Mr. Chair, ladies and gentlemen of the committee, thank you.
I acquired a fair amount of experience with voting methods during the provincial consultations in Quebec. I have not worked on the issue as much in the past few years. The last consultation was in 2007. I am however quite current on the research in the field.
To begin, the study of voting methods dates back to the year 105 AD. Voting methods were first studied by Pliny the Younger when it was noticed that a plurality of votes was problematic if there are more than two candidates. That is the subject of a fairly well-known legal judgment.
This problem was forgotten for many centuries. In the 14th century, the Catalan philosopher Ramón Llull began studying the issue, followed by his disciple Nicolas de Cues in the 15th century.
After being forgotten for a few centuries, the Marquis de Condorcet and chevalier de Borda rediscovered the problem of the plurality of votes during the French Revolution, in the 18th century. Finally, the English mathematician Lewis Carroll also studied the issue in the 19th century.
The purpose of this field of study, known as the social choice theory, is to determine how to choose the best possible candidate.
Another branch of the same field is equity theory, which pertains to proportionality or determining how to distribute seats in the fairest way possible. This was debated at length by the Americans in drafting their constitution in order to determine how they would distribute seats. They worked on this a great deal.
There is something very frustrating about all of this research. Each time, people started over from scratch because none of them knew of their predecessors' work. In the 1950s, the serious work began and mathematicians and political scientists made their contributions.
Once again, the problem is that these are two completely different branches of knowledge. In the field of political economy, people worked on voting methods, and in political science, they studied the effects of the various voting methods. We have everything we need to create a good voting method. The knowledge is there, but it is spread out in three or four fields whose experts do not speak to each other.
As a physicist, interdisciplinary barriers are not a problem for me. So I gathered parts of all this knowledge to get an idea of what should be done.
Official research began in the 1950s. The last original voting method that was invented is the German compensatory system, which dates from the roughly same period. Clearly, not a single voting system in the world right now has benefited from the research done in the last 60 years.
I have also read that the Society for Social Choice and Welfare, a group that works on the social choice theory, had only been consulted once, by the government of Mongolia, during an electoral reform. I will try to explain a few general rules to give you an overview.
There are two main groups of voting methods. There are the methods used to elect a candidate, either a mayor or a president. In our case in Canada, it would perhaps be the Governor General or the Speaker of the House of Commons. This group includes 20 or 25 voting methods such as the transferable vote, the N-round, the Condorcet and the Borda methods and so on. A bit later on, Mr. Côté will tell us about majority judgment voting, a recent innovation that I find very interesting. In short, these methods are used to elect one person, so if you want to elect a president, they are the best methods to consider.
In order to elect an assembly, Montesquieu favoured a method that would best represent the population. That is a completely different kind of voting method and is part of the proportional voting group. There are twenty or so of them, and they also have their share of problems.
As well, there are limiting factors owing to the limitations of the human brain. For example, we can work with series of seven items. We cannot do more than that. In an experimental vote I held with a number of candidates at Laval University in 2007, people lost sight of the seventh candidate. He no longer existed. In France, a similar experimental vote was also conducted. There was a tremendous number of presidential candidates. People were not able to evaluate more than seven candidates. It was beyond their abilities. Regardless of the voting method, we cannot exceed those limitations of the human brain.
Voting methods have an effect, and I doubt I am the first person to tell you that. In a plurality system, there is an economic incentive that encourages you to invest your money in the best candidate and, on voting day, there are just two main parties or two candidates left. For example, if you don't like one of the candidates, you will vote for the candidate who is most likely to defeat the candidate you don't like. This is a purely economic mechanism, which is disappearing though. Some disillusioned people will say, in their disgust with politics, that people will vote more sincerely. We see that in Quebec where this electorate keeps growing.
In proportional systems, there is a distribution known as Lefebvre's law. In plurality systems, it is Duverger's law.
In proportional systems, there is Lefebvre's law, a law in psychology, which corresponds roughly to the distribution of any good or service. Even ice cream flavours follow this law. People vote much more freely. As seen from the outside, a voter who votes freely is someone who votes almost randomly. The factors that a voter considers when voting are extremely complex. They can range from the tone of voice of the person speaking to him to what he ate six months ago—just kidding. A voter can even consider a political act from 20 years ago. So we have this exponential distribution.
