Sunday, April 22, 2007

Voting algorithms

France is voting today. As many of you may know, France uses single-name, two rounds voting procedure, similar to what is being done in many other countries. Every single time I vote, I cannot help but think about the flaws of our voting system, and of the other voting systems commonly in use. And this usually brings me to thinking about the flaws of democracy in general. As a programmer, I want to point out early that I'm thinking about the flaws of the various implementations of democracy, not the flaws of the concept itself.

Flawed voting systems

One of the things that strikes me about the various voting systems that I know about is just how "mathematically" flawed they are. Most of the voting systems can lead to situations where the winner is not really the one the people chose. This is well known in the United States for example, where the so-called popular vote (raw count of votes) may not match the electoral votes (the vote among the few chosen to represent the people). This was the case in the 2000 presidential election, for example.

A similar problem also exists in France for a different, more subtle reason. During the second round, voters no longer have a real freedom of choice, since they can only vote among the remaining two candidates that many of them did not choose. For example, for the current 2007 presidential election, projections indicate that less than 50% of the votes will go to the two winners. So more than half of the population will have to choose during the second round for someone they chose not to vote for during the first one.

This even led to situations where the result of the secound round was hard to understand based on the result of the first one, like in 1981 in France. During the first round, Valery Giscard d'Estaing (right), had more votes than Francois Mitterrand (left), and Jacques Chirac (right) had more votes than Georges Marchais (left). But on the second round, Francois Mitterrand still won...

Why does it matter? Well, democracy means giving power to the people, so shouldn't we try to make sure we actually elect the person that the people chose? First of all, this is quite problematic, because "the people" is not some monolithic entity. Individuals sometimes change their mind, and so do people. One explanation of the 1981 vote could be that folks simply changed their mind after, say, a political debate on TV. But ignoring that aspect, it would seem interesting to have some idea that the actual will of the people was correctly captured at some given instant.

Fair voting procedures

What makes flawed voting procedures really irritating to scientists, engineers, mathematicians, and all those who somehow live in the illusion that humans are logical is that voting procedures have been studied since at least Condorcet in the eighteenth century.

There are actually several voting systems that satisfy the so-called Condorcet criterion, namely that the winner will always win one-on-one against any opponent. So, what's the problem with such methods? Well, it shows well in the current French presidential election: Nicolas Sarkozy and Segolene Royal are both credited with more vote intentions in the first round than the "third man" of the election, Francois Bayrou, yet all projections indicate that Bayrou would win the second round against any opponent... This is a typical Condorcet paradox.

But there are other, more complicated voting procedures that do not have this problem. One of them is the Borda count (also devised in eighteenth century France, which is not a coincidence if you ask me), where you rank candidates by giving them points. Being a consensus voting system instead of a majoritarian one, it is probably more representative of the "average" will of the people than any majoritarian voting system.

Fixing the wrong problems

Many people are aware of issues with their voting system, so they try to fix it. And they usually end up fixing the wrong problem. For example, France, like many other countries, did some experimentation with electronic voting, and it was considered by some as a catastrophe.

What's wrong with the good old ballot box? I mean, it's not like France ever had hanging chads problems, so why bother with slower, more expensive, possibly insecure replacements? Why fix what works, why not fix what does not work? Electronic voting, in my opinion, is very well described like the X window system once was: complex non-solutions to simple non-problems.

I suspect that one reason people prefer fixing the way we collect ballots rather than the way we count votes is the suspicion of fraud. People are so attached to the power given to them by democracy that they don't want risking it by changing the method. Changing the tool is OK, but changing the method might be giving up the power.

Artificial flatening due to random chance

There is another thing that turns out wrong with democracy, it's what I would call the artificial flattening of opinions. In any democratic country, under practically any circumstances, with practically any pair of candidates, a vote that is not very close to 50%-50% is considered a banana-republic score. Is that normal?

To understand why I ask the question, take a panel of random folks, and ask them to vote whether they should walk along a cliff or take a more conservative route. Chances are that you will not get 50%-50% votes, but more like 95% voting against walking along the cliff. But then, ask them to choose at some random point between walking left and walking right, and you will probably get 50%-50%. The vote gets more marked when there is danger, this explains how Jacques Chirac ended up with more than 80% of the votes during the second round when he had less than 20% during the first round.

Similarly, ask a panel of experts to decide whether global warming is caused by human activity, you may get something like 80% of them saying "yes", but if you ask a bunch of politicians who, for the most part, know nothing about the science of global warming, chances are they won't be able to make a clear decision. So "danger" is not the only factor that is important in deciding a vote. Also critical are the ability to perceive it and the evaluation of how important it is.

So the customary 50%-50% score indicate that people, to a large extent, "don't care", that they do not feel that the winner election is going to make a huge difference. This is, in my opinion, the big failure of democracy.

Can this indecision be fixed

I keep thinking that there is a way to fix that, and it would be instantaneous, continuous voting. This kind of continuous democracy is now technically feasible. Why do I think it would be better? Because this would ensure that the will of the people is not decided by so-called "representatives" based on their own electoral, political or even financial interest. But, more importantly, because people, if they are asked frequently, will tend to vote mostly on the things they care about and know something about. On average, I expect that people would therefore tend to vote more "intelligently", and therefore make more contrasted, more informed decisions.

Imagine that today, you would be allowed to vote, for example, on digital restrictions management, electronic voting, euthanasia and the reduction of the VAT for restaurants to 5% (which is a real controversy in France, believe it or not). I know that I would probably not vote on the last one, being not very well informed about the issues at hand. On the other hand, I would definitely vote on the others, because I believe that I have an informed position

No matter who wins this election, there is no chance that he or she would be able to know exactly how I would vote on all these topics. That's another failure of democracy: elected officials should execute the will of the people, not phrase it.

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