A new majority, proportional, with maximal representativity electoral system

Characterized by

1. The present system

1.1 Introduction

We describe hereafter a new electoral system which must replace the one turn uninominal majority voting system actually in force in Québec. Having reviewd the causes of its obsoleteness and other systems in use abroad, we state the principles we will use in elaborating this new system. We design it while keeping most of the present system characteristics just adding a few minimal changes. We demonstrate with a simulation using past electoral data.

1.2 Obsoleteness

The principal cause of the present voting system being obsolete come from the great number of competing party while it was designed for a two party only system. More than two party make less probable a stable government. To maintain a strong link between a governing party and other partners imply negotiations and specific strategies based on compromises which are not easy at all. The second cause making it obsolete is the use of the territorial concept as the base element for the selection of deputy, that is to say the electoral district. It is the source of the recurrent conflict between regional and urban representation. An elected deputy may represent large populations localized in urban districts or low density populations of rural districts. This population inequality lead to a lack of equilibrium between the number of elected deputy and the population they represent. This happen even if the Québec electoral representation commission (QERC) try to reduce those inequalities by an appropriate reorganization of the electoral district frontiers in order to have the population number the closer to the mean. This voting system is known as a one turn uni-nominal majority system because it need a single event to get the vote, because there is only one deputy elected under simple majority for each electoral district and where the party who own the greatest number of districts is running the government. Such systems are in use in Great Britain, British Dominions, Latin America, Sweden and Danes.

Numerous experts already have analysed most of existing electoral systems. One may learn more upon by following these references: Duverger, Elections Canada, O'Neal, Wikipedia.

It must be reminded the important action the Mouvement Démocratie Nouvelle made to bring the government with some changes to the present electoral system. The publication S’informer et comprendre present the stakes, define the voting system, examine the proportional representation concept and finally approve a mixed compensatory solution.

1.3 Other systems

There exist many voting systems, generally used in Europe, making a proportional representation between the global vote and the number of elected party deputy. However, the proportionality is gained only in part. All systems that have been tried up to now are marked by distortions that favor a group or another depending on the compensation method used create the proportionality. Those methods are numerous and here we do not need to make a review since many experts have already studied them. We just need to keep in mind that none of them lead to a true proportionality and even less to a majority government. With such systems it happen from time to time that a state stays without a government for many months since none of the elected party is strong enough to run a stable government and that negotiations must be made between them to reach to an agreement.

1.4 Using lists

Various studies show that the proportional representation can be reached only with the use of lists for the distribution of seats both to the majority and the minority party. It must be reminded that even with the inherent distortions, to render the method is very complicated. This lead some countries to opt for mixed system made of half majority and half proportional system. Clearly nobody has found a miracle solution for a system leading to a majority government with a proportional representation. We propose to show that it is perfectly possible to build such an electoral system. And we can easily start with the actual system with some minor conservative procedural changes to keep its integrity.

1.5 Deputy base

The base on which the deputy is selected rely on the electoral district. The Quebec territory being divided into 125 electoral districts with about 5 millions of voters, this make a mean of 40 000 voters per district. The determination of the electoral district frontiers become a difficult task for the Commission de la representation électorale du Québec (CRÉQ) since it must consider social, geographical and political data. The consequence is that some districts fall apart far from the mean of voters. This fact make deputies associated with very different voting population so that the governing party does not have a real legitimacy. And usually the opposition party are under represented considering the number of their voters. Clearly we must review the base on which the determination of the deputation is founded in order that it represent really and equitably the voting population.

2. A new system

2.1 Principles

To build such system, a new method must enforce two objectives. The first one is to have the same proportion of voters each party has as there are deputies of that party at the national assembly. The second objective is the production of a majority government. And we also need to keep most of the actual system in order to make things simple and easy.

