Nun of Thee Above

UPDATE: FOR REASONS THAT YOU'LL SEE IF YOU READ THE COMMENTS SECTION, THIS WHOLE IDEA TURNS OUT TO BE A BIG PILE OF DOGGY-DO. MY APOLOGIES. I LEAVE THE POST UP ONLY AS A MEMENTO OF MY STUPIDITY.

The proponents of AV claim (and I hope that if you've been following these pages, you'll accept the claim is false) that AV guarantees that the winner has the support of more than 50% of those who voted. Even in those cases that the claim is true, it's still just a quirk of the fact that if a candidate doesn't get 50%, then they are repeatedly given additional votes until they do.

But if we really wanted all MPs to have more than 50% of the vote, even under First Past the Post, it would be quite simple:

If a constituency gives no candidate 50% support, then that constituency doesn't return an MP.

(Note that this approach wouldn't work under AV, since at least one candidate always gets more than 50%.)

It's a radical approach, but it has its pros and cons. The main pro is that it is something that would really encourage candidates to seek a broad base of support. The con is that it would leave many (perhaps most) constituencies unrepresented.

Under FPTP, and under AV, we do have a mechanism to indicate that we don't want any of the candidates to represent us at Westminster - we don't vote. At the last general election, 35% of the UK took that option, more than the fraction who voted for many of the winning candidates.

The problem is, there's more than one reason for abstention. It may be to wish a plague on all their houses, or it may be because we couldn't be bothered, or were away on business, or whatever. We can demonstrate that we really do care enough to go to the polling station, by turning up and then spoiling our paper, but even then there is no way to distinguish between the conscientious abstainer and those can't tell the sharp end of the pencil from the blunt one.

What we need is a genuine box in which to put our cross, labelled NOTA - None Of The Above.

Would it have much effect? Perhaps not.

Under FPTP, the NOTA votes would be counted and would certainly be of interest if NOTA came in third or second or even (dare we hope?) first place. But it wouldn't actually make any difference.

Under AV, NOTA would have less impact. The winning candidate would still get over 50% (it can't be avoided). If a voter put NOTA as their first choice, and then listed the other candidates, then they would be saying, 'I don't want any of these candidates, but if I have to have one of them, here's my order of preference.' Well, the fact is you do have to have one of them, and so your NOTA vote would instantly be dismissed and the process would carry on as normal with your second-choice vote being counted.

But what if, as suggested above, you could have none of them? What if, under FPTP or AV, NOTA was counted like any other candidate and could win. It would be rare I think, but it's an option that would allow voters to truly express themselves. Under FPTP things would be, inevitably, simple. If NOTA gets more than any other candidate then NOTA wins and the constituency returns no MP.

Under AV things are (inevitably) more interesting. The NOTA selection could go anywhere in the list that the voter chooses - top, bottom, or middle. And suppose you list the candidates in the order A, B, C, NOTA, D, E , F. That would be saying, 'I'm happy to have A or B or C as my MP, and of them, here's my order of preference. I don't want any of D, E, F, but if it comes to it, I do still have a order of dislike.'

That's really quite expressive. Under standard AV, however much you loathe and despise candidate F, you still have to list them to get the most of you vote, you put them last, seemingly suggesting that you would like them to be your MP, just that you'd like others more. By putting that NOTA break in there, you're effectively producing one list of candidates you like and another of candidates you don't, and putting the BNP (sorry, candidate F) at the top of that list. (It has to be said that this is a point of perception, not something that directly effects the result, but perception is important.)

There's still one problem, however. In a constituency where NOTA wins, the people don't get a representative in Parliament. The best I can come up with is that the runner-up gets forced to go to Westminster, but doesn't get a salary. I can see the fairness of it, but I can also see how it might produce an MP who slightly less than enthusiastic about their job - which was really the whole motivation for electoral reform.

But that's a detail. The important thing is to modify AV by adding this NOTA option. So who's with me? Who will make their voice heard? Who will climb up onto the roof tops and shout out the slogan to all who will listen:

'Vote NOTA-AV!'

Why Stop at 50%?

I've been too negative - pointing out inaccuracies in claims made in favour of AV, when nobody really cares how the system actually works anyway; it's about the spirit of the change.

So for this post and the next, I'm going to be more positive, and suggest some alterations to the electoral system that might in some small way improve things. (And for this first one, I'm indebted to Katie Piatt for setting me along this line of thought.) Let's begin.

A supporter of First Past the Post, a supporter of AV and a third-world dictator (I won't name them) are sitting in a pub (I will name it - the Good Companions, in Brighton).

