Pizza and Electoral Reform

Politicians have recently been spouting a lot about the inefficiencies of the public sector. Well if it’s true, no better example could surely be found than the politicians themselves. After literally months of hundreds of them pissing around at our expense they finally decided yesterday that there would be a referendum on electoral reform. In the referendum we will be given two choices and asked to vote for the one which we think is the fairer system of electing future governments. The choices will be:

• First Past The Post (FPTP) – our current system
• Alternative Vote (AV)

I will be honest – I don’t know which system is fairer and that is a bit of a problem. I don’t consider myself badly informed with what is going on in the world. I am reasonably good at maths yet still I don’t know off the top of my head which system is fairer.

This is a problem not because of my personal dilemma but because I strongly suspect that I am not alone in not knowing which system is fairer. I am fairly sure there are a large number of people in the country who, like me are going to be asked to decide something they don’t have the information to properly decide.

Yesterday, I asked my Twitter followers which system they preferred. It looked like this:

Wow – almost 1 in 3 of us don’t know. If you are one of those people then look no further. I am going to work it out here on this blog and then we’ll all know. Hoorah! So let’s do it with an example.

15 friends are ordering a pizza to share from The Very Big Pizza Company. There are three options:

• Meat Feast
• Pepperoni
• Margherita

Between them they need to decide on which pizza to get and so they take a vote. Their preferences look like this:

The voters

Summarised, their preferences look like this:

Voters

If they use a FPTP system then only their 1st choice preferences are taken into account so, with six votes, they will get a Meat Feast.

If they use AV however then it works like this:

Round 1

• Meat Feast – 6 votes
• Pepperoni – 4 votes
• Margherita – 5 votes

In AV, Pepperoni with the fewest first choice votes at the end of round 1 gets eliminated and the Pepperoni lovers’ second choice votes are added in for round 2…..

Round 2

• Meat Feast – 7 votes
• Margherita – 8 votes

Margherita is the winner.

Two different systems – two different results. While we’re here though, let’s look at another system called the Borda Count. In this system 3 points are awarded for a first choice, 2 for a second and 1 for a third. Points are all added up to determine the winner. It’s a bit like what happens in the Eurovision Song Contest.

In this system we find the following:

Borda Count Results

Pepperoni, with 34 points has won.

Three different systems – three different results. So what does all this tell us? It tells us that the voting system we employ can make a big difference to the outcome of the election. With three different systems and the same set of preferences we observe 3 different outcomes.

You might think I intentionally set the group’s preferences such that this would happen. Yup, I did. But it may not be too far from reality. Imagine that it’s May 2010 and Meat Feast is the Conservatives, Pepperoni is the Lib Dems and Margherita is the Labour Party. The different outcomes here have essentially occurred because:

• More people preferred the Conservatives as a first choice than preferred either of the other two (but importantly not an overall majority)
• The Lib Dems are most often the second choice of both Conservative and Labour voters
• Lib Dem voters are more likely to prefer Labour than Conservatives*

* I’m not sure whether this is actually the case but it doesn’t make it an implausible set of preferences.

So I have looked at three different voting systems and they produced three different winners but which is the fairest? Nope, I still don’t know. Let’s keep going.

First, let’s go back to the FPTP system where the group have decided to vote for Meat Feast.

They phone up The Very Big Pizza Company. Before they can place their order, they are informed that unfortunately there are no more Pepperoni pizzas left. Doesn’t matter, right? In the vote Meat Feast came first, Margherita second and Pepperoni came last. The fact that Pepperoni isn’t on the menu doesn’t cause a problem. Or does it?
Anna, on the phone relays this message to the group and they do the FPTP vote again based on Meat Feast or Margherita. Now Margherita wins on the FPTP method!

To me this seems like a big problem. In a fair electoral system, if people prefer Meat Feast to Margherita then the outcome should always reflect this, irrespective of whether or not Pepperoni is available.

FPTP says that if Pepperoni is on the menu then Meat Feast is better than Margherita and if Pepperoni is not on the menu then Margherita is better than Meat Feast!