2.2 Two turns

First of all, it is clear that it is impossible to reach those objectives with a single turn of vote, two turns are needed. The first turn will show the vote received by each party for each electoral district. This will be used to compute the global vote each party got throughout the Quebec. Then it will be possible to compute the proportions of the vote for each party and later attribute accordingly the electoral districts to each of them. Up to now nothing much different from the actual system. The first difference happen at the second voting turn where only the two party who received the two greatest number of votes at the first voting turn are to compete. Since only two party are on the list, this will bring a majority party. This way, the dispersion of the vote as it appeared at the first voting turn due to third party disappear by forcing the voters to select a governing party form the two who received the greatest number of votes at the first turn. Since the winning party get a majority of votes, this party will receive the same proportion of seats at the national assembly making it the leader of a majority government. The second difference come from the method chosen to attribute the balance of the seats to the opposition. Each party forming the opposition will receive the same proportion of seats as the proportion of votes it got at the first voting turn. Then every party get the same portion of seats as the same portion of votes it got, so for the proportionality. For example let us consider a second voting turn where the winning party got 60% of the vote. It will get the same portion of seats at the national assembly that is 75 seats (0.6 x 125). The balance of 50 seats (125 - 75) is for the opposition. If we suppose that five party got enough votes to get at least one seat in the proportion of 46%, 24%, 14%, 10% and 6%, then each will get 23, 12, 7, 5 and 3 seats respectively. This way each elected party has a proportion of seats the same as the vote it got and we have at the same time a majority government.

2.3 Attribution of the electoral districts

This being, it must be determined which electoral districts will belong to a given party and by the way which deputy will be elected. In order to obey our first objective, we must maximize the weight of votes that each party represent so we select the electoral districts who got the greatest number of votes for a given party. This way the vote associated to a given party reflect the most its representativity. Each party being attributed the number of seats it own and following our example, the governing party will be attributed the 75 districts who ranked with the greatest number of votes for that party. And the same for each of the opposition party. Always in order to follow our first objective, it will be necessary to proceed to the attribution of the districts in a determined order. Necessarily, we must begin the attribution according to the increasing number of seats the party got that is to say first by the party who got the least of seats and finish by the government party who got the most. This is to make sure that the party who get the least seats see itself attributed the districts who produced the greatest number of votes for it. Doing inversely beginning by the government party, followed by the opposition party who own the greatest number of seats and so on, the opposition party who hold the least districts may not see themselves be given the districts that voted the most for them because those districts may have been collected by other party, breaking our first objective.

To resume, the strategy to determine the representatives at the national assembly is to not use the electoral district anymore but rely on the use of the global vote. Instead the votes of the party within the electoral district is used to determine to which group it will be associated that is the party who won that district.

3. Implications

3.1 The fractions

Two kind of numbers are present in the attribution process. The number of seats available is an integer while computing it from the proportion of votes lead to a fractionary number. This conundrum is solved by completing any fractionary numbers to the next higher integer if its fraction part is equal to or greater than a half. This is done first while determining the number of seats the governing party hold and then for each party of the opposition. Because of this rounding process, the total number of computed seats may differ from the real one. Then the rule to balance the numbers will be to add or substract a seat according to the case, firstly to the opposition party who got the greatest number of seats, then to the second opposition party who got the next greatest number of seats and so on as necessary.

3.2 Automatic normalization

Since the attribution of the electoral districts for a given party rely on the number of votes that party got in that district, it is clear that in order to make sure to be selected all party will look for that a district has the greatest number of voters as possible. This will modify the actual attitude in favor of the normalization of the number of voters towards the desired mean since all electoral districts will compete together for the greatest number of voters. This will ease the work of the CRÉQ in face of the determination of the electoral district frontiers.

3.3 Same date elections

Having always a majority government bring naturally its temporal stability and it may not be defeated by the opposition. Unless the government decide for strategic reasons to proceed to anticipated elections, the elections will be at a fixed date.

3.4 Replacing a deputy

Let us remind that the attribution process of the seats at the national assembly rely on a selection of electoral districts in favor of a party each of them being represented by a deputy of that party. The deputy is indirectly elected, it is its electoral district that is selected. So if a seat become vacant due to a sickness, a death or a withdrawal of the party, the seat always stays associated to the electoral district and the party. The only change is its representative and its replacement is the responsibility of the party or the party association of that district. Consequently an election is not necessary as it could happen within the actual system. The sole difference is that the selected representative will be automatically a deputy. So a deputy cannot change of allegiance or be an independent one. He must resign and step down. This will influence the ethic of the deputation where loyalty and strong values will be put forward.