This has repercussions. Let us consider the last election to try understand the impact of a voting method.
If we change the voting method, the outcome will not be the same. In the interest of transparency, I should say that I have been a Green Party candidate in the past. The Green Party could win votes, but the bigger parties would not win as many. Parties we have never heard of could emerge, such as a federal party similar to the wildrose party. The number of parties will increase.
When we do simulations, we cannot take the results from the last election and fit them into the new voting method. You would not get the same results.
With proportional voting methods, the best way to do the distribution from a mathematical point of view is what is known as the Webster—Sainte-Laguë method. In a purely proportional system, it is essentially the usual rounding. Mathematically, the simplest method is the best. The only drawback is that the usual rounding “fails” from time to time. From time to time, two parties will have the same ratio, although one party has twice the number of votes as the other party. As a result of division, both would go from +1 to -1 at the same time. We cannot get the exact number of MPs. Assume there are 338 seats. We would go from 337 MPs to 339 MPs, and there is no way of arriving between the two.
In the past, I built measurement instruments. In the United States, it happens once every 3,500 years when they do the seat distribution. It is clear that it would happen after two elections. Elections in which two candidates win the same number of votes are not supposed to happen, but it does happen all the same. That is something that will have to be included in the elections act because it can fail.
Lefebvre's law means that when there is an electoral threshold, for each percent of this threshold, 3% to 3.5% of the ballots go into the garbage. It starts getting complicated when the threshold is above 5%. In Turkey, the electoral threshold of discarded ballots is 10% to 40%. It is proportional, but it is not very different from our system. So we need to aim for low thresholds.
In a proportional system, everyone thinks you need 50% of the votes to get a majority. That is not the case though. Typically, if a party wins 44% or 45% of the votes, it will have 50% of the seats and form a majority. Here, it is 38%. That does not change the dynamics very much. The only difference is that, in a proportional system, coalitions can be formed more easily and there will be more majority governments. Just because it is a proportional system, that does not mean that a party needs the majority of votes to win the majority of seats.
This works relatively well on the whole, except for the stability problem with proportional systems. Problems can arise in two cases: if it is too stable or if it is not stable enough. It is really a combination of two factors, the degree of fragmentation of society and the degree of proportionality. This requires some thought. In a proportional system, the largest party wins about 30% of the votes. If Lefebvre's law applies in pure form and it is a uniform society, the biggest party will get 30% of the votes and will form a coalition with another party. The problem is that there have to be several parties in order to form a coalition. Otherwise, the same party is always in power with the coalition party on the other side. Then things freeze up.
There has to be enough parties. If the system is not proportional enough and if there are not enough parties, the situation remains completely stable and nothing changes at all. If there are really too many parties though, unstable coalitions are formed between three or four parties. The way society is organized is what determines the success or failure of proportional systems.
We have a fragmented society in Canada, but not as fragmented as elsewhere. We have the equivalent of four or five major political regions. In Belgium, for example, society is divided in two and Lefebvre's law applies twice. Moreover, Belgium has completely ridiculous electoral laws, resulting in an incredibly large number of parties. This complicates matters. Italy has the same problem. We tend to forget that Canada is an old country that has been around for 150 years. Countries in Europe such as Germany or Italy have a much shorter history. These are further considerations.
There is another important aspect. In a regional proportional system of whatever type, if there are fewer than six MPs, it is no longer proportional. The electoral threshold is based on the number of MPs and even with rounding off, you can only get half. With six MPs, you would have about 6% of the electoral threshold at most. It would be better with seven or eight MPs.
In Canada—you know Canadian geography as well as I do—, that is problematic. Prince Edward Island, for example, does not have six MPs. I mention that because in Zurich, Switzerland, someone went to court arguing that there were three candidates in his electoral district and that he would be voting for a party that has less than 10% of the seats. He pointed out to the court that the constitution declares everyone to be equal, yet his vote would never count and there is no possibility that it would in the future. The court found in his favour and that is why a mathematical solution to the problem had to be found.
In the Parliament of Canada, we have just about the right number of MPs. Theoretically, the optimal number would be 327, but we have 338. So we are very close. We do not have too many MPs and we do not have too few either. The opposite is true in some provinces in Canada where there should ideally be more. Moreover, a proportional system does not really have an impact on the representation of women.
In Canada, we have one of the worst contexts ...