The FPTP supporter says, 'Under my system, the winning candidate has the highest number of votes.'

The AV supporter says, 'Ah! But under my system I can guarantee that the winning candidate has more than 50% of the votes.'

The dictator says, 'That's nothing. Under my system I can guarantee that the winning candidate gets 100% of the votes.'

As it turns out, both the FPTP and the AV supporter are understating their positions.

In FPTP, we can make guarantees about percentages. If there are four candidates, then it is guaranteed that the winner will get more than 25% of the votes. If there are three candidates, then it's 33%. If two, then 50% (the equivalent of the last round of AV) and if there's only one, then you can guarantee 100% support (the dictator's system).

So if we want, as AV claims, more than 50% support for the winner but still have FPTP, that's easy - we just restrict the number of candidates to two. The problem is obvious - how do we determine those two?

AV is essentially an answer to that question. It manages it all in one election, but effectively takes multiple votes across a series of elections. If there are four candidates in total then we have a vote between those four. The loser drops out and their votes are transferred to the next round of three. At this stage we can only be sure that one candidate gets at least 33%, so again we drop out the loser, transfer the votes and now have an election of two in which someone (it's mathematically guaranteed) gets more than 50% and the result is called.

But why stop there? Why halt this repeated process of dropping out the losing candidate? Now the second place candidate drops out, his votes are transferred to the only remaining candidate, and the winner can be declared as having 100% support.

But that's silly. Clearly no one believes that the winner has 100% support, in just the same way that no one believes it in a dictatorship. The winner may be the most popular candidate, but the 100% support is meaningless - it's just an inevitable consequence of the mathematics.

But in just the same way, under AV as it is proposed, the 50% is meaningless - it's just as much an inevitable consequence of the maths, a statement which though true, cannot be false. I'd like to see a winner under AV who didn't get 50% of the vote.

I say that the percentage is meaningless, but perhaps a better term is 'not interesting'. If I were to tell you that the last five presidents of France all got more than 50% of the vote in the final round, it would not be interesting. And I use the term in a slightly technical sense - by 'not interesting' I mean it provides no information that you couldn't otherwise have inferred. French presidents have to get more than 50%, just as AV candidates do - that's the system.

However, if I told you that in 2007 Sarkozy won with 53%, whereas in 2002 Chirac won with 82%, that would (might) be interesting. Clearly there was something different about Chirac's election compared with Sarkozy's. (There was - Chirac was standing against the fascist Le Pen.)

But under AV, as currently proposed, we don't get that sort of information. If I were to tell you that in one constituency the winner was Smith with 53% and in another the winner was Jones with 58% the actual percentages tell you nothing of interest. Jones my actually be less popular than Smith.

Why? Well in Jones' constituency, voting went to the final round. Jones got 58% and his opponent got 42%.

But Smith reached the 50% finishing post while there were still three candidates left. He got 53% and his opponents got 20% and 27%. If the AV process had continued to the next stage and the third place candidate had dropped out then the redistributed results might have given 63% (or more, or less) to Smith and 37% to his opponent. Now Smith's 63% can be more fairly compared with Jones' 58%.

So why is this not the way AV is proposed to work? Why do we stop counting as soon as one candidate passes 50%? Well, it could be argued (I have done) that the purpose of elections is primarily to choose an MP, not to divine other related information. But I'd also argue that getting other information is useful, if it doesn't affect the actual result, which this doesn't.

It could be argued that counting every constituency through to the final round would be expensive, but we already know that there is no additional cost to AV elections, so even if my proposal proved to be twice as expensive, twice nothing is still nothing (and that's the simplest bit of maths you're likely to see on this blog for a long time).

It could be that proponents of AV realise that if this approach were followed then in some seats (safe seats under FPTP and still safe under AV) this extra transfer of votes might mean the winner getting maybe 80% or occasionally 90%, and that's getting a bit too close to the dictator's 100% and could give away the game that all the percentages are just artefacts of the system. I doubt it, because I doubt many of AV's proponents have thought it through to that extent.

But that's my proposal. If AV succeeds at the referendum, make a slight amendment to it:

In every seat, counting should carry on to the final round of two candidates, even if a winner can be determined earlier, so that comparison of winning percentages across constituencies operates on a level playing field.

Any takers?

I'm Backing AV 110%

(Sorry to go on about it, but I'm just fascinated by mathematics.)

