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:


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?



About RedEaredRabbit
My name is RedEaredRabbit, King of Kings. Look on my works ye Mighty and despair.

27 Responses to Pizza and Electoral Reform

  1. 2legs says:

    That’s decided then, I’m going to vote for pizza in the referendum.

  2. Richard says:

    I think what we really need are open primaries so we can select the candidates we want to stand, rather than arguing about imperfect systems to choose between candidates than no-one really wants in the first place.

    I also think there are much more pressing issues than a switch to AV. Who really cares about this other than Lib Dem activists? On the other hand, a lot of people would like us to leave the EU, and both the Tories and the Lib Dems promised a referendum on this in their manifestoes; so where is it?

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  4. Daniel Bolton says:

    Another excellent blog post.
    The point i would like to raise however is what is the point of change, the system we have now, seems to reflect the general wishes of the country. It was a shock when the Liberal Democrats didn’t win more seats but unfortunately the mood of the Nation seemed to think it was right for the Conservatives to gain power and they have just about managed that.
    Also it appears to me that AV promotes tactical voting, in which people vote for something they don;t nesseccarily want to stop a certain party gaining any votes from, example voting BNP over the Conservatives, when course the Conservatives is a better option.

  5. Dan Brusca says:

    “Some people also praise FPTP for its strength in delivering a majority government with a minority of votes.”

    Supporters of FPTP often point to the idea that it has a strong tendency towards producing majority governments, rather than hung parliaments, as one of its strengths. Truth is though that there’s nothing inherent in FPTP that leads to such outcomes.

    What FPTP does is entrench the position of the dominant political parties. For much of British electoral history we’ve had two dominant parties, initially the Tories and the Liberals, latterly the Tories and Labour. However if we’d had three dominant parties, polling around 30% each, FPTP would equally have entrenched perpetual hung parliaments.

    On the broader point of electoral reform, we need to consider what we want parliament to be. Do we want a parliament of representatives or a representative parliament? Both FPTP and AV produce the former, but not the latter.

    Given the subjugation of individual MPs to the party system, the idea of a parliament of individuals elected to primarily represent the interests of their constituents has been lost, so I feel parliament should instead reflect where broader political opinion lies, as manifested in the strength of individual parties at the ballot box. That’s why I favour true proportional representation via STV, but sadly nothing approaching that is on offer.

  6. FoleyIsGood says:

    @Daniel I think you are exactly wrong re tactical voting. With FPTP, your preference may be for a candidate with little perceived chance of beating the front runner, who maybe you really don’t want to win; so you vote for the second placed candidate instead. Tactical.

    With AV you simply list candidates in your order of preference, no thinking about tactics is needed.

    Good post btw!

  7. Andrew says:

    One element on which I’m unclear.

    At the end of the first round of AV we eliminate pepperoni, meaning that in the next round 11 votes are eliminated from the pool entirely. If we left it that way the decision would be made off the back of just 4 votes – not a representative sample by any means.

    However, in the results above the second round totals are Meat Feast 7 and Margherita 8, implying that those 11 disappeared votes have been redistributed among the remaining candidates. If this is the case, did you do this arbitrarily (well, you know what I mean, arbitrarily so that the numbers suited the point you were making in this post as you mentioned above)?

    Unless we were to hold separate rounds of voting e.g.
    1) First round happens on 6th May, counting takes place overnight
    2) Pepperoni is eliminated
    3) Voters who assigned pepperoni as their second choice are then asked to go back to the booths on 8th May to redistribute their second choice votes

    I don’t see how we can know where those 11 votes for the now disappeared pepperoni should go.

    • If you look at the raw data, four people chose pepperoni as a first choice.
      Three of them chose margherita as a second choice an one chose meat feast as a second choice.

      Therefore after the first round elimination, 3 votes are added to Margherita and 1 vote is added to Meat Feast.

  8. James says:

    I quite strongly disagree with the assertion that the Borda system is fairer than either of the two on offer. There’s nothing inherent in the Borda system that would mean it will always produce a winner who would win in a run off against any other candidate and, in fact, it’s the one system in which some of the lies that are being presented about AV would actually be true. You mentioned that you had rigged the numbers in your example to support your illustration, and in it you show the candidate who was coming last on first preferences going on to win. That’s not the full extent of it though: under the Borda system it would actually be possible for a candidate to win who was nobody’s first choice. Specifying a second preference actually harms your chances of getting your first choice elected!

    The Borda system is also dependent on an assumption that you can in some way put a numerical value on people’s level of support for candidates, something which is clearly false. My commitment to the candidate I vote for is entirely subjective, and it is not the job of an electoral system to try and measure it in that way. The fact that I prefer one candidate over another doesn’t mean that I prefer them two points more.

    From what you’re saying, it sounds like you much prefer something like the Schulze method, but I suspect that’s a level of complexity the electorate at large might not be quite ready for!

    • I think “rigged” may be a bit strong. I intentionally used a set of results that would help illustrate the differences between the three systems.

