Thank you very much, Mr. Chair.
I would like to thank the committee for this opportunity to share my research findings about a voting system that I call “rationalized majority”. The word “rationalized” means two things. First, it means “appealing to reason and not only to mathematics”. Secondly, it means “that uses ratios”.
The concept of ratios is familiar to everyone; we see it in finance and in other fields. Ratios are mathematical results applied to phenomena and that include an element of constancy. The definition of ratio I am using here is essentially the percentage of elected representatives in relation to the percentage of votes. It is quite simple.
There are historical ratios that have been identified by various researchers. I mention a few of them in the brief I submitted. Generally speaking, historical ratios are based on the party's role. For the party forming government, that is, the party that has the majority and is elected, it is about 1.2. That is the percentage of MPs in relation to the percentage of votes. For parties forming the official opposition, it is approximately 0.8. For third parties, it is about 0.5, but with many exceptions. The numbers are sometimes much higher.
We do not have to stick with these ratios. The ratios for third parties, for instance, can be much higher, which could be very interesting to examine in certain cases. For a parliament with 300 seats, for instance—we are not far from that—, a party could win 5% of the seats and 20% of the votes. This is of course true for a number of third parties, which is embarrassing and frustrating. In this case, the party's ratio would be determined by 5% of MPs to 20% of the votes. The result is 0.25. The party forming the official opposition would have a ratio of 0.8. So the number of MPs there should be is calculated as follows: 0.8 × 20% × 300 = 48. If by chance the party already has 5% of 300, that would be 15. So the party would be awarded 33 more 33 MPs.
If a party is one of the third parties, the ratio is lower. For example, 0.5 × 20% × 300 = 30 MPs less the 15 it already has. So the party would be awarded an additional 15 MPs. Depending on the party's role as determined by the results in a first-past-the-post election, additional seats are awarded to certain parties.
I have studied the federal elections from 1963 to 2015 and the ratios obtained are pretty much in line with what I just told you. There are some outliers though. Since 1984, for instance, the ratio obtained by the party forming government ranged from 1.5 to 1.22, for an average of 1.28 since 1963. This is very close to the historical ratio. For the party in official opposition in Canada, the ratio is 1. In the end, it is nearly proportional. That is an average. For a third party, the ratio in Canada is 0.85, but can be as high as 1.6. It varies from case to case. In 2006 and 2008, the ratio was 1.6. The third party with the most votes had a ratio that was as high as that of the party forming government, which is rather strange. This is one of the unpredictable aspects.
Secondly, MPs are awarded by rationalization, that is, people vote the same way they do now without any change. Mathematical adjustments are made after the fact. Theoretically, we could take the 2015 election results and apply this system by awarding MPs based on the ratios.
I have also calculated the number of MPs that would have been added to the Parliament of Canada if we had applied the rationalized system since 1963. I will not go into the details, but 111 MPs would have been added over these 17 elections. That is an average of 6.5 more MPs per election, which is not that many. All the same, it is more interesting than what is happening in Germany.
I also did a comparison with the mixed system in Germany.
It should be noted that initially, in 1949, there were two votes. Each voter had two votes, one to elect a riding representative by simple majority, as in our electoral system, and another that was purely proportional.
The German parliament was initially divided in two in a way. Some representatives were elected by simple majority and some were elected proportionally. This led to appalling imbalances in some cases. Many excess representatives were elected, exceeding the proportional ratio. This led to a very elastic house of representatives, which could have a highly variable number of representatives from one election to another. Above all, it contradicted the fundamental rule of proportional representation in that some political parties had far too many representatives.
Fifteen years ago or so, the Karlsruhe constitutional court decided to apply full proportional representation, but by offsetting the excess representatives elected by simple majority by reducing the number of representatives elected proportionally. I hope you are following me. So, for the overall result to be proportional representation, a political party with too many representatives elected by simple majority would have fewer than it should have by proportional representation.
Here, too, there is a problem. Some parties had so many representatives, even in excess of what the proportional system took away from them. The German house of representatives is therefore still elastic. Some people say it could reach 700 representatives, although in principle there are 598 seats. That has not happened yet. Right now, there are about 630 representatives. That is how Germany's mixed system works.
I wanted to transpose this system to Canada based on the results of federal elections since 1963 to see what it would look like. The simulation is not exact. It is not possible to transpose the percentage of votes obtained by the various parties in a first-past-the-post system to a mixed proportional system, especially not the German mixed system. As a result, one has to bear in mind that the calculation cannot produce exact results. It does give some indication, however.
There is an interesting point in defining a proportional system. There is a purely proportional system, which has incredible limitations that I will not go into.
Let us look quickly at Italy, which has that kind of system. It has the same drawback as all purely proportional systems, namely, that the parliament becomes completely ungovernable. To counteract that, the number of parties must be reduced or the governing parties must be given a true majority of representatives. Italy decided, however, that, in the case of a minority government, the party was awarded representatives. That is quite unusual. Since a majority is needed, the party is awarded more representatives.
That said, the current German system does not work that way. I made that point earlier and I do not need to repeat it. In my simulation of the German system in relation to Canada's system, I used our current Parliament. It has 338 seats at present, although the number of seats has been much lower. Two calculation methods can be used, either divide by two or multiply by two so that part of the House is elected by simple majority and the other part by a strictly proportional method with compensation, as is the case in Germany's mixed system at present.
Under this system, there are no additional representatives if a party does not have at least three representatives with a majority. So under this system, the small parties get their wings clipped. The system I am proposing, however, really gives the small parties an extra chance, without impeding the governing majority or the official opposition. This has many benefits.