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Chris Hallquist on voting

Two days after my post about Eliezer Yudkowsky’s posts about voting, another Less Wrong user, Chris Hallquist, posted some counterarguments. He discusses median voter theorem and Duverger’s law. I found it difficult to follow at times, but a commenter helped:

There’s the classic economic textbook example of two hot-dog vendors on a beach that need to choose their location – assuming an even distribution of customers, and that customers always choose the closest vendor; the equilibrium location is them standing right next to each other in the middle; while the “optimal” (from customer view, minimizing distance) locations would be at 25% and 75% marks.

This matches the median voter principle – the optimal behavior of candidates is to be as close as possible to the median but on the “right side” to capture “their half” of the voters; even if most voters in a specific party would prefer their candidate to cater for, say, the median Republican/Democrat instead, it’s against the candidates interests to do so.

This explains why politicians all look the same without putting them in a class and calling it class warfare. I am not sure whether to be worried that there is at least one voter as far from David Cameron as I am but in the opposite direction, or relieved that David Cameron is Prime Minister and not that person.

In any case, one solution is to move the median, which I suppose is what Samizdata is all about.

19 comments to Chris Hallquist on voting

  • jamess

    One problem with the illustration: when the beach is 2 miles long and it takes 1 mile to walk to buy ice cream and another mile to walk back, that customer doesn’t buy ice cream.

    When the Conservatives are the closest party to my political views I don’t vote for anyone.

  • Rob Fisher (Surrey)

    Good point, jamess. Another (pointed out in the article’s comments somewhere) is that the beach has multiple dimensions.

  • Jamess has it right I believe. One vendor sets up at the 75% mark, and the other sets up at the 74% mark. Result: half the people at the beach don’t bother with the long walk.

  • Rob Fisher (Surrey)

    Billll, if that was true, the 74% party could guarantee winning an election by becoming the 73% party. Or someone could set up a 25% party and win that way.

  • Jason

    Forgive me if I’m being slow here, but why isn’t the equilibrium point for the hot dog salesmen anywhere equidistant between side-by-side in the middle and at the 75/25% point?

  • GoneWithTheWind

    The solution is to “mandate” that the citizens must buy a frigging hot dog. Then to make it fair anyone who is in a union, an illegal alien or a person of color gets the hot dog for free and everyone else pays for that subsidy. Some will balk at this so you have to make sure you control the media so that anyone who complains about payng more for a hot dog is accused of being racist, anti-immigrant or has white privilage. Once we can succeed at this we can charge whatever the hell we want for those frigging hot dogs and even contol who gets them and who doesn’t. Maybe once we have total control we can even be honest about our socialist/communist/fascist dreams of our fathers…

  • Well, I reckon this beach hot-dog vendor theory only works with an electorate that has a one-dimensional objective function.

    But perhaps politicians like the theory (posted by PeterisP as linked), as they are simple people: just wanting to be elected – what happens then is not very important (at least to themselves).

    Best regards

  • Rob Fisher (Surrey)

    Jason, the equilibrium point has to be at 50%, because if the vendors are at 75/25, one of them will realise he can get more customers by moving closer to the middle. Since they both do, they both move closer to the middle until they are both in the middle, at which point there is no advantage to moving anywhere else.

    This is why GoneWithTheWind’s idea of mandating a hot-dog purchase makes no difference. Well, unless people choosing not to buy hot dogs are not evenly distributed along the beach, that is.

    Unlike Nigel Sedgewick, I think it still works with multiple dimensions; there is still a median somewhere, no matter how many dimensions.

  • Rob Fisher (Surrey)

    Ok, well there is a geometric median: http://en.wikipedia.org/wiki/Geometric_median

  • Bruce Hoult

    Add a 3rd hot dog vendor an what is the equilibrium?

    I’m not sure that there is one.

  • Bruce Hoult

    Hmm, actually 25/50/75 might be an equilibrium, with market/voter shares of 37.5%, 25%, and 37.5%.

    The middle one can’t change their share by small moves, they can only favor one of the other two while disadvantaging the other. A sudden jump to 24.9 or 75.1 will result in the same 25% share (while ceding 50% share to one of the others).

    The 25 & 75 guys will lose a little share if they move to more extreme positions, but if they try to gain share by moving to the center then they give the 50% guy a reason to leapfrog them.

  • bloke in spain

    Why do you have to resort to mathematics to work out optimum positions for hot dog vendors on a beach? Or textbook economics, for that matter? Try looking at the real world & real beach vendors & you might learn something.
    The are are two answers to the problem & they depend on how long the beach is. On a short beach the median point is more efficient for both sellers due to the “best place to open a shoe shop is in a street full of shoe shops” rule. They can access the entire market & compete on quality of deal. But as the length of the beach increases there comes a point where the furthest reaches become either unaware of hot dog vending or insufficiently motivated to make the trek. At this point the two vendors will separate because they’re gaining more potential customers at their periphery than they’re losing in the shared territory. The one that moves first will be the one least competitive on quality of deal.
    But it’s a good example for voting patterns because it emphasises there’s no simple answers & electorates, like beaches, do not always stay in the same place.

  • Rational

    I hate friggin hotdogs. Burn ‘em both to the ground, build a bar on the ruins. Much better.

  • “one solution is to move the median”

    There’s another, which is looking more and more attractive with each passing day.

  • …or there’s Mr. Rational’s solution, which is less messy than mine.

  • I can’t believe that nobody has pointed out that some people will trek past one hot dog stand to buy their food from another, “because I’ve always bought my hot dogs there.” This is also (possibly even more) true of voters.

  • Jason

    Right, got it Rob Fisher, cheers, the hot dogs aren’t static but the voters, sorry consumers, are. All ketchup, mustard etc being equal. Piece in the speccy this week about how voters probably wish the politicians/hotdog suppliers were a little more static.

  • Surellin

    Bruce, the median for the third vendor is farther away to either side of the middle. I don’t think it would be as far as the 25% mark, but close. He can get all of the business between him and the end of the beach, and part of the business between him and the two at the middle. In political terms, after the first two parties new parties go farther to the fringes. Now, does his entry into the market drive one of the two center vendors toward the opposite end?