It will come as little surprise to long-time readers of this blog that I will be voting yes in the alternative vote referendum on Thursday. But now that the focus of this blog is less on politics, I haven’t actually written much about it. With just a few days to go, until polling day, I have decided that now is the time.

The deceptive claims of the No to AV campaign have been comprehensively taken apart umpteen times elsewhere, I am sure. But one section of the No to AV leaflet particularly irritated me.

It shows a group of four runners crossing a finish line on a running track. A big arrow points to the trailing runner who appears to cross the finish line in fourth place: “The winner under AV”. The message? “Awooga! AV is unfair because the loser wins!”

I don’t know a great deal about athletics, but I am pretty sure that there is a fixed finish line. The first person to complete the set distance wins the race. It might be 100 metres. In this photograph here, it is the man in blue who ran 100 metres first.

But what is the distance in a voting system? I have tried to work out what it is under first past the post, but I cannot tell. Here are some examples from last year’s UK General Election. Can you see where the finish line is?

It is pretty clear in Kirkcaldy and Cowdenbeath, where I used to live. With 64.5% of the vote, a clear majority were in favour of the Labour candidate.

In my neighbouring constituency of Dundee East it is somewhat less clear. No party received a majority of the votes. Second-placed Labour took 33.3% of the vote. But the winning SNP took 37.8%. It’s not very cool. The SNP might not be what the majority of voters wanted.

Anyway, we have narrowed the first past the post winning threshold down to something between 33.3% and 37.8%.

But looking at the results for Argyll and Bute, the “finish line” analogy becomes really confusing. The first-placed Lib Dems took only 31.6% of the votes. But Labour had 33.3% of the votes in Dundee East, and came only second there.

In first past the post, the finish line changes position. In fact, there is no finish line. It doesn’t matter if you don’t get a majority of the votes. Theoretically you could get an extremely low share of the vote, far from a majority, yet still win under first past the post.

So which is the system where the loser can win?

Alternative vote sets a threshold where candidates must aim to gain the support of the majority of voters. A candidate is not deemed to be the winner until he crosses the finish line, which is unambiguously 50%.

(It is theoretically possible for a candidate to win under alternative vote without crossing that threshold — but only in unusual circumstances and after all other options have been exhausted.)

Alternative vote may not be perfect (although the perfect voting system doesn’t exist anyway). But it is a whole lot more desirable than the current rotten system.

The decision to vote

A series of posts

1. A pathetic situation
2. Five disturbing things about democracy
3. How should politics be reformed?: Part 1
4. How the new politics might look: part 2
5. European election leaflets: The main parties
6. European Parliamentary Election literature: small parties
7. A second opinion
8. I decided! And I decided to vote

Here it is: that post I’ve been sitting on for upwards of a year. Before I start, I am going to make a few introductory notes about what I do and don’t mean when I call democracy disturbing. I find that all too often debates about this subject are clouded by dogma, which leads to poor thinking and boilerplate arguments.

Before some cheesy person wheels out that Churchill quote about democracy being the worst system apart from all the other systems, yes of course I have heard it. And it is true. I am a democrat because I believe it brings about favourable conditions. For instance, there is the correlation between democratisation and higher GDP per capita. (Whether democracy is cause or effect does not matter. If the value of the higher GDP per capita is greater than the cost of democracy per head — as it almost certainly is — then democracy is a price worth paying.)

Furthermore, I should define more closely what I mean by democracy. Most of the flaws I will point out are actually problems with elections rather than democracy as a whole. Aspects of democracy such as civil liberties, human rights, freedom of speech, the rule of law, due process, and so on and so forth, are of course things that I am deeply supportive of. This will become clear in my first point.

I tackle the issue not from an anti-democratic perspective. Far from it. My problem is with the approach which sees democracy almost like a religion which ought not be questioned — what Bryan Caplan in his book The Myth of the Rational Voter called “democratic fundamentalists”:

Its purest expression is the cliché, attributed to failed 1928 presidential candidate Al Smith, that “All the ills of democracy can be cured by more democracy.” In other words, no matter what happens, the case for democracy remains untouched.

No case should remain untouched. That is why, for me, there is not enough scrutiny placed on democracy. There is a fear of investigating it, because the benefits of democracy are perceived to be so self-evident that anyone who stops to ask what the disadvantages are is instantly regarded as a fool. That must be dangerous. If we agree that the system is imperfect, the only way to improve the situation is to investigate it and have an awareness of what the problems are.

Just as a final point, much of my thinking in this area came about as a result of the research I did for my dissertation, which was about the “paradox of voting“. In case you want to read more about voting behaviour, I have uploaded my dissertation here.