      In the Borda Count the voter just ranks the candidates in the order they prefer, the system then assigns points. The voters aren’t being asked to score them out of 3 or anything.

      I don’t by any means think it is perfect but I think the other two throw away information that the Borda Count uses.

      I also don’t think it is a big problem that it can select a winner who was no one’s first choice. Suppose there are 10 Grand Prix drivers, 9 finish the season with 1 win each and no other finishes. The 10th gets 9 second places and no wins. It wouldn’t be unreasonable in those circumstances to award the championship to the driver with 9 second places.

      You do make a very well reasoned argument though and I don’t think either of us is right or wrong. We just see things a little differently.

      Oh, and I had a look at Schulze. Yep – too complicated.

      • James says:

        🙂 Well, you chose a set of results that illustrate the strengths but not the weaknesses of your preferred system…

        A lot of people clearly do find the idea that the idea of a winner who’s no one’s first choice a problem, as it’s falsely being put about as a reason to vote against AV. I don’t really think voting is like a Grand Prix. We’re not trying to find some mythical objective best candidate. We just want to find the preferred choice of most people. It’s hard to see someone as the preferred choice of the majority, when everyone would have chosen another above them.

        The real question though is, knowing specifying a second preference could harm the chances of my first choice getting elected, why would I do it? It’ll be better for my first choice if I vote only for them. If I want to keep another candidate out it’ll be better for me to vote tactically and first preference the person with the best chance of beating them, harming my first choice still further. AV avoids all of those issues, being not just fairer than the present system, but also practical.

        But, you know, thanks for at least posting something that tries to look honestly at the issue. As you say, better than a lot of people are doing!

      • I didn’t mean to choose a set of results which showed only strengths of the Borda Count and I’m not really sure I did. The set of results was chosen simply to illustrate that different methods could lead to different results with a perfectly reasonable set of data. Borda Count chooses Pepperoni. It’s up to the reader to decide whether they think Pepperoni is the best choice given the whole set of preferences. Looking at the summarised data alone I couldn’t really say which one was the fairest victor.

        I like Borda Count better but I don’t think that the data in my table says that one is any better than the other – just meant to help show the differences.

        I think Borda Count assumes that everyone must rank all candidates rather than penalising people who do or don’t put second or third choices. While that in itself causes problems, I suppose it’s all a case of weighing up the problems with that system vs the problems with any of the others.

      • Brad Beattie says:

        Too complicated? Maybe the wikipedia page could use some cleaning, but consider this description:

        I agree that it’s more complicated than FPTP, but it’s not that different complexity-wise from the other systems we’re describing.

      • Hello Brad.

        I agree that system is definitely worth a look when there are 4 different candidates as in the example on the link but on the ballot paper I had last year there were 10 candidates. That would mean 45 individual answers required from each voter! I think although it could be argued as more fair than FPTP it might not be practical. Remember the queues of people who didn’t get to vote using FPTP last year? Given the number of answers each voter would need to give it would probably increase voting time significantly and would therefore require many more polling stations and voting staff in order to get through all of the voters.

        Thanks for providing an alternative suggestion though!


      • Brad Beattie says:

        > That would mean 45 individual answers required from each voter!

        The example that I’ve shared was specifically tailored to small candidate sets and non-balloted scenarios (a friend wanted something other than FPTP for book club choices).

        If we can use ballots, we can limit the number of questions per voter to N (where N is the number of candidates); Just have the voters rate each candidate out of 5 stars or so, then infer the pairwise preferences from that ballot. The approach has worked well for me on

      • Your Zombie vote is brilliant!

        I do see a problem with applying this to a general election though. Suppose I were a Labour voter. I would vote Labour 5*. I would vote everyone else 0*.

        Although in reality I would probably be better off with a Conservative government than a BNP government, knowing that the Conservatives were more of a threat to my first choice I would unfairly mark them down.

        If you could prevent people from abusing the system then I think this could be the fairest one but it is so open to being abused….

      • Brad Beattie says:

        > I do see a problem with applying this to a general election though. Suppose I were a Labour voter. I would vote Labour 5*. I would vote everyone else 0*.

        Note that your ballot scenario is no different than Labour 1*, others 0*. Also no different from Labour 5*, others 4*. All it’s inferring is the pairwise comparisons between your rankings (that is to say, we’re not using the magnitude, just the ordering). Setting it up as a ratings ballot is only for ease of use as people do 5-star ratings all the time (restaurants, movies, etc).

        See for another conversion example.

      • My scenario of Labour 5* everyone else 0* not being any different to Labour 1* everyone else 0* was my point. If people decide to vote tactically then this system is no different to FPTP.

      • Brad Beattie says:

        > My scenario of Labour 5* everyone else 0* not being any different to Labour 1* everyone else 0* was my point. If people decide to vote tactically then this system is no different to FPTP.

        Ah, I see what you’re aiming at there.

        Labour:5 Conservative:0 BNP:0 generates Labour>Conservative, Labour>BNP.