3.5 Independents

This system does not favor the independent candidate since he is the sole representative of its own party. To be equitable and to follow our rules, we must consider a virtual party made of all the independent candidates. This is their global vote that decide if they may own an electoral district. If so, the electoral district where the independent candidate has the greatest number of votes will be selected as an independent one.

3.6 Opposition

Considering the actual system, the official opposition is the party who will loose the most of its power because within this new system, we force a majority government and the proportionality of the representatives. This party will have a reduced number of electoral districts.

3.7 The chief of a party

The electoral district selection process may not select the district of the chief of a party. This is a lesser problem since any deputy already selected may resign in favor of the party chief. This is not a dishonour but only a selection constraint of the process. It could be the rule that if the chief of a party does not see its district selected for its party the representative of the last selected district for the party resign in favor of its chief.

3.8 Strategic vote

It will not be a wise strategy not to have a representative in any district because the attribution process is based on the number of votes a party got. Consequently the strategic vote shall disappear since it is of no value in this system.

3.9 The electoral districts

This system keep intact the electoral districts without any territorial modification. Regional and urban representation is preserved. A deputy will always be associated to a district but the selected one may vary as it is actually the case. This is of no value to consider the strength, the size, the representativity between rural and urban districts. Each of them keep its characteristics. Change happens internally to a district by a different determination of the party winning the district. The choice is not the result of a contest between local forces but determined globally by the global vote. This is a good advantage to keep intact the electoral districts without any modification.

3.10 The voting system

The voting system is maintained without any modification. However it is repeated two times. The first time, the citizen make a single choice of candidate belonging to a single party with a single ticket which is put in the voting box. This is what will determine the proportional representativity of the opposition. The second time the citizen always using a single voting ticket make its choice between two party and drop it in the voting box. This determine the governing party.

3.11 The elector

A note on the elector options facing this system. For example what can do the elector who opt for the party «P» but do not wish to vote for its party representative «R» in his electoral district. The vote at the second turn is more important for determining the party than at the first turn. By voting at the first turn for the representative of a party other than the one he favor or could be the government party, he maximize the chances to see this representative «R» be selected since the selection process is based on the number of votes in the district. It is then clear that this system priorise independently both a representative and a party. This is contrary to the idea that the vote is only for the party and cannot make a difference for the representative.

4. Application

4.1 Example

In order to show how this system may be used and to discover its simplicity, we use the data from the fall 2014 Québec election. This data make the first turn. We make an arbitrarily manipulation of this data to create a second turn where there are only two party. Then follow the stages as described earlier leading to the composition of the national assembly. These operations are processed on large tables that may be downloaded at the Download section of the main menu.

4.2 First turn

Table 1 shows the first turn results mainly the number of votes each party got with the corresponding percentage.

PartyNumber of votesPercentage
PLQ 1 757 071 42%
PQ 1 074 120 25%
CAQ 975 607 23%
QS 323 124 8%
ON 30 697 1%
PVQ 23 163 0%
PCQ 16 429 0%
IND 15 361 0%
PN 7 539 0%
BP 2 690 0%
PMLQ 2 016 0%
PE 1 645 0%
PSP 1 291 0%
MPQ 521 0%
EA 400 0%
PUN 241 0%
QRD 163 0%
PI 126 0%
UCQ 58 0%
Total 4 232 262 100%
Table 1 - First turn

4.3 Second turn

To build a second turn, we use the first turn data where we arbitrarily merge the data form third party to the two who got the greatest number of votes on the first turn. Our choice are CAQ(part), PVQ, PCQ, IND, PN, PMLQ, PSP, MPQ and UCQ merged with PLQ and CAQ(part), QS, ON, BP, PE, EA, PUN, QRD et PI merged with PQ. Table 2 show the second turn votes.

PartyNumber of votesPercentage
PLQ 2 408 813 57%
PQ 1 823 449 43%
Total4 232 262100%
Table 2 - Second turn

4.4 Seats

The Quebec Liberal Party being majority with 57% of the vote it get 71 deputy or electoral districts. The balance or 54 seats are distributed to the opposition party proportionally to the votes they got at the first turn. So the Parti Québecois get 24 seats, the Coalition Avenir Québec get 21 seats, Québec Solidaire get 7 seats, Option Nationale get 1 seat, The Green Party get 1 seat and no seats for the remaining party. Tables 3 to 10 show this.

