DEMOCRACY<br>BUILDING Switzerland's Refined
Proportional Election System

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Democracy Building: Election Systems

Switzerland's Refined Proportional Representation System

There is and endless debate on proportional vs. majority election systems. Some interesting peculiarities in Switzerland's election system refine a basically proportional election system in a unique way so that it features the essential positive aspects of the majority election system while avoiding it's fundamental drawbacks. The Swiss system allows voters who take the time to choose individual candidates while those wishing to simply vote for a party can do so.

Switzerland is a federal state with 26 cantons of different size (15,000 to 1,240,000 inhabitants) with far reaching rights of autonomy including cantonal parliaments and governments. For historical reasons, constituencies for Switzerland's National council (larger chamber of parliament) correspond basically to the cantons, so that five small cantons may send only one deputee to the National council, while the largest may send more than 30 deputees.

This article deals with the procedures applying for the majority of constituencies where more than one seat is to be allacoted. More or less the same procedures are used to elect cantonal parliaments. Minor differences among cantonal procedures are due to the fact that cantons have been a "playground" to test refined rules and new democratic procedures for almost 200 years. While the impact of changes is limited on the cantonal level, the way politicians and citiziens are dealing with new rules in practice can be assessed in detail. When it comes to implement changes on the federal level, discussion is based on known facts rather than on ideological arguments.

Basics: lists and candidates

As in any proportional election system, a number of political parties are the key players. They represent different views on how public affairs should be dealt with and how tax money is to be raised and spent. Parties may nominate candidates and put them on a list. The seats are allocated to parties according to the number of votes each party gets.

Other proportional election systems are based on a simple "choose your preferred party and put their list into the box" principle, parties are allocated a number seats and individual members of parliament are assigned according to the position they have on the list. While these systems are easy to understand, they have a serious drawback: they don't allow voters to choose what kind of personalities are going to represent them.

This is where the specific add-on features of the Swiss system come in: while the principle of parties presenting candidates on lists still applies, Swiss voters may alter these lists in several ways in order to choose individual candidates. Basically voters get a set of party lists by mail some weeks in advance to the election date. Typically there are between 10 and 20 party lists, depending on the number of parties actively participating in the elections and one blank list to choose from.


The first and simplest of these feature is called cancelling: Voters may cancel any candidates they don't like on the list of there preferred party. While this does not change the weight of the vote for the party as such, it will be used to determine which candidate(s) of this party will actually get the seat. This feature helps to eliminate extreme candidates that may be good at influencing decision makers in their party, while having problems to convince even a majority of the party's followers.


The second feature works the other way round and is called cumulating: Each candidate may be put on a list once or twice The total number of candidates' names on a list must be less or equal to the number of parliament seats in the constituency, however. So in order to cumulate a candidate on a given list, another candidate must be cancelled.

Voting for candidates from different parties

Voters have even more possibilities to vote for individual candidates they prefer: candidates from another party may be written onto the chosen list of the preferred party. Of course, there must be a free line on the list to do so - or one of the names printed on the list must be cancelled first to create a free line. Candidates from other parties may be cumulated, too, as long as there are free lines to place them.

How the votes are counted

Basically, the valid votes for individual candidates are counted regardless of the list they appear on - whether printed or cumulated by hand or brought in from the list of another party. Then all votes for candidates of a certain party are added, plus the blank lines on lists with less candidates names than seats to be allocated, as long as there is a party label in the header of the list. If a printed party list is used, the header is already printed; if voters choose to use the blank list they may put a party name to the header, or they may leave the header empty. In the latter case, blank lines are not counted. So if voters cancel individual candidates from a party list, this won't affect the number of votes for this party, it will only have effects on the ranking of the candidates within their party. Putting candidates of another party on a list reduces the number of votes for this list, however, while it gives votes to the party of these "cockoo" candidates.

Once the number of votes for the parties is added up, the seats are allocated to the parties proportionally to the number of votes. In the next step, the most popular candidates of each party will be chosen.


Let's assume there is a constituency with 5 seats to be allocated and there are three parties A, B and C participating in the election. Parties A and B are big ones, they present lists with five candidates each (a1, a2, a3, a4, a5 and b1, b2, b3, b4, b5). Party C is smaller, on their list there are only 2 candidates c1 and c2, each already cumulated, plus a blank line.

We may assume that a relatively large number of voters will choose one of these three party lists and put it into the election box without changes, for example 42,000 choose party A, 32,000 choose party B and 11,000 choose party C.

For party A we assume that 4000 voters use list A, but cancel candidate a5, 3500 use list A, but cancel candidate a1, 2500 use list A, but cancel candidate a2 and 1000 use list A, but replace candidate a5 by candidate a4 (cumulated).

For party B we assume that 2500 voters use list B, but cancel candidate b4, 1500 use list B, but cancel candidate b2, 1000 use list B, but cancel candidate b1 and 1000 use list B, but replace candidate b4 by candidate b3 (cumulated).

For party C we assume, that 1000 voters use list C, but cancel candidate c1 once, and 1000 voters more cancel candidate c1 twice. Note that these voters may not cumulate candidate c2, since his party has already put him twice on the list. Practical experience shows, that this 'pitfall' will cause to a few, but not too many invalid votes. It seems that an overwhelming majority of those voters using the specialities like cancelling, cumulating and voting for candidates from different parties are able to handle the intricacies involved, while those who would be overstrained with that simply use an unchanged list.

Next possibility to be considered in this example: Some voters will use the blank list and write candidates from different parties on it. If they leave at least one blank line, it would even make sense to put a party name as header in order to have the blank line counted for this party. In our example we assume that 1000 voters choose a blank list and write candidates a5 and b4 twice and candidate c1 once.