        Labour:5 Conservative:3 BNP:0 generates Labour>Conservative, Labour>BNP, but also a Conservative>BNP. Your preferences for Labour over the other two parties are maintained.

        With that in mind, there’s little tactical advantage to ranking Conservative:0 (though I’ll concede that there are scenarios where tactical voting can occur). Still, I’d argue that it doesn’t devolve into FPTP and it’s still stabler than AV. Wikipedia has a decent summary of the criteria met by this method:

      • James says:

        I’ve just been reading all around the voting system pages on Wikipedia again and, I have to say, I think later-no-harm is a much more important criteria than the site gives it credit for.

        When I stood in an AV election in my students’ union a few years ago, one of the most common questions I got about the voting system was “does putting a second choice harm the chances of my first?” I’m really surprised it’s not come up more in the discussion of this referendum. Unless you can somehow obfuscate the fact, I can’t see many people deliberately sabotaging the chances of their first choice being elected.

        I think FPTP’s failing of the Condorcet loser criterion is probably its greatest weakness. The principle of looking for a Condorcet winner seems like a good one, but until there’s a system that does it whilst retaining later-no-harm, I think you’re going to struggle to get people to vote honestly.

        Nice videos though Brad. I wish we had some that clear and simple that linked to information about the AV referendum.

      • Brad Beattie says:

        > I think FPTP’s failing of the Condorcet loser criterion is probably its greatest weakness. The principle of looking for a Condorcet winner seems like a good one, but until there’s a system that does it whilst retaining later-no-harm, I think you’re going to struggle to get people to vote honestly.

        The downside is that the Condorcet criterion is incompatible with later-no-harm ( A rough proof of this is to note that Condorcet methods need to inspect all possible preferences. Later-no-harm methods need to ignore preferences until necessary. So yeah, we can’t have both.

        I think we’re mostly on the same page, though we weigh these criterion differently. A while back I made a tool that lets you sort criterion by priority, then it tells you what voting methods meet your ordering: . I didn’t know about later-no-harm at the time, but it wouldn’t be too difficult to add in.

        Makes me wonder under what conditions later-no-harm is objectively more important and likewise with the Condorcet criterion. How do we take this beyond “I think this criterion is more important” to a more reasoned “This criterion is of higher priority when…”.

        Anywho, food for thought. Cheers. 🙂

  9. Andrew says:

    Ah I see, so the first round votes are ADDED TO the second round votes if no one wins outright in the first round. For some reason that’s never clicked before.

    Thank you!

    Of course fans of proportional representation would ask why they couldn’t all just order enough of each pizza that everyone gets a share of what they like best. What do the vegetarians do in the parliaments where Meat Feast and Pepperoni win? They go hungry.

    I think I’m overstretching your metaphor.

  10. a6ruled says:

    i struggle with this

    AV is a a complicated idea – it’s not my field but i guess you’d need some horribly complicated mathematical modelling to understand what’s likely to go on with it – the killer complexity in that for me is where you don’t have to rank all the candidates (apparenly you do in Australia but not always) – so some people rank all 6 some rank 3, some just put a 1

    if mrs a6, our friend john and i were voting on pizzas and the choices were: pepperoni, anchovy, goat’s cheese

    john would vote
    1: pepperoni
    2: goat’s cheese
    3 anchovy

    the thing is though that ranking says nothing about strength of preference – john likes pepperoni and goat’s cheese about the same but he likes them *much more* than anchovy – he’ll eat anchovy though

    i would vote
    1: pepperoni
    2: anchovy

    and that’s it – i would rather have ‘no pizza’ than goat’s cheese

    mrs a6 would vote
    1: goat’s cheese

    she’s vegetarian. . .

    i am confused and worried by this – the ranking element worries me

    we can’t think of the ranking in sensible human terms because it’s still a made-up system – we’re not sucking ‘real’ preferences out of people heads here we’re giving them a system within which to try to achieve some sort of objective

    if i had the choice, i wouldn’t rank conservative or UKIP. but if lots of conservative voters had UKIP as a second choice and i hadn’t put conservative as my second choice would that advantage UKIP? but then if i have to rank all of them then i my find one of my (forced) choices electing someone i don’t want.

    ps: if you failed to follow that, think how i feel

    • I agree that ranking doesn’t say anything about the strength of the preference but I don’t think any system on here is perfect. I just think FPTP throws away a great deal of useful information which in using a ranking system the others try to take into account.

      I don’t think some people ranking more choices than others is a problem. If there’s only one you like and you dislike all other equally then just vote for one – as soon as your choice is eliminated you don’t give a toss who wins anyway.
      If you dislike Conservatives but dislike UKIP more then rank them in that order. Your conservative preference would only be taken into account if the people you ranked above them were eliminated.

  11. McDa says:

    I agree AV is is not the best but it is more democratic and ‘Hobbsean’ because it allows more people more choice…Lovers of FPTP remain enfranchised as they retain their option to vote just for one candidate and reject all others, while the rest of us who think we should have options are also catered for and those who reject the whole thing can still turn their back on their right to vote and stay at home.

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