PartyNumber of votesPercentageNumber of seats
PLQ 2 408 813 57% 71
Opposition 1 823 449 43% 54
Total4 232 262100% 125
Table 3 - Seats
PartyNumber of votesPercentageNumber of seats
PQ 1 074 120 43% 24
CAQ 975 607 39% 21
QS 323 124 13% 7
ON 30 697 1,2% 1
PVQ 23 163 0,9% 1
PCQ 16 429 0,7%
IND 15 361 0,6%
PN 7 539 0,3%
BP 2 690 0,1%
PMLQ 2 016 0,1%
PE 1 645 0,1%
PSP 1 291 0,1%
MPQ 521 0%
EA 400 0%
PUN 241 0%
QRD 163 0%
PI 126 0%
UCQ 58 0%
Total 2 475 191 100% 54
Table 4 - Opposition

4.5 Electoral districts given to PVQ

RankDistrictNumber of votes
1 Notre-Dame-de-Grâce 1 318
Table 5 - PVQ district

4.6 Electoral districts given to ON

RankDistrictNumber of votes
1 Taschereau 1 513
Table 6 - ON district

4.7 Electoral districts given to QS

RankDistrictNumber of votes
1 Gouin 16 155
2 Mercier 13 228
3 Laurier-Dorion 9 330
4 Sainte-Marie-Saint-Jacques 8 437
5 Hochelaga-Maisonneuve 7 926
6 Rosemont 6 930
7 Rimouski 4 851
Table 7 - QS districts

4.8 Electoral districts given to CAQ

RankDistrictNumber of votes
1 Chauveau 22 679
2 La Peltrie 21 386
3 Chutes-de-la-Chaudière 21 288
4 Arthabaska 19 393
5 L'Assomption 18 719
6 Granby 18 441
7 Mirabel 16 359
8 Beauce-Nord 15 761
9 Blainville 15 075
10 Montarville 14 999
11 Rousseau 14 667
12 Vanier-Les-Rivières 14 535
13 Borduas 14 331
14 Montmorency 14 323
15 Lévis 14 131
16 Repentigny 13 889
17 Terrebonne 13 707
18 Johnson 13 621
19 Drummond-Bois-Francs 13 600
20 Saint-Hyacinthe 13 245
21 Masson 13 235
Table 8 - CAQ districts

4.9 Electoral districts given to PQ

RankDistrictNumber of votes
1Verchères 18 467
2Matane-Matapédia 18 025
3Joliette 17 477
4Bertrand 15 232
5Berthier 15 070
6Labelle 13 806
7Saint-Jérome 13 647
8Jonquière 13 487
9Saint-Jean 13 486
10Lac-Saint-Jean 13 159
11Saint-François 12 725
12Bourget 12 525
13Groulx 12 484
14Charlevoix-Côte-de-Beaupré 12 201
15Taillon 12 148
16Pointe-aux-Trembles 12 021
17Vachon 11 983
18Laval-des-Rapides 11 902
19Beauharnois 11 891
20Chambly 11 722
21Richelieu 11 695
22Marie-Victorin 11 614
23Richmond 11 521
24Bonaventure 11 380
Table 9 - PQ districts