One of the headline reasons being put forward in favour of AV is that it means that no one can become an MP without winning more than 50% of the vote (assuming every voter uses all of their votes, which is a detail I'm not too fussed about). I'm not sure this is such a great thing, since some of that support might be, to say the least, grudging, coming from voters who could actually think of six or seven candidates that they would rather have had than the winner for whom their vote was finally counted.

However 50% is still 50%. And what's really great about AV is it's not only the winner who gets more than 50% of the vote, so might some of the losers.

Let's return to the constituency I mentioned in my last post, but give it a more definite result. First-choice votes go:

Labour: 15,000

Liberal: 11,000

Tory: 9,000

The Tory drops out and let's suppose 7000 of his second-choice votes were for the Liberal. The Liberal now has 18000, which is more than 50%, and wins. First-choice votes of one candidate plus second choice votes of another gives greater than 50%.

The trouble is, the Labour candidate also got more than 50% if you add the first choice votes of one candidate and the second choice of another. The Labour first-choices plus the Liberal second-choices (assuming a reasonable split) also come to greater than 50% . (It's actually mathematically possible that the Tory could get more than 50% too if the Labour candidate's second choice votes were largely for the Tory - but that's unlikely).

So 50% is a necessary but not sufficient condition to win an AV election. How then is the winner decided? We could go back to a FPTP-style approach, where it's the candidate with the highest number of votes (first and second choice combined), but in this example, that would probably be Labour. Here the Liberal wins with more than 50% of a particular set of first and second choice votes, but still fewer than the combination of votes that Labour got, but didn't get counted.

So the total number of votes cast is more than 100%?

Let's consider the definition of percentage. The percentage of votes for a candidate is:

(n / T) * 100

where n is the number of votes received by the candidate and T is the total number of votes overall.

But that term T could actually have several meanings. It could be the total number of voters, or the total number of votes cast or the total number of votes counted. (It could also be the total number of eligible voters, but turnout is a problem under any system.) Under FPTP those three definitions of T are all the same thing, because FPTP is one person-one vote.

But AV gives several votes to each voter. (You can argue that it's a good thing, but you can't deny it - the voter gets to indicate support for more than one candidate. It may not be that multiple votes are counted, but multiple votes are cast.) If you go with T being the number of voters, then it's clearly true - the winning candidate has more than 50% of the vote. In this case, 51%.

But if T is the total number of votes cast, with three votes per voter (assuming that there were no other candidates and that every voter used all their votes) that gives a total of 105,000 votes - and the winning Liberal candidate gets (18,000 / 105,000) * 100 = 17%.

On the other hand, if T is the number of votes counted, things get more complicated. In the first round, 35,000 votes were counted. The Tory dropped out and so in the second round a further 9000 votes were counted, giving a T of 44,000. So now the winning Liberal candidate's percentage is (18,000 / 44,000) * 100 = 41%. Not a bad result for a winner under FPTP, but this is AV, which supposedly guarantees the winner gets more than 50%. You may think I'm being unfair, counting those second-choice Tory votes into T with the same weight as first-choice votes, but if you do, then you must surely also object to them being counted into n (the votes for the winning candidate) with equal weight - that's one of the main objections that many people have to AV.

So the question that we must all answer, whether we are pro or anti or could not care less, is:

What is your definition of T?

Electile Disfunction

I won't deny it; I've been mildly opposed to the Alternative Vote ever since Gordon Brown first mooted it as an opening gambit in his attempts to form a coalition government with the Liberal Democrats back in 2009, over six months before the general election.

But one objection that I'd never really held with was the idea that AV is complicated. All the voter has to do, so they say, is write down the numbers 1 to 9 (or whatever) in order of preference. It's simple - in much the same way that solving a Sudoku is simple (or indeed that playing the flute is simple, according to Monty Python).

But the more I think about it, the more complicated it gets. Problems can occur in many areas, but the one I'd like to focus on is the phenomenon of the second choice marginal.

Let's consider an imaginary constituency with just Tory, Liberal and Labour candidates (or one in which other, less popular candidates have already been knocked out in earlier rounds of AV). I use real party names rather than abstractions such as A, B and C not to express any party bias, but because it's easier to follow and easier to decide whether such a scenario could really happen. Suppose the first choice votes are roughly:

Labour: 15,000

Liberal: 10,000

Tory: 10,000

'Roughly?' I hear you bellow. 'Surely we must be accurate here.' Well, yes and no. If this were a First Past the Post election, then those kind of round numbers are quite clear enough to show that Labour wins. Of course, even under FPTP we have marginals if the two leading candidates are close, and then accuracy matters, but under AV we also have the possibility of this kind of second choice marginal (or, indeed, third, fourth of fifth choice) where precise counting even for second place really matters.

