent or wavering on the topic. In this schematic Party A only has to approach the median - or water down their policy on the matter - to a much smaller degree than Party B.
Sorry, I can't get into too many details about the exactness of this type of graph, but hopefully this explanation will allow you to see it in a different light and reflect on its data. JesseRafe 02:01, 7 April 2007 (UTC)

I think this image is very useful. It explained the basic thrust of the article to me in a single glance! It might benefit from a couple of more labels for people unaccustomed to interpreting such a graph, but overall it was very helpful to me as a reader. I must take issue with Jesse's comment above, though. The median is not the center of the X axis, it's the position along the X axis where the size of the left and right slices cover an equal area. Also, not all opinion graphs need be bell-shaped. A highly polarized opinion graph would have two humps, and it's easy to think of an example that would have many humps.

Here are some suggested changes to the graph:

• Strike the arrow at the right of the X axis. There is nothing further to the right than 100% support for choice B. (or add an arrow to the left)
• Drop the entire Y axis line.
• Spell out the L, M, and R labels. Try adding the words 'left' and 'right' floating in the whitespace above the curve. The median might be represented by a pale vertical line and the word median above it.
• Consider making the curve asymetric. This will allow the median to be distinguished from the mean, by having the median also positioned asymetrically. Maybe the hump could be shifted left, and the red area shrunk a bit. Then the median line could be visibly off center. On the other hand, such a change may introduce additional confusion for some readers by adding another avenue for misinterpretation.
• Change the caption to something like this: "A conceptual graph of a one-dimensional policy space, with potential voters represented as two-dimensional space bonded by a curve. Candidates A and B currently have the support of a shaded area, and attempt to attract more uncommitted voters by migrating their posotions toward the moderate center.

By making the graph look a bit less graph-like, you clue the reader that it's not meant to be properly quantitative, but conceptual. Anyway, I like the graph, even in its current form. I'm sure it can be adjusted or just left as-is. --Loqi T. 03:32, 15 May 2007 (UTC)

What about this: make a series of 3 graphs, with the first as an initial condition (neither at the median), the second like the first but with the formerly losing candidate moving to the median and winning, and the third at equilibrium.
CRGreathouse (t | c) 20:24, 3 July 2007 (UTC)

## Normal Distribution

I don't think it is necessary that the graph forms a normal distribution. Claiming the /median/ voter would always give a majority, regardless of the shape of the curve, no?

Exactly. What if the issue is "how tough should the law be against pedophilic murder"? The median voter would probably be far away from the median possible position (say, giving only a few years prison, or 50% of all people arrested for pedophilic murder automatically go free). Sagittarian Milky Way 00:06, 21 September 2007 (UTC)

## Is this a good way to write a sentence?

The median voter theory, also known as the median voter theorem and the median voter model, is a famous voting model positing that in a majority election, if voter policy preferences can be represented as a points along a single dimension, if all voters vote deterministically for the politician that commits to a policy position closest to their own preference, and if there are only two politicians, then if the politicians want to maximize their number of votes they should both commit to the policy position preferred by the median voter.

So it says "if blah blah, if blah blah blah, and if blah blah, then if blah blah, ...." Michael Hardy (talk) 02:53, 17 April 2008 (UTC)

## Majority cycle trap

Searching for the "majority cycle trap" on google gives exactly one hit - this article. What is it? 212.130.46.190 (talk) 14:26, 14 November 2008 (UTC)

## Rename

Shouldn't we move this to "Median Voter Theorem" which is a phrase much more common in literature (at least that part of it with which I'm more familiar)?radek (talk) 15:47, 17 April 2009 (UTC)

Good point. I moved it. CRGreathouse (t | c) 23:27, 6 February 2010 (UTC)

## Need to clarify things up a bit

With regard to when the theorem holds and when it doesn't and the issue of single peaked preferences and single dimensional choice space: Basically, single peakness gets you everything - it is a sufficient condition for the theorem. Of course, the converse is not necessarily true; the result does not necessarily fail if preferences are not single peaked, though it might. The thing about single-dimensionality arises because if the choice is over just a single variable, then single peakness follows from concavity of the utility function (which is a standard assumption). So essentially what we have is (single dimension)+(concave utility)-->(single peakness)-->theorem. Now, again, the converse is not necessarily true. You could have multi dimensional choice space (and concave utility) and you could still get the result, though you might not. The difficulty arises because it's hard to define a single valued "median" in two+ dimensions.radek (talk) 19:17, 17 April 2009 (UTC)

## Information considerations

Should the ``Shortcomings" section be broadened to include other problems with the theorem? There are two related to information:

• On the voters' side, the theorem relies on the implicit assumption that all voters are perfectly informed about the candidates' platforms. This makes the existence of campaign contributions a paradox. There are models in the literature that resolve the paradox by allowing for uninformed voters (e.g., McKelvey, Richard, and Peter Ordeshook, 1985, ``Elections with Limited Information: A Fulfilled Expectations Model Using Contemporaneous Poll and Endogenous Data as Information Sources," Journal of Economic Theory 36:55-85; or Baron, David P. , 1994, ``Electoral Competition with Informed and Uniformed Voters", The American Political Science Review, Vol. 88, No. 1, pp. 33-47).
• On the candidates' side, the theorem depends on there being no uncertainty regarding the location of the median voter. In the presence of uncertainty about the location of the median and positional preferences on part of the candidates, policy platforms diverge.

Is there a systematic way of incorporating this into the article, however? Certainly there are many other refinements in the literature, these are just the ones I'm familiar with. Is there perhaps a good review article on the subject that could be referenced? Tpudlik (talk) 00:13, 7 February 2010 (UTC)

The first assumption isn't implicit: "if all voters vote deterministically for the politician who commits to a policy position closest to their own preference". But it is certainly a strong limitation regardless!
CRGreathouse (t | c) 02:00, 7 February 2010 (UTC)

Dr. Winer has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

The writing is not elegant. It is not incorrect though.

It would be useful to compare the median to a Condorcet winner (an outcome that beats any other in a pairwise sequence of majority rule votes. See R. Congleton, The Median Voter Theorem, Encyclopedia of Public Choice.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Winer has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : Ferris, J. Stephen & Park, Soo-Bin & Winer, Stanley L., 2008. "Studying the role of political competition in the evolution of government size over long horizons," POLIS Working Papers 111, Institute of Public Policy and Public Choice - POLIS.

ExpertIdeasBot (talk) 15:44, 24 June 2016 (UTC)

Dr. Caleiro has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"The median voter theorem implies that voters have an incentive to vote for their true preferences."

As is known, the median voter theorem has numerous applications, namely in the determination of the amount of public good to be provided. As is also well known, there is a problem in the revelation of preferences by individuals about the desirable amount of public good but, on the other hand, in the median voter theorem it seems to be assumed that this problem does not exist since it is considered that politicians have the full knowledge of the preferences of voters. This raises the question: what if the voters take a strategic vote, distorting their electoral preferences so that the final outcome of the votes is closer to their true peak in preferences? In this context, would still be valid the median voter theorem?

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Caleiro has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference : Caleiro, Antonio, 2008. "How Can Voters Classify an Incumbent under Output Persistence," Economics Discussion Papers 2008-16, Kiel Institute for the World Economy.

ExpertIdeasBot (talk) 19:06, 30 August 2016 (UTC)