4.10 Electoral districts given to PLQ

RankDistrictNumber of votes
1 Robert-Baldwin 36 763
2 Nelligan 36 494
3 Saint-Laurent 31 454
4 Jacques-Cartier 30 823
5 Chomedey 30 604
6 Vaudreuil 27 750
7 Jeanne-Mance-Viger 27 007
8 D'Arcy-McGee 26 983
9 Marguerite-Bourgeois 26 251
10 La Pinière 25 955
11 Pontiac 25 659
12 Acadie 24 211
13 Mont-Royal 23 297
14 Gatineau 22 852
15 Lafontaine 22 476
16 Fabre 20 614
17 Marquette 20 342
18 Westmount-Saint-Louis 20 297
19 Saint-Henri-Sainte-Anne 19 795
20 Chapleau 19 697
21 Lotbinière-Frontenac 19 296
22 Soulanges 18 925
23 Papineau 18 330
24 Louis-Hébert 18 327
25 Hull 18 213
26 Brome-Missisquoi 18 103
27 Rivière-du-Loup-Témiscouata 18 086
28 Bourrassa-Sauvé 17 905
29 Châteauguay 17 876
30 Roberval 17 816
31 Vimont 17 584
32 Côte-du-Sud 17 348
33 Verdun 17 172
34 Beauce-Sud 17 055
35 Charlesbourg 16 934
36 Sainte-Rose 16 520
37 Mille-Îles 16 499
38 Anjou-Louis-Riel 16 049
39 Viau 15 945
40 Bellechasse 15 843
41 Laporte 15 804
42 Jean-Talon 15 492
43 Outremont 15 368
44 Huntingdon 14 115
45 Maskinongé 13 658
46 Crémazie 13 440
47 Orford 13 055
48 Portneuf 12 779
49 Laviolette 12 422
50 Sherbrooke 12 380
51 Argenteuil 11 676
52 Trois-Rivières 11 658
53 Jean-Lesage 11 645
54 Champlain 11 615
55 Dubuc 11 386
56 La Prairie 11 110
57 Mégantic 10 840
58 Rouyn-Noranda-Témiscamingue 10 644
59 Chicoutimi 9 640
60 Deux-Montagnes 8 913
61 Iberville 8 602
62 Duplessis 8 513
63 Abitibi-Est 8 476
64 Saint-Maurice 8 244
65 Nicolet-Bécancour 8 038
66 Abitibi-Ouest 7 615
67 Sanguinet 7 301
68 Gaspé 6 513
69 Ungava 4 615
70 René-Lévesque 4 366
71 Îles-de-la-Madeleine 4 137
Table 10 - PLQ districts
This new system bring a majority governemnt of the Québec Liberal Party with 71 seats for a representativity of 57% of the vote. The opposition is made of five party having 54 seats for a representation of 43% of the vote. The opposition is made of the Parti Québécois with 24 seats (43%fo the vote), the Coalition Avenir Québec with 21 seats (39% of the vote), Québec Solidaire with 7 seats (13% of the vote), Option nationale with 1 seat (1,2% of the vote) and the Quebec Green Party with 1 seat (0,9% of the vote). The following table resume the situation.

Seats distribution

Actual Seats 70 30 22 3 0 0 125
% 56 24 17,6 2,4 0 0 100
Actual Votes 1 757 0711 074 120975 607323 12430 69723 1634 183 7824 232 262
% 41,52 25,38 23,05 7,63 0,73 0,55 98,85
2nd turn Votes 2 408 8131 823 449 4 232 262
% 56,92 43,08 100
Governement seats 71,15
Opposition seats 54
OppositionVotes 1 074 120975 607323 12430 69723 1632 426 7112 475 191
% 43,40 39,42 13,05 1,24 0,94 98,04 100
Seats 23,43 21,28 7,05 0,67 0,51
Final Seats 71 24 21 7 1 1 125
% 56,80 19,20 16,80 5,60 0,80 0,80 100
Party electors 1 193 210319 608 337 38466 857 1 513 1 318 1 919 890
% party electors 67,91 29,76 34,58 20,69 4,93 5,69
% party represented62,15 16,65 17,57 3,48 0,08 0,07 100,00
Table 11 - 2014 Elections

4.11 Élection 2018

We apply this methodology to the 2018 election data. The table showing the complete operations is downloadable through section Download of the main menu. Here we show a resumé of the seats repartition.