So FPTP is cack then. Let’s look at the AV in comparison. After the AV vote they phone up The Very Big Pizza company to order their Margherita and find that Meat Feast is off the menu. Now Pepperoni wins. Bollocks.

If AV is a fair system then if it prefers Margherita to Pepperoni when Meat Feast is on offer, it should prefer Margherita to Pepperoni when Meat Feast is not on offer.

Aaargghh. All I have done so far is to find that neither is fair.

When you look at the summarised table of votes above, AV does have a clear problem. Pepperoni had loads of second place votes but these all got ignored because it was eliminated before they could be taken into account. 11 people liked Pepperoni second best but the system treated it the same as if no one had liked it second best.

When you look at FPTP though – it doesn’t just ignore all the second and third place votes for Pepperoni. It ignores, by definition, everything that wasn’t a first choice vote.

My view is that when you need to make a decision about something, you should take as much of the available information into account as possible. AV, while not perfect takes more information into account than FPTP and it is on that basis I think, a fairer system.

Let’s not though, forget about our third option – the Borda Count which we sadly will not get the option to vote for. That system takes every preference into account and I therefore think it is a fairer system than either of the two from which we can choose.

Formula 1 uses something not too far from the Borda Count to decide the world champion. Would Formula 1 be fairer if driver’s second places, third places etc were not taken into account when deciding the World Championship? Bernie Ecclestone thinks so but I don’t. I think a driver with 5 wins, 8 second places and 2 third places has more claim to be World Champion than a driver with 6 wins and 9 races that they didn’t finish.
The Borda Count system is by no means perfect but it allows us to take a lot more information into account than a simple FPTP.

This is not the whole picture though. Even if everyone agreed on the fairest system they would not all necessarily vote in the same way. For a start, some systems are more likely to benefit certain political parties. The Conservatives don’t really think FPTP is the fairest possible electoral system, they just think they will have a better chance of winning a majority than they would with the others. If the party you like the best is going to do better out of a particular system why would you want to vote for an alternative in which they would do worse?

Also, the best system may not be the fairest system. FPTP is the simplest system by far – one cross in one box and you’re done. The more complex the system becomes the harder it is for people to understand and cast their vote. A clever mathematician could come up with a brilliantly fair voting system but if a significant proportion of the electorate didn’t understand it or couldn’t work out how to fill in their ballot papers, it would be worthless.

Some people also praise FPTP for its strength in delivering a majority government with a minority of votes. That doesn’t necessarily sound like a good thing to me but if people really think it is a good thing then why should they not vote for a less fair system in order to achieve it?

Irrespective of these there is something much worse which will undoubtedly have a strong influence on the result of the referendum – the campaign of misinformation which I can see on the horizon, heading for our shores like a giant wave of bullshit. Political parties, unions and other groups will no doubt know which of the two systems benefits them the most and they will undoubtedly be feverishly preparing their campaigns to scare the public into believing that one system means 100 years of darkness to the UK.

On the Today Programme the other day, James Frayne who ran the successful campaign for the Conservative Party to vote No to a North East regional assembly said that because Nick Clegg is so unpopular, the best tactic for the No2AV campaign (yes, they’ve already made a name like a fucking X-Factor band) would be to say if you vote AV you will get Nick Clegg in government again.

It’s shameful that on one hand we will be given a chance to vote to change the electoral system and on the other hand we will be drowned in this kind of crap designed solely to mislead us. Will any political party in the next few months spend time and effort really trying to explain the underlying good points and bad points of each system in a bid to assist the voters into making an informed choice? I hope so but I don’t think so.

So – what have I concluded?

• AV has big problems and probably isn’t a great system but it is fairer than FPTP
• The Borda Count is fairer than either of them but isn’t available
• A fair system is not necessarily the best if it is overly complex to understand
• Even if people agree on what the fairest system is they will still not necessarily vote for it
• There will be a massive campaign of misinformation which will significantly influence the choice of voters

Well, to be honest, I’m disillusioned by the whole thing now. Bollocks to this. Anyone for Pizza?

RedEaredRabbit