[lbo-talk] Hotelling's model [was: Bush expected to announce candidacy any day now]

Wojtek Sokolowski sokol at jhu.edu
Fri Feb 20 08:25:51 PST 2004


Shane:
> All we can do is to use our remaining liberties toward
> the creation of a political alternative to them--just as
> in every past election since 1864. For those of us who
> find it more comforting to act *as if* this was a real
> election (and I haven't yet excluded myself from that category)
> the rational course would be to promote the strongest
> possible alternative candidacy and then, in late October,
> organize a one-to-two or three trade-off of (say) Nader votes
> in close states (say Florida, Missouri, Ohio) for Dumbocrat votes in
> uncontested states like California, New York, Texas, Indiana,
> Mississippi, etc.

I think that election IS *real* in the sense that people do vote and their votes are tallied more or less accurately (some irregularities here and there notwithstanding), and that tally decides who is and who is out. The problem is not with the lack of choice, but the number of choices relative to the width of political spectrum - which can be approached by the so-calld Hotelling's model: http://ingrimayne.saintjoe.edu/econ/International/Hotelling.html

In essence, the Hotelling's model is a graphic exposition of the Analysis of Variance (ANOVA) which Hotelling perfected, whose main goal is the reduction of the total variance in a set (which can be graphically represented as the sum of the distances between each individual point of the set and the set's mean) by subdividing this set into sub-sets with different means. By so doing, the sum of variances within each subset will be smaller than the total variance in the entire set.

To translate that into politics, "variance" represents compromise that an individual voter makes by voting for a political candidate. If we graphically represent political spectrum as a line running from Left to Right, and voters distributed along that line, the overall measure of political compromise would be measured by assessing differences between political positions of voters and those of political parties. What is more, it would also depend on the number of political parties.

Since for the time being, the US system is a duopoly and that is unlikely to change any time soon, let's consider a two-party solution. Following Hotelling's model, each party has the incentive to move to center, because it will reduce the compromise that some of the centrist voters have to make by still keeping their voter on the extremes. Even if the compromise for the fringes introduced by this shift to the center becomes too great and the fringes stop voting altogether, the gains in the center will more than off-set that loss. This is an exemplification of the basic rule taught in Research Methods 101 that, absent other information, the mean is the best predictor of a value within a set, because it minimizes the error (or variance, if you will). That is to say, if you were to predict a value without prior knowledge what it actually is, then discover the actual value and measure the difference between your prediction and actual value (error), and did that over and over again, the sum of all errors would be the smallest if each your prediction was the set's mean. In political terms, you would maximize your following if you "govern from the center."

However, that situation hinges on one crucial assumption - namely that the total variance within the set is relatively small - that is - that the spectrum of political views held by the voters is relatively narrow. If that assumption does not hold, the number of votes gained in center may not be enough to offset the number of votes lost on the fringes. The ANOVA solution to this problem is to subdivide the set into two subsets with the respective means farther apart from each other. In political terms, that means that the respective parties will move moderately to the left and right. That will allow them to capture the fringe votes (which in broader political spectrum are more numerous) which will offset the losses in the center.

In conclusion, this suggest that the parties will move to the right and left, respectively, if there is enough evidence of political polarization. The Nader-trader schemes will not do the trick. A much better strategy is to develop a sensible left programs that is attractive to the mainstream (than means that granola chomping and goofy clothing is OUT) to attract sufficient number of people to change the "Hotelling's calculus." That means - significantly more than the likes of Mr. Nader or even Mr. Kucinich currently attract.

Wojtek



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