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Tuesday, 19 April 2011

My 2 cents on voting systems

"First past the post" electoral systems have their faults and I wouldn't say they are perfect, but the merits of AV have been over-hyped. The argument that the winner of AV has more than 50% of the support of his constituents is simply wrong. For a start, around 50% of them will not vote and of those who actually do count towards his score a fair proportion may well be second preference votes. Not much of a show of support when Mr Apathy gets 50% first choice.

But, in fact, the results under AV can be quite ridiculous and I give the following by way of an example.  The colours used here are for example only and should not be taken to express any particular prejudice.  The numbers and the backstory are not particularly extreme and may fit many constituencies.

Imagine a hypothetical constituency where 49.9% of the electorate vote for the Red candidate, 25% vote for the Yellow candidate and the remaining 25.1% of the vote is taken by a motley assortment of Blue, Purple and Violet parties.  (OK, 49.9% is pretty borderline but in reality anything from 45 to 50% is not uncommon, and the story wouldn't be very different).

It turns out that the Yellow candidate used to be the Red Party MP, but he defected a few years back when it looked like he was going to be deselected, so as a result no Red party voters will put the traitor down as their second choice, and since the rest of the field are far too Blue/un-Red, most of them don't put down any second choices.

On the other hand, because the current Red candidate is seen as quite a good MP and the candidates of the various-shades-of-blue parties all have reputations as shysters and chancers, nearly all of the voters who put the Yellow candidate as their first choice put the Red candidate as second choice.  Perhaps they feel guilty about the defection.

The Blue, Purple and Violet candidates realise that they each have no chance of winning and tell their supporters to vote tactically and put the other blue-ish candidates as their second and third choices, the Yellow party candidate as their fourth choice but to omit the Red candidate.  Voters being like sheep and not wanting to be herded don't do exactly this and a few (say 0.2%) actually put Yellow as their second or third candidate.

So the Red candidate is the first choice of 49.9% of voters and the second choice of 25% of voters (i.e. first or second choice of 74.9% of the voters), while the Yellow candidate is the first choice of 25% of voters and the fourth choice of 25.1% (i.e. first to fourth choice of 50.1% of voters).

Looking at it in terms of which candidates voters don't want to win, the Red candidate has been omitted from the voting slips of 25.1% of the voters, while 49.9% of them have not voted for the Yellow candidate

The Red Candidate has twice as many first preference votes (49.9%) as the Yellow candidate (25%).

The Yellow candidate has been rejected completely by almost twice as many voters (49.9%) as the Red candidate (25.1%)

Who wins under AV?  The Yellow candidate, of course, because AV is so much more "fair".

FPTP may have its faults, but nothing as egregious as this.


Len said...

2nd or 3rd preference is still support. So your in opening paragraph, "a fair proportion may well be second preference votes" is somewhat irrelevant; support is support.

The apathy of non-voters is a problem under FPTP too. In fact, if you ask many people why they don't vote, it's because their perception is that their first choice candidate doesn't have a chance of winning so their vote would be wasted. Under AV, that wouldn't be the case.

You've deliberately made the numbers in your example as marginal as possible - it's a very convoluted and not very realistic example. Every voting system has its flaws, but things like what you've described would be pretty rare under AV; whereas with FPTP it's very common for MPs to be elected with support from the majority of voters.

Alex said...

Actually the 45%:25%:10%:10% (and the rest) split of the vote is quite common, so I would expect this sort of circumstance to arise quite often.

The only thing contrived about it is that the level of egregiousness is so high. This example isn't created to show a marginal injustice but a whopping great one with quite plausible figures not very different from the one's in my own constituency.

Richard said...

I'm confused, doesn't Red win with the 2nd pref Yellow votes?

Alex said...


No, Red doesn't win based on its second preferences, and that is one of the defects of AV.

As soon as Yellow gets over 50% of the vote the competition stops and Yellow is the winner. The second and later preferences of all the candidates eliminated in the final round are never taken into account.

Richard said...
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Richard said...

Humour me, I find this veh complicated.

By round 3, we're left with Red 49.9%, Yellow 25%, the last surviving Bluish at 25.1%?

So Yellow gets binned before it has a chance to benefit from the 4th pref Bluish votes ?

What am I missing?

If the numbers are R49.9%, Y25.1%, B&c25% I think it works, the last B is dumped and Y reaches 50.1%?

Alex said...

Enough of the blue-ish voters vote for Yellow before the fourth round that Yellow gets through.

Richard said...

D'oh, I missed this bit:

"Voters being like sheep and not wanting to be herded don't do exactly this and a few (say 0.2%) actually put Yellow as their second or third candidate".

This inattention to detail may explain why I'm a pig farmer rather than a Megabank VP and Master of the Universe.

Alex said...


No matter the precise numbers, I hope you take the point that not only does the person who comes second actually come first, but there are quite plausible numbers under AV where the person who gets the most first choice votes, the most second choice votes and the highest number of overall votes comes second under AV.

Richard said...

Indeed so, and I'm intending to shamelessly pass your excellent illustration off as my own in the coming days, now I've got the 'rithmetic nailed down.

Have a Pimms on me.

Alex said...

Thank you. As it happens we have a few people coming for drinks at 6, so I may do just that. Happy Easter (not that farmers have Bank Holidays AFAIK).