Talk:Median voter theorem

message: 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)
thread_title:  Normal Distribution 

message: This article now begins as follows:
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:: 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.
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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)
thread_title:  Is this a good way to write a sentence? 

message: 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)
replies: text: See Condorcet paradox.radek (talk) 15:48, 17 April 2009 (UTC)
thread_title:   Majority cycle trap 

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

message: 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)
thread_title:  Need to clarify things up a bit 

message: Dr. Winer has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
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*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)
thread_title:  Dr. Winer's comment on this article 

message: Dr. Caleiro has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
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)
thread_title:  Dr. Caleiro's comment on this article 

message: Harold Hotelling does indeed reason that "political candidates' platforms seem to converge during majoritarian elections." However, that doesn't seem relevant to Black's work.  — Preceding unsigned comment added by 85.171.133.169 (talk) 18:04, 18 August 2017 (UTC)
thread_title:  Relevance of Harold Hotelling 

message: There are two section of this article which end in "∎", which I interpret as Q.E.D. However, Wikipedia:WikiProject Mathematics/Proofs#Style says to just end the section at the end of the proof, or to collapse proofs so they can be skipped. I'm not sure what section header to give to the material that follows "∎" in these cases, but perhaps someone with more expertise can rearrange things to comply with the Manual of Style? -- Beland (talk) 05:42, 16 March 2021 (UTC)
replies: text: It’s helpful to have a visual clue indicating the end of a proof. Presumably the tombstone caught on to avoid the need to artificially break the text with a new heading whenever a proof comes to its end. Why the MoS deprecates it I have no idea. It’s true that some readers may not have encountered it, but if you eschew everything that readers may not have encountered you end up with babyspeak. Colin.champion (talk) 08:10, 16 March 2021 (UTC)
thread_title:  Ending of proofs 

message: The term of art "median voter" is not defined anywhere in the article.  What exactly is the magical property Marlene has?  You can't state a theorem without definitions.  And the "theorem" should be extended to cover even numbers of voters and multiple medians.  It would be even nicer to extend the theorem to show that pairwise median voting satisfies Arrow's axioms (IIA in particular) on the domain of single-peaked preferences.
: I hadn’t thought that “median voter” was a technical term at all: I’d thought it was a regular construct derived from the familiar term “median”. Colin.champion (talk) 06:35, 29 April 2021 (UTC)
replies: text: However I have a lot of sympathy with your other two points, though I don’t feel I’m in a position to address them.
* My impression is that the median voter theorem is generally seen as giving enlightment concerning the behaviour of elections with large electorates, and that one voter more or less is considered to be lost in the noise. This may be a sloppy approach, but Wikipedia can’t steer a different course than the literature it relies on. For instance a thorough treatment might require the Condorcet Criterion to be extended to require that if a subset of m candidates tie with each other and beat all the rest of the field, then the final winner is restricted to this set. 
* I haven’t seen a succinct and satisfying interpretation in a trustworthy source of the relationship between the median voter theorem and Arrow’s impossibility theorem, but if anyone knows of one, it might well improve the article. Colin.champion (talk) 07:13, 5 May 2021 (UTC)
thread_title:  What is a "median voter"?