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Democracy, Voting and The General Will: The concept of the Median Voter Theorem

November 6, 2010

Everyone has their own preferences when it comes to how they want their country to be governed. It is no surprise that no two people will have the exact same ideals and interests, so how do we end up with so many people identifying themselves with the same political party, such as being a “Democrat” or a “Republican”?

The answer is intuitive: these people choose the political parties that most fit their ideals. Suppose in an overly simplified version of politics, that the government in charge would have to decide how much tax they want to impose on a certain good, say cigarettes. In the hypothetical situation where there are only 5 distinct options, $0, $20, $40, $60 and $80, let’s say that the population’s opinions are as described by the graph below:

So apart from the normal spread of random opinions for whatever personal reasons the population has, there would be the hardcore smokers who would advocate no tax and the hardcore anti-smoking campaigners who would advocate the largest amount of tax they can find. The majority resides on two extremes, so what happens?

According to the Median Voter Theorem, the median (or halfway point basically) will be chosen. In this case this would be a $40 tax. This is not because the most people would agree with that number, but because people will be the least upset. If we took the tax to be at its maximum at $80, then we would have uproar from the smokers, and if we had no tax, then those against smoking with a conviction would also be visibly upset. By choosing the midpoint, then less of the population would be prone to disagreeing strongly with the new policy.

In reality, it’s much more complicated than this. When people adhere to a political party, they seldom do it for a difference of only 20 dollars on a sales tax on a product they may not even consume. But the concept of upsetting the least people and being close to the midpoint and hence a “non-radical” political party still stands, as they appeal to the largest number of people. The tempering down of the more extreme and less popular ideals leads to the will of all being trimmed by our democratic system, into the general will.

For a more technical, definitive and mathematical approach to this, check this out:

  1. aaronyan1123 permalink
    November 7, 2010 5:15 PM

    Your discourse is interesting. I never heard about the Median Voter Theorem before. It seems good to briefly explain the example of tabacco tax. How do you find out this theory? Is this theory applied to the real government decision?

    • tungyat permalink
      November 8, 2010 1:45 AM

      I believe it is applied in real life to some extent, I learnt this off behavioral economics at one point, as it’s an example of the Nash’s equilibrium (for any economics people here).

  2. Trevor Cookler permalink
    November 7, 2010 5:37 PM

    I had never heard of the MVT before but it definitely makes sense to me. The using of cigarettes is an easy example to follow, and the way you described how this process works in relation to upsetting the least amount of people was great. To spark a little bit of conversation do you think that Rousseau should have implemented this MVT system as opposed to his idealistic approach of commonly uniting all people to agree on laws? Secondly, is this theory as simple as it sounds? What if there are three parties involved? Then the median would sit at exactly where the middle party wants. Just thoughts to consider.

  3. tungyat permalink
    November 8, 2010 1:49 AM

    Absolutely, which is why we see the more extreme parties such as the extreme right in France being more marginalized and almost ridiculed. They have relatively little political leverage as they simply upset too many people to gain sufficient popularity to form a majority government in a democracy. As for Rousseau, I personally prefer his ideals of a common united population, since if this worked it would effectively reduce a lot of social tension when it comes to some people feeling as if they are not heard at all. Again, it’s hard if not impossible in practice, so I feel like its a matter of balancing between the diversity and popularity of opinions in a political system.

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