More marginals? Isn't that one of the key aims of AV; to force parties to genuinely campaign in more seats, rather than just focussing on the few marginals that matter so much under FPTP? True enough, but you might find that what they're campaigning for isn't quite what you'd expected.

Under AV the winning candidate needs to get more than half the votes cast, so in this case the winning post is 17,500. (Odd, isn't it, that it's AV that actually has the fixed finishing post, and so-called First Past the Post that doesn't?) No one here has 17,500, so we have to consider those second choice votes.

We can ignore the Labour second choices, because they're never going to be counted, though they'll probably be mostly for the Liberals. The Tory second choices are likely to be mostly Liberal too. Admittedly there may be a lot of support from Tories for, say, UKIP, but we're assuming they've been eliminated by now. At this stage, a Tory's second choice can only be Labour or Liberal (or nothing, but that's another story).

As for the Liberal voters, let's assume they spilt 50-50 amongst Tory and Labour. In reality, there might well be more of a bias towards Labour, but it doesn't much matter. With Labour only needing around 2,500 to win, the Liberal spilt could be up to 75% pro Tory, and the mathematics would still be much the same.

So, we had Liberals and Tories on about 10,000 each. Time to be specific. Let's suppose that the Liberal got 10,005 and the Tory 10,000. The Tory drops out and his second choice votes get allocated. We've assumed they're mostly Liberal and very few Labour, and so it seems reasonable that the Liberals will pick up the extra 7,500 they need and will win. This is exactly the sort of result that AV is supposed to achieve. The Liberals come second in the first round, but win on the second round.

But just suppose it goes the other way. Suppose it's the Tory who gets 10,005 and the Liberal 10,000. Then the Liberal drops out and his second choice votes get reallocated. We've assumed it's a 50-50 spilt, so Labour gets 5,000 more votes and wins. Just read that again:

The Tory is more popular than the Liberal and therefore Labour wins.

And on top of that, the difference is the matter of just a few votes. Under FPTP a few votes will matter in a marginal, but at least there a vote for Labour will help Labour, a vote for the Liberals will help the Liberals. Here it's the swing between Tories and Liberals that determines a result between the Liberals and Labour.

So what's a Tory voter to do? In this particular constituency, they know that their favoured candidate has no chance of winning, so the next best option is for the Liberal to win. But if they vote Tory first and Liberal second, that actually increases the chance of Labour winning, by pushing out the Liberal on the first round and thereby getting his second choices counted. It's a better bet for the Tory to vote Liberal first and Tory second, so that the Tory drops out and his second choice votes go to the Liberal. It's classic tactical voting; if you're a Tory afraid of Labour, vote Liberal.

In fact, it's better than tactical voting under FPTP. Not only does the Tory vote for the Liberal mean one more vote for the Liberals; if it makes the Tory candidate drop to third, it means thousands more votes for the Liberal as all those second choices get counted.

And it's not just Tories who can vote tactically. Remember the set up: Liberal second place is good for the Liberals; a Tory second place is good for Labour. So why don't a few hundred Labour supporters tactically vote Tory? It costs a few hundred votes, but if it pushes the Liberals into third and reaps a few thousand Labour votes it's a worthwhile reward.

In both styles of tactical voting, there is a powerful psephological lever in operation. Switching a small number of votes away from your first choice party can actually liberate a huge number in favour of the result you want. It may take a fair deal of voter management from the political parties, but guess what? - they're good at that.

And what about recounts? Let's go back to that scenario where the Tory gets 10,005 and the Liberal 10,000. That means Labour wins. The Liberal isn't happy and there's only five votes in it, so it's worth asking for a recount. But the thing is, the Tory (with Nick Berry's Every Loser Wins ringing in his ears) isn't happy with it either - because Labour wins. So both the winning and the losing candidate (in the second and third place play-off) will be asking for a recount. At least under FPTP it tends to be the loser who wants a recount and the winner who doesn't. It puts the returning officer in a difficult position of perhaps having to act against the requests of both candidates.

And will those candidates have enough information to decide whether a recount is worthwhile. With different second choice voting patterns, it's quite possible that the Labour candidate would win regardless of who comes second. Would the Tory and Liberal candidates know that before deciding whether it's worth bickering over the few votes that determine second and third place?

Of course, we've been looking at a specific example which won't occur everywhere. But with 650 constituencies, this sort of thing could crop up more than once, along with other permutations that aren't even dreamt of here.

Putting the numbers 1 to 9 nine in order has never been more of a challenge.