Having got all of the caveats and explanations out of the way, it is time to move on to my five points.

1. Democracy is not guaranteed to uphold freedoms

This is more or less a rehash of The Devil’s Kitchen’s post which I referred to yesterday. Above I said that “aspects such as civil liberties, human rights, freedom of speech, the rule of law, due process” are important. Arguably, these have all taken a battering by recent democratically elected governments.

Wave goodbye to your right to peacefully protest, have a fair trial and take photographs in public. Say hello to ID cards, the database state, endless reams of CCTV footage, mass DNA collection, control orders, detention without charge and extraordinary rendition. Thanks, democracy!

2. Tyranny of the minority

Most people are familiar with the concept of the tyranny of the majority. Thanks to the system of democracy adopted in this country, it doesn’t even take a majority to construct a tyranny. In the 2005 General Election, 9,562,122 people voted for Labour candidates. Assuming a population of 60 million, this translates to around 16% of the population.

The votes of this small percentage of the UK’s citizens has given the Labour Party 55% of the seats in the House of Commons, a majority of 67 seats. What gives the government the right to rule the country with such dominance? Not the people, that’s for sure. Only 16% of the people expressed a preference for the current government. In fact it is the way the system is constructed, and nothing else, which gives Labour its “legitimacy”.

That brings me neatly on to…

3. The system can’t be fixed

Arrow’s Impossibility Theorem states that there can be no voting system which will be able to fulfil a number of desirable criteria:

• The Pareto principle — if everyone prefers x to y then y should not be elected
• Anonymity — every voter should be treated equally
• Neutrality — every candidate should be treated equally
• Independence of irrelevant alternatives — the ability of x and y to win an election should not be affected by the entrance of a candidate z
• Transitivity — if x is preferred to y and y is preferred to z then x should be preferred to z

Independence of irrelevant alternatives is the one that riles up proponents of electoral reform the most. Just think of Ralph Nader, or the farcical events of the 2002 French Presidential election. In this case, the voting system is far more important than the voters themselves. The fifth item on the list refers to Condorcet’s paradox, whereby attempts to find a winner of the election leads you on an endless circle.

We can argue among ourselves about which voting system should be adopted. But (and I’m not saying this will necessarily come as a surprise to anyone), you will never find a system that will please everyone. It will be a matter of choosing the least worst option, as every system has a fatal flaw of some kind. For what it’s worth, my preference is Single Transferable Vote — but that’s a matter for a different post in the future.

For more along these lines, read this post about a talk I attended a couple of years ago. It was given by economist Eric Maskin en route to collecting his Nobel Memorial Prize in Economics. He had some very interesting views on electoral reform.

4. An individual vote is almost worthless

If you are concerned with affecting the course of history by having your say on major political issues, going to cast your vote in an election is more or less a complete waste of your time and energy. It is said that you are more likely to be killed on your way to the polling station than to actually cast the deciding vote.

The probability the the outcome of an election will hinge on your vote is minuscule. Even under the fanciful assumption that in a two candidate US Presidential election each other person is likely vote for either candidate with a probability of 0.5, the probability that your vote will be the deciding vote is 0.00006.

Yet the costs of voting are actually rather large. You have to spend time and possibly money learning about each of the candidates and their policies. The time and money spent travelling to the polling booth is not exactly negligible in the context of the minuscule probability of your vote actually meaning a damn thing.

Of course, this doesn’t mean that voting is wrong. People don’t vote because they believe it will affect the outcome. They vote because it makes them feel good. But the fact that you need to resort to non-instrumental incentives in order to justify the act of voting leaves wide open the possibility that people with bad motives (or motives with bad effects) are more likely to vote…

5. Many who do vote base their decision on prejudices

In his very interesting book The Myth of the Rational Voter, Bryan Caplan said that the fact that people vote can be explained by the fact that they like to hold certain political beliefs. Let’s call our voter a sheep. He may hold suboptimal opinions and support policies that would actually make him worse off. This might be due to social pressures, a sense of self-image or whatever. It is, after all, all too common to meet someone who votes Labour just because their dad did.

It is precisely because a person’s vote is so worthless that sheep are encouraged to vote. They like to go and vote because it makes them feel good, reaffirms to themselves their ideological loyalty and so on. But sheep never stop to think if the policies they support would make them worse off. They don’t have to because their vote doesn’t matter anyway. The cost of ideological loyalty is low. Indeed, the benefits of it are enough to outweigh the costs of voting.