Last, but not least, an example of bringing in a candidate from another party: We assume that 1000 voters use list A, but they replace candidate a1 by candidate b3 and 1000 voters use list B, but they replace candidate b2 by candidate c2.

Candidates Votes from lists of type Total votes
Unchanged Cancellations Cumulations Blank Mixed
a1 42,000 6,500 1,000 0 0 49,500
a2 42,000 7,500 1,000 0 1,000 51,500
a3 42,000 10,000 1,000 0 1,000 54,000
a4 42,000 10,000 2,000 0 1,000 55,000
a5 42,000 6,000 0 2,000 1,000 51,000
blank lines 0 10,000 0 0 0 10,000
Total party A 210,000 50,000 5,000 2,000 4,000 271,000
b1 32,000 4,000 1,000 0 1,000 38,000
b2 32,000 3,500 1,000 0 0 36,500
b3 32,000 5,000 2,000 0 2,000 41,000
b4 32,000 2,500 0 2,000 1,000 37,500
b5 32,000 5,000 1,000 0 1,000 39,000
blank lines 0 5000 0 0 1,000 6,000
Total party B 160,000 25,000 5,000 2,000 6,000 198,000
c1 22,000 1,000 0 1,000 0 24,000
c2 22,000 4,000 0 0 1,000 27,000
blank lines 11,000 5,000 0 0 0 14,000
Total party C 55,000 10,000 0 1,000 1,000 67,000
Grand total 425,000 85,000 10,000 5,000 11,000 536,000
Table 1

Allocation of seats to parties

In a first round, the number of valid votes (in our example 536,000) is divided by the number of seats (5). To win a seat in the first round, a party needs 107,200 votes. So party A is assigned two seats and party B one seat. To allocate the remaining two seats, the remaining votes (271,000 - 2*107,200 = 56,600 for party A, 198,000 - 107,200 = 90,800 for party B and 67,000 for party C) are considered. So party B is allocated a second seat and party C one seat.

Allocation of seats to candidates

Elected individual votes party strength
a4 55,000 50.6 %
a3 54,000 50.6 %
b3 41,000 36.9 %
b5 39,000 36.9 %
c2 27,000 12.5 %
Table 2

Comparison to standard proportional and majority election systems

From the result of our example election we see clearly that the Swiss system preserves both the obvious advantages of the proportional election system and the advantages of the majority election system: There is a proportional representation of a reasonable number of parties (not just two), nevertheless the most convincing candidates do have a fair chance to be elected even if their party chooses not place them on top of their list.

What would be the outcome of the same election, if the majority election system or a usual proportional election system had been used instead? The answer given in table 4 below is based on the fact that voters will most probably make different choices adapted to the particular characteristics of the election system used. That said, let's see the basic trends anyway.

To have a comparison with the majority election system we have to make a few realistic assumptions. Our example constituency would be divided into five small constituencies of more or less same size (107,200 active voters) and voters would have to choose from candidates a1, b1, c1 in constituency 1 and from candidates a2, b2, c2 in constituency 2 etc.

As small parties usually can be established in cities more easily than in rural areas, it makes sense to assume that one of their candidates comes from the city, the other from the suburb and the majority of the 65,000 voters supporting the party (not counting mixing) come from those two areas as well. In the more rural constituencies for a majority election, the party will not be able to find candidates and their followers have to choose between parties A and B. So the overall numbers of votes for parties A and B will be slightly higher at the cost of party C in a majority election system. Further, let's assume party A is more popular among the urban and suburban population while party B is more popular in rural areas.

Based on these considerations, a realistic outcome in a majority election system might look like this:

Candidate Constituency 1 Constituency 2 Constituency 3 Constituency 4 Constituency 5
a1 65,600 - - - -
a2 - 54,000 - - -
a3 - - 56,000 - -
a4 - - - 52,200 -
a5 - - - - 51,800
b1 31,800 - - - -
b2 - 44,200 - - -
b3 - - 51,200 - -
b4 - - - 55,000 -
b5 - - - - 55,400
c1 9,800 - - - -
c2 - 9,000 - - -
Table 3

On the level of party representation the strongest party, A, would probably win a third seat in a majority election system, while party C would not be represented in parliament.

A closer look on the candidates shows - and this may come as a little surprise - that even the majority election system would not necessarily result in selecting the most popular candidates from parties A and B, while the Swiss system does! Table 5 shows the elected candidates for the three election systems as well as the number of votes they get in the Swiss system (as a means to compare their popularity).

Majority system Proportional system Swiss system
Candidate votes Candidate votes Candidate votes
a1 (49,500) a1 (49,500) a4 55,000
a2 (51,500) a2 (51,500) a3 54,000
a3 (54,000) b1 (38,000) b3 41,000
b4 (37,500) b2 (36,500) b5 39,000
b5 (39,000) c1 (24,000) c2 27,000
Table 4

Cantonal variants

Please note that there may be slightly differing rules for elections on cantonal (federal state) and communal level. All 26 Swiss cantons have their own constitution and are free to choose their own detailed procedures within some guidelines given by the federal constitution. The cantonal level has been a "laboratory" for testing new rules for almost 200 years. Almost any particularity of Switzerland's unique system of democracy - regarded as a privilege by most Swiss citizens irrespective of their political and ideological preferences - has been tested on cantonal level before it was introduced on the federal level.


Though the refined proportional election system used in Switzerland may look a little bit complicated at first sight, long-term experience shows that voters are able to express their political will quite precisely using this system and there is no higher degree of invalid ballots than in other election systems. The Swiss system combines the advantages of both the proportional and the majority election system while avoiding their major shortcomings. In most cases those candidates that really convince the electorate have will get elected, while in other systems, even in the majority election system, internal party considerations have more influence.

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