## Politics on the real line

Imagine that a divisive subject of political debate can be represented by the real line. Say abortion: Zero is mealy-mouthedness, minus ten is a sentimental pro-lifer, minus twenty Pastor Splittlefleck of Jesus Loves Embroys Babies Church, Arkansas. Plus ten is a pragmatic pro-choicer, plus twenty a pissed-off feminist. (I myself am plus twenty-five or thereabouts.) Minus and plus fifty start both to be people you don’t want to spend time with; and so on.

Let us say each politician needs to pick a point on this spectrum to be his/her chosen stance. Let us say each voter has a stance of his or her own, and votes the politician whose stance is closest to it.

Now it is mathematically clear that if you have a politician that picks a position, the most advantageous position for any other politician to pick will be one that is as close as possible to that of the first one.

Say Chuck D. Democrat picks the position +5. What position should Erich R. Republican pick to maximize his votes? It might be that at and around +5 there’s a huge concentration of voters; remember, nothing says opinions have be equally divided on the spectrum. If half of Chuck’s voters are over +5, and half are under +5, then Erich’s smart bet is to sidle to either side of him, to +4.5 or +5.5; I myself think the former is more natural. That way all those whose opinions are +4.75 or less choose Erich, because he’s the closest; and if the midpoint of opinions is close to +5, that’ll give Erich almost half the votes. If Erich can then entice people to move their opinions lower, he can leech people away from Chuck, and gain a majority. (A person who used to be +4.9 but now is +4.2 votes, as far as this opinion is concerned, now for Erich instead of Chuck.)

If we further assume that the two candidates on this spectrum are “locked”, that is, Erich’s position is always less than that of Chuck — that is, Chuck is locked being “the progressive” and Erich “the conservative” — then Chuck can’t even leap over Erich and find the majority there. Seems both candidates are destined to rush at each other, both trying to grab as big as part of the spectrum “behind” himself or herself as they can.

Now, indeed, one would think that in a two-candidate system the logical outcome would be that all candidates agree with each other about everything; that way each gets half the votes, and basically statistical randomness resolves the elections. (Well, it seems like the only direction where your votes will always increase; and if you happen to meet at the exact midpoint of all the votes, nothing improves your 50/50 lot.)

This however assumes that people will vote for the closest candidate, no matter how far he or she is. This is not so in real life: If the candidates are +2 and +4, the -20 people will not be much inclined to vote for either. And even the United States isn’t in this regard a two-candidate system: there are plenty of people with different positions inside both the Democratic and the Republican parties, and this means the +2 Republican can be swiftly back-stabbed by a -10 Republican — suddenly all votes below -4 fall to the new guy, and the +2 Republican may be voted out of existence, because his/her/its +4 rival still collects all the over +3 votes, leaving only the uncertain sustenance of the [-4,+3] segment. In this way the best position, if there’s no-one new coming in, is to always become more like your opponent; but the risk is someone new coming in behind your back and stealing the majority of your votes.

Indeed, if your opponent is +4 and you are +2, the new guy should pick +1 for maximum popularity — except he (she?) thereby risks the same theft she (he?) is subjecting you to. There might be a somewhat stable solution where the two candidates are exactly so far apart that the risks balance: you will not move closer to your opponent for risk of backstabbing, and and you will not move farther for the risk of him following and eating your votes. (But this then asks, how good are political actors in gauging these risks? And is this what politics is really all about?)

I think one could model this thing with Matlab or something; have at the beginning two randomly placed actors and a gently fluctuating distribution of public opinion (basically a function from the real line and time to the non-negative reals, a.e. zero outside a bounded set, if you know what I mean); have each actor move its opinion in small steps in the direction of increasing popularity (determined by integrating the closest-to-me fraction of the public opinion function); and whenever a large enough segment its distant enough from the closest actor, have it spawn a new one; and if an actor falls below a certain threshold of attracted votes, kill it off. The results could be pretty; also, perhaps interesting. (Also, perhaps someone at the Democratic HQ is muttering “We need that in our Vote-o-Van!” while over at the Republican one they scream “We have a leak! The Crushidominator has been leaked!”) And there’s no problem except computational power and common sense that prohibits moving from the real line to two-, three-, or n-dimensional cases, with two, three or more opinions simultaneously chosen for! With this model, I will rule the world of politics forever bwa ha ha ha!

(I won’t do it, because I’m not that kind of a mathematician. Imagine this said in the tones of “I’m not that kinda girl, mister!” I’m too lazy and patricianly prejudiced to do applications.)

This all now assumes that politicians are moral-less opportunists who flock to whatever position brings them the most votes; the joke should be obvious here.

### One Response to “Politics on the real line”

1. Bob O'H Says:

Hm. You should havea chat to Stefan Geritz in Helsinki – I’m sure he’d find this amusing, and it’s close to his area of research (adaptive dynamics).

I wonder – what happens in >1 dimension? And what if a politician has a personal position, and they don’t want to diverge too far from that (either because of scruples, or because they don’t want to be seen as hte opportunistic scum they are)?