Those who hold no strong ideological loyalties, and who may therefore be expected to enter the polling booth ready to judge fairly based on all of the information they have gathered, are actually far less likely to vote. This is because they feel no warm glow from the act of voting for their favoured party.

As such, the traits of voters are the sort of traits you would normally expect to find on a football terrace. They will trudge along to express their tribal feelings, and will keep on doing so even in the driving rain, even if their football team is rubbish and the game is low-quality.

One might say that the political party you support is rubbish and the state of politics just now is low-quality. Who wants to buy a season ticket? Is it not better to leave that sort of behaviour on the football terraces?

Eric Maskin seems to be quite an interesting person. He lives in a house that was once occupied by Albert Einstein. I imagine that would make a great pub quiz question. Perhaps even more startlingly, Eric Maskin dresses up as Albert Einstein at Halloween.

Professor Maskin came to Edinburgh en route to Sweden to talk about voting systems, a topic related to mechanism design.

Arrow’s impossibility theorem implies that no voting system is perfect at satisfying a number of desired criteria. These criteria are:

• The Pareto principle — if everyone prefers x to y then y should not be elected
• Anonymity — every voter should be treated equally
• Neutrality — every candidate should be treated equally
• Independence of irrelevant alternatives — the ability of x and y to win an election should not be affected by the entrance of a candidate z
• Transitivity — if x is preferred to y and y is preferred to z then x should be preferred to z

That fourth one is probably the one that grates with most proponents of electoral reform. We can reel off instances where independence of irrelevant alternatives has been violated. For instance, had Ralph Nader not run in 2001 then Al Gore would almost certainly have become President of the USA. A fragmented left in France allowed Jean Marie Le Pen to enter the final run-off with Jacques Chirac in 2002, when there was every chance that Lionel Jospin would have won such a face-off.

Interestingly, Eric Maskin thinks that if the SDP / Liberal alliance hadn’t run in 1983, Michael Foot’s Labour party would have won the general election. What a thought!

Just thinking about this sent me under a dark cloud. The design of institutions clearly has a disturbingly massive effect. The voting system is much more important than the voters themselves, particularly when you couple this thought with the paradox of voting.

The system that Eric Maskin concentrated on is Simple Majority Rule. This method has voters submitting rankings of candidates, just as in Single Transferable Vote. Then you take these rankings and use them to compare candidates in a head-to-head scenario, two candidates at a time. By comparing just two candidates at a time, you get rid of the problem with independence of irrelevant alternatives. If one candidate is preferred over another by >50% of the voters, he wins the election.

Well, almost. Unfortunately, this system is susceptible to Condorcet’s paradox. For instance, >50% of voters may prefer Labour to the Conservatives, >50% of voters may prefer the Conservatives to the Liberal Democrats and >50% of voters may prefer the Lib Dems to Labour. In other words, simple majority rule violates the transitivity principle.

The view of Eric Maskin is that to worry about transitivity is too pessimistic. For him, the Condorcet paradox is possible, but highly unlikely. This is because candidates can be lined up on a spectrum from left to right, and voters tend to vote in accordance with these positions.

As such, he suggests that simple majority rule is good as a least-worst voting system as it meets all of the desired criteria apart from transitivity which is unlikely to be violated. No other voting system works this well as often.

Of course, because the possibility of the Condorcet cycle even exists, there must be a tie-breaker. This is probably cause for a whole new debate in itself!

The talk provided some food for thought. For several years now I have been convinced that there needs to be a move away from the First Past the Post system. For the past few years I have been strongly in favour of Single Transferable Vote.

During the talk, one person in the audience specifically asked Eric Maskin about Single Transferable Vote. He said that STV can still violate independence of irrelevant alternatives, and pointed out that a similar system to STV was used in the 2002 French election.

I’m not entirely convinced that STV is all that similar to the run-off system used in French Presidential elections. The main problem with the French Presidential election (and the other examples that have been highlighted), as Proferssor Maskin pointed out, was the fact that voters were unable to rank candidates. Well, voters can rank candidates in STV.

Nevertheless, Condorcet cycle aside, I find the simple majority rule approach quite appealing. Yet we hear very little about it. If you are interested in electoral reform, I would say it is worth looking into a bit.

• Slides from Professor Maskin’s presentation (PDF file)
• An accessible article on this topic from the Scientific American (PDF) by Partha Dasgupta and Eric Maskin
• A more academic primer on the topic (PDF)
• More about Eric Maskin from Marginal Revolution
• Interview with Eric Maskin conducted by Adam Smith (heh). This interview does a really great job of outlining what mechanism design theory is and how it affects our everyday lives