<p>I'm studying Down's Median Voter Theorem which states that if voters have single-peaked preferences over <strong>two</strong> alternatives arranged along a one-dimensional political spectrum, a majority rule voting system selects the outcome most preferred by the median voter.</p>

<p>As I understand it, single-peaked requires that each agent has an ideal choice, and for each agent, outcomes that are further from his ideal choice are preferred less. But isn't this trivially satisfied when two alternatives are considered (provided agents are not indifferent): If I prefer Clinton to Trump, then my preferences are single peaked over all possible choices.</p>

<hr>

<p>I understand that singele-peakedness is far from trivial in $N&gt;2$ alternatives, but $N=2$ is required for MVT. From wikipedia:</p>

<blockquote>
  <p>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.</p>
</blockquote>

CC BY-SA 3.0
2018-04-07T12:59:23.377Z
Since you don't provide a link to the Wikipedia source, I cannot say anything about that source. But the median voter is certainly not about voting over two policy outcomes alone.
Michael Greinecker
CC BY-SA 3.0
2018-04-07T13:28:31.583Z
It's literally the wikipedia page on MVT.
pafnuti
CC BY-SA 3.0
2018-04-07T14:09:34.170Z
That Wikipedia page has no formal statement of the MVT, and it is fairly pointless to argue about such a "theorem."
Michael Greinecker
CC BY-SA 3.0
2018-04-07T14:13:53.687Z
I'm not arguing about the ""theorem"", I'm seeking clarification about single-peakedness when the number of alternatives is 2.
pafnuti
CC BY-SA 3.0
2018-04-07T14:42:22.283Z
Every preference profile over two alternatives is single-peaked if there are no indifferences.
Michael Greinecker
<microeconomics><political-economy><public-economics><voting>
Isn't it trivial that preferences are single-peaked over two alternatives?
pafnuti
# Isn't it trivial that preferences are single-peaked over two alternatives?

(Asked by: username_0 on 2018-04-07)

I'm studying Down's Median Voter Theorem which states that if voters have single-peaked preferences over **two** alternatives arranged along a one-dimensional political spectrum, a majority rule voting system selects the outcome most preferred by the median voter.

As I understand it, single-peaked requires that each agent has an ideal choice, and for each agent, outcomes that are further from his ideal choice are preferred less. But isn't this trivially satisfied when two alternatives are considered (provided agents are not indifferent): If I prefer Clinton to Trump, then my preferences are single peaked over all possible choices.

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I understand that singele-peakedness is far from trivial in $N>2$ alternatives, but $N=2$ is required for MVT. From wikipedia:

> 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.

**Tags:** microeconomics, political-economy, public-economics, voting

> **Comments:**
> **username_1**: Since you don't provide a link to the Wikipedia source, I cannot say anything about that source. But the median voter is certainly not about voting over two policy outcomes alone.  
> **username_0**: It's literally the wikipedia page on MVT.  
> **username_1**: That Wikipedia page has no formal statement of the MVT, and it is fairly pointless to argue about such a "theorem."  
> **username_0**: I'm not arguing about the ""theorem"", I'm seeking clarification about single-peakedness when the number of alternatives is 2.  
> **username_1**: Every preference profile over two alternatives is single-peaked if there are no indifferences.  

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## 0 answers

