Numbers Games

There is an Australian Federal Election due in a few weeks, and for those of you unfamiliar with political system of Teh Best Country In Teh World Ever, the skinny is that the focus is on the House of Representatives, which has one hundred and fifty something electorates, each electing one member. The party who wins majority of those electorates generally claims government, regardless of who wins the overall “popular vote”. There is no separate presidential election, even though practically speaking, the modern game is dominated by “presidential” leaders.

Now, here’s a little game-theory contrivance that shows that raw number-of-seats aren’t the only story – small numerical changes can have big practical consequences, and big numerical changes can have small practical consequences. I forget where I originally read it (searching the web for [25 26] is most unhelpful), but here it goes.

Suppose you have a parliament of 100 seats (or call them 100 senators, if that makes you feel better) and that you need 51 to pass legislation. There are four political parties (called A, B, C, and D), and party discipline is very tight – all members vote as a block with their party colleagues. Naturally, your party is the A team.

If each party controls 25 seats, then obviously each party is equally powerful. Now suppose there is an election and only three seats change hands, so that the A/B/C/D split is now 23/26/26/26.

A relatively small change, in terms of numbers, but you (and the rest of the A team) are now useless. You can’t make up the 51 with one other party, any other two parties could make the 51 without you, and if you joined a coalition of three (or more) parties, they could just ditch you (and then wouldn’t have to make any concessions to keep you on-side) and keep their 51-ness. Your negotiation power is zero.

Now suppose, more realistically, that there are two dominant political parties, say B and C, and you (A) and D are minor parties, say a split of 3/48/48/1. This is a drastic fall in your number of seats, but in terms of on-paper (i.e. modulo things like ideology, mandates, and reality in general) negotiating power, you are now as powerful as B or C, and more powerful as D (since D is as irrelevant as A was in the 23/26/26/26 example). Out of A, B, and C, a coalition of any two can form the 51, and hence all three are equally powerful (assuming iron-clad party discipline).

Of course, this is all contrived, e.g. I don’t see the Liberals teaming up with the Greens (a minor party) to trump Labor in the forthcoming parliament, but it’s an interesting example (IMHO) anyway.

As an aside, for those of you Aussies not living in marginal electorates and feeling neglected from the barrels of pork raining down in those areas, I’ve previously blogged a wacky idea for dismantling the notion of electorates altogether, but in light of this example, the lack of a party to enforce party discipline would instead accentuate this sort of volatile coalition-forming and post-electoral opportunistic negotiation. Hmm…

What does this blog post mean? I have no idea. Then again, I woke up this morning from dreaming all my teeth crumbled and fell out, and I have no idea what that means either. Except that I should probably floss more often. Hey, while I’m there, I should probably backup my disks too…


#1 ethana2 on 11.03.07 at 7:05 pm

Dreams where your teeth fall out or tornadoes are everywhere mean that your brain feels like dreaming about something unpleasant. What you said is not an uncommon way for a dream to be unpleasant. I’ve had several dreams where I lose all my teeth. I’m always relieved to wake up. Same with the tornado ones…

#2 Drone on 11.06.07 at 5:31 am

“If each party controls 25 seats, then obviously each party is equally powerful. Now suppose there is an election and only three seats change hands, so that the A/B/C/D split is now 23/26/26/26.”

I’d say this situation has a far more dire consequence … 23 + 26 + 26 +26 = 101. Election fraud!

#3 Sigi on 11.07.07 at 12:31 pm

>Naturally, your party is the A team.

This chap knows altogether TOO MUCH about my private life.

#4 Nigel Tao on 11.08.07 at 11:41 am

> 101. Election fraud!

D’oh! I used to be numerate. These days I outsource that to computers.