Maths of the voting system referendum

Let's be honest, there's a lot of ridiculous arguments coming out from both sides in the Yes to AV and No to AV camps. I decided to write this short guide to my understanding of the referendum so far, partly to clarify my thoughts, and partly to help anyone who may be thinking along the same lines as me. I welcome comments and other points of view, as well as any "yes" or "no" arguments I may have missed out.

I've tried to be as fair as I can as I haven't yet decided myself which way to vote, although I'm currently hedging towards "yes" -- not because of any political allegiances, or indeed the strengths of any of the two campaigns' arguments as we'll see, but because of the maths.

Acronyms (in case you needed to know) are First Past The Post, the current electoral system, and AV, the proposed new electoral system.


"No" campaign arguments

1. "It's too expensive; the money should be spent on soldiers / children / sweets for midwives"
   The referendum is already taking place, so the argument is moot. In terms of the actual cost of running the elections, it's admittedly going to be more time-consuming to count the votes under AV. But talk of electronic voting machines being necessities is disingenuous; if they are ever introduced, they would cost pretty much the same if used for FPTP elections. This argument is quite a desperate one; the same argument could be used to say "the NHS is too expensive" or "the Royal Family is too expensive".
   
2. "It will let extremists get in"
   This is an important argument. The argument goes that more people are likely to vote for smaller parties with AV, so parties such as the BNP stand a real chance of getting in. Yet, because of the requirement in AV for candidates to reach 50% of voter support, this actually makes it harder for the likes of the BNP to win.
   
   For Nick Griffin to become an MP, at least 50% of all voters in his constituency must put him down as one of their choices, AND enough of them have to put him down as their first choice for him to be able to get through the first round (and so on for however many rounds it takes). Is that ever really likely to happen?
   
   And yet, if it did happen, then by the arguments of democratic representation he should win (especially as he would have won under FPTP too anyway; in fact he could win with just 20% of the vote under FPTP if the other 80% was split across a number of other candidates, each with less than 20%). Democracy is no good if you tell people that their majority-elected candidate can't be an MP, no matter how much of a dick he may be.
   
3. "It destroys the principle of one person, one vote"
   An important point. This is how I see it: if the result of a FPTP election was inconclusive, everyone would be polled again, and again, until the result was clear. But this isn't counted as voting multiple times, as everyone has the same opportunities to vote each time.
   
   AV sets the bar for winning at 50%, so it simply has the effect of increasing the likelihood that the first round of voting gives an inconclusive result. Everyone is therefore "re-polled", but the least successful candidate drops out. This would mean that anyone who voted for that candidate actually loses their vote; so these people's second choice vote is used instead. It's still only one vote per person that actually gets counted by the time a winner has been found.
   
4. "It's too complicated"
   It's clearly not so complicated that the Tories, Labour, and many other political bodies use it to elect their leaders. The Electoral Commission leaflet which dropped through everyone's doors recently explains it clearly with diagrams so I won't repeat it here. Needless to say, from the voter's point of view the only difference is that they can either still choose just one candidate, as under FPTP, or they make a second, third, fourth, etc. choice in addition should their first choice candidate drop out of the re-counting in subsequent rounds.
   
5. "We want to stick one up at Nick Clegg"
   The anger over the Lib Dems' U-turns is understandable, particularly over issues such as tuition fees and spending cuts, but using petty personal vindictiveness as a reason to vote for or against such a historic change to the way the country is run is shooting yourself in the foot.

"Yes" campaign arguments

1. "It will make MPs work harder for your vote"
   I think a lot of MPs already work very hard. Mine certainly does. By the implication of this argument, if one candidate works less hard, another candidate will get their votes by default, so that's no different from FPTP either. Ultimately, someone will win in each constituency under FPTP or AV, even if they're just the best of a bad bunch. A pretty weak argument, yet it's the main thrust of the "yes to AV" campaign.
   
2. "It maintains the principle of one person, one vote"
   See point 3 in the "no" campaign. As well as maintaining one counted vote per person, AV would reduce the effect that a handful of marginal seats has on the overall make-up of Parliament. At the moment, sometimes the Tories or Labour win enough marginal seats from each other to give them an outright majority of MPs in Parliament. The majority of voters in the other "safe seats" under FPTP have a much smaller effect on the final national outcome, but AV increases the likelihood that elected MPs represent the constituents' preferences by eliminating tactical voting (see below).
   
3. "It's proportional"
   No it's not. It levels the playing field in constituencies with more than two candidates (i.e. pretty much all constituencies) but Parliament is still made up in exactly the same way: the biggest number of seats wins. So the electoral system is still FPTP at its heart, and it will still be possible for any party to win control of Government with less than 50% of the national vote.
   
4. "We want to stick one up at David Cameron"
   See number 5 in the "no" campaign....

The Maths

As you can see, neither camp has particularly killer arguments; certainly not strong enough to sway me one way or the other either way. The reason I'm hedging towards "yes" is not towards political allegiances of any kind, but because of the multi-party political system we use, and the maths behind it.

Let me explain:

Imagine a constituency, much like any other around the country today, where traditionally there is one party which does well (say the Tories) and another which is the main contender (say Labour). The electoral system is FPTP. If you're a left-of-centre voter (e.g. Lib Dem or Green) you have to vote tactically to stop the Tories winning; your vote has to go to Labour regardless of your true allegiences if you want a left-of-centre candidate to win. The system only allows for two real contenders and therefore encourages tactical voting whenever there are more than two candidates.

Now imagine the same constituency under AV. You might be a Green person at heart, but rather than having to vote tactically for Labour to stop the Tories, you can safely vote for the Greens knowing that if, as expected, hardly anyone else does, your vote isn't simply thrown away. If you put Labour as your second choice, and the Greens are eliminated early in the counting, then your vote still counts towards a left-of-centre candidate. AV allows a level playing-field for all parties in constituencies with more than two contenders whilst ensuring that a voter's true left/right preferences are recognised, which eliminates the need for tactical voting.

(It's easy to imagine these scenarios for a right-of-centre voter too, eg. preferring UKIP whilst voting tactically under FPTP for the Tories to keep Labour out, before I get accused of bias).

So that's the maths behind the voting system. In a country with just two main parties, such as the USA, FPTP makes sense. In the UK, which prides itself on smaller and independent parties, FPTP squeezes them out in favour of the two biggest parties, whichever ones they may be (and they may not always be Conservatives and Labour). I guess your choice is between these two principles.