Seats distribution

Actual Seats 74 32 10 9 0 0 0 125
% 59,2 25,6 8 7,2 0 0 0 100
Actual Votes 1 509 4591 001 039649 505687 99967 87059 05322 8633 997 7854 033 545
% 37,42 24,82 16,10 17,06 1,68 1,46 0,57 99,11
2nd turnVotes 2 213 7651 819 780 4 033 545
% 54,88 45,12 100
Government seats68,60
Opposition seats 56
OppositionVotes 1 001 039649 505687 99967 87059 05322 8632 488 3572 524 117
% 39,66 25,73 27,26 2,69 2,34 0,91 98,58 100
Seats 22,21 14,41 15,26 1,51 1,31 0,51
Final Seats 69 23 14 15 2 1 1 125
% 55,20 18,40 11,20 12,00 1,60 0,80 0,80 100
Party electors 1 012 734331 875 169 870190 2323 766 3 371 836 1 712 656
% party electors 67,09 33,15 26,15 27,65 5,55 5,71 3,66
% party represented59,13 19,38 9,92 11,11 0,22 0,20 0,05 100,00
Table 12 - Elections 2018

4.12 Discussion

The 2014 and 2018 elections made majority government with nearly the same numbers of seats (56% and 59,2%) but with percentages of votes less representative (41,52% and 37,42%). The new system would have made similar proportions of seats (56,80% and 55,20%) but with the same proportions of votes (56,92% and 54,88%) which is much better than the actual system. For the opposition, the actual system has brought only three opposition party (2014 and 2018) while the new system would have given five (2014) or six (2018).

Adopting this new system imply to review the subsidizing mode of the elected party. Actually only the governmental party, the opposition and the second opposition, if it fill specific constraint, are subsidized. The equity principle imply to subsidized all party and this could be in proportion to the number of seats it hold. The method or formula shall be adopted by the national assembly.

It worth mentioning that this system favor a change of customs and behavior. This will be the case while determining the electoral district frontiers and for the loyalty of a deputy to its party. Another advantage is the ability of the elector to make an independent choice of the party and the deputy.

A compensation mixed proportional system as it may be introduced make major changes to the voting system. It use lists of candidates. To the actual electoral districts it add a superposition of new regional districts. It use new and complex methodologies to dispatch seats with inherent distortions. And the more numerous are third party the more problematic is the formation of a government.

Mister Christian Dufour, politician and jurist, presented a paper on August 18 2016 in Ottawa to the Special committee of the Commons on the electoral reform. He also published a book titled "Le pouvoir québécois menacé, Non à la proportionnelle". His analysis of electoral systems shows that the craze for proportional systems without approbation by people is a dangerous endeavour. He believes that even with the distortions the actual system may have facing numerous parties, it is preferable that Quebec stays with it.

4.13 Electoral evening

We have created a simulation tool for a second run that determines the seats distribution under an eventual majority and proportional government. In the event of a modification to the electoral system, this tool authorize anybody to determine according to his or her knowledge of the situation a repartition of the votes given to the third parties on the first run to the two parties that headed it. Enjoy this game that you will find here. This tool helps to follow the vote evolution the same way traditional media do but without talks and publicity.

5. Conclusion

5.1 Résumé

To conclude, we consider to have build a new electoral system based on the actual one that we modified very slightly. It follow rigorously the rules that make the proportional representation real. It always produce a majority government assuring its stability. It is based on the global vote instead of the electoral district. It use an original method to determine the seats or the districts represented. It preserve the present structure, the electoral district and the voting system. Truly this system reach the looked for objectives: And more, this system offer some extra advantages: This system apply the economy principle by the preservation of the actual system and is really of a less complexity than a mixed system making use of lists and compensation methods. This is the most simple system, the most practical and the least expensive that may be adopted. It may be used right now and its application need only a simple change of the computational method used by the Director General of Elections.

Why make complicated when it can be done better and simpler?

6. References

6.1 Biblio

[Canada] Élections Canada, Examen des systèmes électoraux – Partie 2 – Monographie des systèmes électoraux, 1990-1999.

[Dufour] Christian Dufour, Le pouvoir québécois menacé, Non à la proportionnelle!, 2019.

[Duverger] Maurice Duverger, Les différents système électoraux, 1965.

[MDN] Mouvement Démocratie Nouvelle, Vers un nouveau mode de scrutin, cahier 1, S’informer et comprendre, 2009.

[O'Neal] Brian O'Neal, Les systèmes électoraux, Mai 1993.

[Wikipedia] Wikipedia, Système électoral.



First publishing: 28 avril 2013

This document is the subject of a continuous update, the last having taken place on: