Monday, 4 April 2011

The Durian Candidacy - or why AV is more democratic than FPTP

There are exactly one hundred diners who use the works canteen for a nice, healthy, lunch that involves fruit. Only one fruit is served. That fruit is served each and every day for four to five years. Why do the canteen management arrange things in this way? Is it because it’s more efficient? Does it save money? Is it because of some weird dietary theory? Or is it that I need to mirror the choice of one representative in a parliament that will last four to five years? Probably the last. Whilst the diners won’t have a choice of fruit each day and will never have an individual choice of fruit, the canteen management are responsive enough to allow them to collectively decide on the fruit once every four or five years.
There’s a fruit election with apple, banana, cherry and durian as the candidates.

Judging the outcome of the election

We’re going to look at the outcome of the election under First Past the Post (FPTP) and Alternative Vote (AV) and judge which system leaves the diners best off.

The principles in judging the outcome are:
1. If your favourite fruit is chosen then you are best off.
2. If a fruit that you like is chosen in preference to a fruit that you like less then you are better of than you would have been had the other fruit been chosen.
3. if you're “best off” you're also “better off”
4. If you are not better off then you are worse off

So, say you want banana. If banana is chosen, then you are best off. If cherry is chosen and you prefer that to apple then you are better off than you would have been were apple chosen. If apple is chosen and you prefer apple to durian, but prefer cherry and banana to apple, then you are better off than had durian been chosen, but worse of than if banana or cherry had been chosen.

Under AV the diners list the fruit in order of preference, under FPTP they just list one: the first in their AV list.

The outcome

Durian is reputed to taste absolutely delicious and smell utterly disgusting. I’ve found that a bit of an exaggeration (it tastes quite nice and pongs a bit), but it is a fruit that divides opinion. Some are passionately for it, some equally passionately against it. The same cannot be said for other fruits. I don’t particularly like apples but, if push comes to shove, I’ll eat one and am not going to ban you from even taking an apple near me (seriously – durian is banned from many hotels and public places in the Far East). If people don’t put durian down first, then they’re likely to put it down last. Durian is likely to get very, very few second preferences under AV. That said, people who like durian tend to be very enthusiastic about it. If they like it then they like it way more than other fruits. Durian is likely to get a lot of first preferences, under AV, and votes, under FPTP.

So let’s assume that durian gets most votes under FPTP and most first preferences under AV.

The outcome of the election under FPTP is that durian gets chosen. Under AV durian may get chosen. If more than 50 people listed durian as first preference then durian does get chosen.

If less than 50 people choose durian then the fruit with least votes gets eliminated. The diners who voted for that fruit are now counted as having voted for their second preference. If there is still no majority the fruit with the least votes gets eliminated and the votes of the diners counted against that fruit are re-assigned.

Let’s say that apple got eliminated first, then cherry and the count now shows banana and durian with the final tally of votes as follows:

First preferences - 30
Second prefs, from apple - 7
Second prefs from cherry - 17
Third prefs from apple – 5
Total - 59

First preferences - 35
Second prefs, from apple - 3
Second prefs from cherry - 3
Total - 41

Banana gets chosen under AV, whereas durian gets chosen under FPTP.

Which leaves the diners better off?

Those who put banana first preference are best off under AV. Those who put banana second preference put either apple or cherry first (they wouldn't have been counted for second preference had they put durian as first preference). So they prefer banana to durian and, so, are better off under AV.

Those who put banana third preference did so because they chose cherry second preference (and apple first). Even though banana is low down on their list of preferences, banana is still higher on that list than durian (otherwise that third preference would be listed under durian).

Each of the groups of diners in the banana column is better off for banana being chosen against durian. Each of them would be worse off were durian to be chosen. And there is a majority of them. The outcome of AV (banana) leaves a majority of the diners better off than the outcome of FPTP (durian).

The same ranking of outcomes can be applied to elections of MPs. There is something “better” about your second choice candidate being elected as opposed to your third choice; even if “better off” might sound a bit awkward. Perhaps “better represented” is term to use. And, contra other arguments against AV, even your sixth or seventh preference candidate better represents you, and is a better outcome for you, than your eighth or ninth.

There are scenarios where AV does not ensure an optimal outcome. But in these situations, neither does FPTP. Where FPTP differs in outcome from AV, AV ensures a majority of the electorate have a better selection than under FP.

There are lots of arguments against AV other than the democracy of the outcomes in individual cases.

AV helps extremists, like the BNP, for eample.

Only it doesn't, if it did then the BNP wouldn't be so opposed to it. But there are still some good arguments. Like:

AV is complex and expensive to count.

But then I've counted AV and, actually, it's a piece of cake. And, as Eddie Izzard pointed out, the main additional cost is in pencil lead. Ok. So those two were bad examples, but there are good arguments for FPTP over AV other than the outcomes in individual constituencies. The point of this post was that that particular argument was bogus, regardless of any merit of any other argument. Like:

AV counts losers votes twice.

But no, look at the example above. 100 diners, 100 votes in the final tally. Oh well. There must be some good arguments for FPTP over AV.....