July 19, 2008

The Hotelling–Downs model of Two–Party Competition and the Median Voter Theory

My favourite topic from Public Choice is the Hotelling-Downs model of Two-Party Competition (Though it was never actually covered). First introduced in a paper by Harold Hotelling in 1929, the model still holds today. What’s impressive about the model is its simple, it’s realistic, and it’s something which one can observe in any pluralistic political process.

The intuition behind the model is as follows: Voters have single-peaked preferences. They hold a certain “bliss point” along a single dimension. For example, taxation. You would be okay with a 10% tax-rate. You find it reasonable, but anything greater or less you prefer less to your bliss point of 10%. The same can be applied to political ideologies among other things. In the US system, you have a bliss point along a Left-Right political system. You could be a ultra-liberal and be on the far left of the spectrum or be very conservative and be on the right. Or you could be moderate and be in the middle. What follows is that the median voter will always decide the election. In the median, you will have at least 50% of the vote.

What this means is that if a candidate wishes to win a two-party election, he must take the position of the median voter. He can not take any other position for fear of losing. In the United Kingdom, the labour party attempted to do so in 1983, and lost miserably. If you decide to go on the fringe, be prepared to lose if a country is made of moderates. This is the reason why you have career politicians, vigorous opinion polling, and intrusions into candidate’s personal lives. In a presidential election, the result will come down to a candidate’s personal charisma and not necessarily their policies.

For an example of the model in action, take the recent Democratic and Republic primaries. The two parties seem completely polarised, the Democrats talking about universal health care, liberal immigration, and ending the war. The Republicans talking about family values, closing borders, and abortion.

What happens first is that each candidate has to appeal to their base, and that means taking on positions many find radical. It’s easy to illustrate this point with the Republicans: just consider their stance on gun control. What happens after, once the party candidates are elected, is a dramatic shift from both candidates to the center. Instead of battling their ideological positions in the Democratic debates, it’s reduced to sound bites of “I also agree with the Senator” and “God bless America.” No candidate will risk taking his true position (This can be modelled as a Prisoner’s Dilemma, but that’s for another time). This is why the Hotelling-Downs model predicts that both candidates will converge to the position of the median voter.

However, the model rests on one major assumption. Single-peaked preferences. In a two-party system, it’s reasonable to suggest that preferences are single-peaked. If you’re a party Democrat, but believe that abortion should be illegal, unless you have a strong enough ideological belief in that single issue you won’t necessarily adopt a package of Republican policies for that single issue. I’ll leave it at that for now, but the truth is it’s even more complicated for a two-party system. However, once you get into parliamentary elections- the model falls apart completely. To consider why, look at the following diagram:

This might be a little complicated, but all it says is that no party can satisfy the median voter. A “cycle” can occur. Party X can beat Party Y which can beat Party Z which can beat Party X. That’s why parliamentary elections are a nightmare to model. You can only offer rough a priori predictions, but because there is no “core”, you can’t offer any certainty.

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