Carry on Condorcet

Who cannot criticize an election when only 36% of the vote wins an election? After all, that is what happened to British Labour in the UK 2005 general elections. So John Quiggin calls for electoral reform, and a scrapping of the First Past the Post (FPP) system used in that election. Not only would it be good for British democracy, he argues it would also be good for Labour. Under a preferential system, he assumes:

On the plausible assumption that Labour would get 70 per cent of Lib Dem and Welsh/Scottish nationalist preferences, and the Tories would get 70 per cent of the rest, I estimate a two-party preferred Labour vote of about 57 per cent.

Unfortunately, the comments got thread jacked by one "Benno", claiming (and at times aggressively so) that the Condorcet system should be the way to go. To quote him (perhaps out of context):

I will roll anybody who claims that PV is superior to Condorcet.

Hardly a debating argument. But is he right? Let us compare and contrast with single member elections - elections where only one candidate can win. 

"First past the post" is the simplest electoral system. The voters put just one tick (or cross, or whatever) next to their favorite candidate. The electoral office count up the votes for all of the candidates. Whoever gets the most wins the election. That's the status quo in Britain, and we see it didn't work very well.

It's sole advantage is its simplicity. That can be an advantage if the electorate has a low level of literacy, as is happening now in Ethiopia. One common tactic is for the ballot papers to provide both the candidate's name, and a picture or icon representing the party. But for electorates with high levels of literacy (such as Britain), you can expect the voters to be able to read the candidate's names, and be able to write beyond one.

And therein lies the disadvantage of FPP - the old "tactical voting". You really like A, you think B is so-so (but more electable), and C are complete and utter bastards. Since you don't want C to win, you have to choose between A and B. But a vote for A deprives B of enough votes to win, so C romps in. Thus you hold your nose and vote for B. A is effectively a "wasted" vote. This sucks. I think we can do better than that.

The alternative is to let the voters rank the candidate one after another. Your favorite candidate gets "1", the second gets "2", and so on. These are known as preferential systems. In this system, you can vote A, then B, then C... and you've done your best for A to win, and C to lose. (This will probably end up with the compromise of B winning, but at least there's now a chance that A will romp in.) There are several ways to do this,  but we'll look at two: IRV and Condorcet. Which one is it going to be?

IRV (Instant running voting) is a the system used in lower house Australian elections - although everyone there knows it as "preferential voting". The votes number every box in their chosen sequence. The electoral office counts everyone's vote, and stacks them by first preference. Who has the smallest pile - the least number of first preferences - drops out. Now their preferences are distributed to other piles going by their second preferences. Then the next smallest pile is eliminated, and are split up to other piles by the highest remaining preferences. This goes on until you have two piles left - with one hopefully larger than the other. There is your winner. 

Condorcet counting is a stranger beast altogether. I'll quote the Wikipedia article:

Ballots are counted by considering all possible sets of two-candidate elections from all available candidates. That is, each candidate is considered against each and every other candidate. A candidate is considered to "win" against another on a single ballot if they are ranked higher than their opponent. All the votes for candidate Alice over candidate Bob are counted, as are all of the votes for Bob over Alice. Whoever has the most votes in each one-on-one election wins.

But the next paragraph shows a problem with the system:

If a candidate is preferred over all other candidates, that candidate is the Condorcet winner. However, a Condorcet winner may not exist, due to a fundamental paradox: It is possible for the electorate to prefer A over B, B over C, and C over A simultaneously. This is called a majority rule cycle, and it must be resolved by some other mechanism.

So you choose one of the various paradox-resolving methods - there are about 6 or 7 mentioned in the article. But as "Benno" says, you only need one count to decide the winner. But is that really an advantage?

In an election, you want transparency, and transparency is not only assumed by honest electoral officers, by also by scrutineers – supplied by the political teams running for the election – to look at the papers as they are being counted. You can use optical character recognition or what ever fancy technique you want... but if you can't produce ballots to be counted, it ain't worth shit. (Even open source electoral systems could have bugs, and as for those who aren't, think Diebold.)

As an ex-scrutineer, I can assume you that IRV is quite easy to scrutineer. You observe (but don't touch) the electoral staff stacking ballots in separate piles by their first preference. You can almost go on autopilot. But if you see a 1 go into the wrong pile, or a 2 into another, you could request (not order) the electoral officer to have a look at it. Once preferences are redistributed, you look for 2's on the ballots. And so on. It is slow, and sometimes monotonous, but it is sure., and it doesn't take too much mental strain to do. You look at one ballot paper at a time, and there is only one piece of information important at each stage.

God knows how you would scrutineer a Condorcet election. Let us say you have n candidates on a ballot paper. You have to consider their ranking against the (n - 1) candidates. Split the multiple by two (if candidate A is ranked against B, you don't need to rank B against A). For each ballot paper, you have to check that the electoral officer did the right thing with n(n-1)/2 pieces of information. Now assume you have a couple of hundred of other ballot papers... you would go mad. And we haven't encountered a Condorcet paradox yet. Now imagine your average scrutineers (which are generally normal men and women, even if a little high on the party hack-o-meter) deal with jargon like "Smith set" and "Schwarz set" and "Minimax". It is going to strain the scrutineers. They're going to need the metaphorical cigarette break every five minutes. You don't want that. I've dealt with honest electoral staff - in Australia. That's the exceptiom, not the norm. 

And as you can see, Condorcet is harder to understand than IRV. That's not a sneer; a lot of things in life are hard to understand. But it is a big hurdle when you are dealing with an electoral system used by everyone. Systems should not only be fair - they should be seen to be fair. And the jargon of Condorcet has a danger of frightening people. It may not happen (although it sounds like perfect scare-campaign material), but you have the ever-present possibility of sending the voters back to FPP territory.     

Another big hurdle for IRV detractors (as say, from the Condorcet camp) is that it has been empirically tested. For example, Australia has over 100 years with the system, beginning with Queensland in 1893, and extended to federal elections in 1918. My rough estimate of the ballots cast under the system in that time span would be in the order of a 100 million, at least. And only for Federal elections for the House of Representatives. You'd double that for State Elections. IRV has been shown to work  Condorcet has also be implemented for such institutions as the Debian and UserLinux project. But these are small institutions, and the electorate has been pretty limited in number. It hasn't had the mass-market exposure of IRV. 

I admit I am biased towards IRV; it has been the electoral system I have lived with, scrutineered, and even worked with (as an electoral officer in an University election). I find it intuitive to understand. However, I don't have anything against Condorcet. It may be a more mathematically thought-out electoral system, in that it satisfies more electoral "criteria" than IRV. But I feel at this time that such criteria are really irrelevant to the punters.

This brings us back to British Electoral reform, which would probably be kicked off by a Royal Commision. Submissions would be requested. Recommendations would be presented back to Parliament. Hopefully, the recommendations would include a British wide-referendum on replacing FPP by some preferential or proportional alternative. Even better, Parliament acts upon it, and passes an Act for this purpose. Best of all, the "Benno"s of this world shut up, or at least learn how to be polite. It doesn't matter if they support IRV or Condorcet. The rudeness he displayed on JQ's thread would go down badly with a confused electorate. With enemies like him - the first past the post  system doesn't need friends.