Musings on electoral systems: geometric means in Bern

One of the challenges in designing any political system is the question of how to ensure proportionate representation and influence for racial and ethnic minorities. Two of the world’s best-known political scientists have offered different solutions. Arend Lijphart (in works such as Patterns of Democracy) has painted a picture of ‘consociational democracy’: proportional representation, parliamentary government, grand coalitions, and policy consensuses forged by bargaining between group elites. (Think the Netherlands, Belgium, or post-1998 Northern Ireland.) Donald Horowitz focuses on pre-electoral coalition-building, and boosts the alternative vote as a means of forcing candidates to reach out to other groups. (Unfortunately for him, his preferred example – Fiji – has never implemented the system fully and has never found a political modus vivendi between its Fijian and Indian populations.) Across the world, the push for minority representation yields a variety of arrangements – India’s reserved seats for scheduled castes and tribes, New Zealand’s Maori seats, and the United States’ racially-gerrymandered electoral districts to name just a few.

Being cleaved many ways by its linguistic (German-French-Italian) and religious (Protestant-Catholic) divisions, Switzerland is fertile ground for experiments in minority representation. One of its largest cantons, Bern, is something of a microcosm of the nation as a whole, with a small French-speaking minority in the north dominated by German-speakers elsewhere. After the Catholic French parts of the canton seceded in 1979 to form the canton of Jura, Bern realised it needed to meet the aspirations of the remaining (Protestant French) areas. It does this in two ways: guaranteed seats in the legislature and executive (like all Swiss cantons, Bern has a popularly-elected plural executive), and the creation of a 24-member quasi-legislative body for the region (the Conseil du Jura bernois) with power over certain culturally-sensitive matters.

Every four years, the Bernese people elect 160 members of the legislature (Grand conseil) and seven members of the executive (Conseil exécutif). The former has 160 seats, elected by proportional representation in large multi-member districts (see here for a previous post on Switzerland’s unique twist on PR). The Bernese Jura elects twelve of these, while the French-speaking community of Bienne-Seeland elects another three. At the same time, and using the same electoral system, the Bernese Jura elects the twenty-four members of the Conseil du Jura bernois. The executive election, however, is the most interesting, and uses a method to ensure fair representation unique in the democratic world.

Bern’s executive is elected by a two-round majoritarian system, common among Swiss cantons (some use a one-round majoritarian system, and two use proportional representation). One of the seven seats is reserved for a candidate from the Bernese Jura. If such a candidate obtains a first-round majority, they are elected, provided that among all candidates from the region, they had the highest ‘geometric mean’; otherwise, the candidate from the region with the best geometric mean in the second round is elected. The figure in question is the square root of the product of the candidate’s votes in the Bernese Jura and their votes across the canton (eg. a candidate obtaining 1000 votes in the region and 20,000 canton-wide would have a geometric mean equivalent to the square root of 20,000,000).

The use of the geometric means ensures that if two French-speaking candidates run equally well across the canton, the one who polled better in the Bernese Jura is elected, while if two candidates poll equally well in the Bernese Jura, the one with more votes in the rest of the canton is elected. In this way, candidates are given incentives to appeal to voters outside their region, but the preferences of the people of the Bernese Jura cannot be denied by the election of a French-speaking candidate whose support comes disproportionately from German-speaking areas. In recent years, a campaign for the popular election of the federal multi-member executive has proposed this method for ensuring that French- and Italian-speaking regions of Switzerland continue receiving their usual two seats should their proposal be adopted.

The ‘geometric mean’ method allows for the entire electorate of Bern to vote for its executive (as opposed to, say, having the German-speaking majority elect six and the Bernese Jura elect one) while deviating slightly from the one-man-one-vote ideal to give a geographically concentrated minority the opportunity to elect the candidate of its choice. One can imagine it being adapted for geographically dispersed minorities, provided there were some means of segregating their ballots from the rest of the population. It is designed for a multi-member majoritarian election, and might not be adaptable to proportional elections. Nevertheless, the constitutional protections for the Bernese Jura are an interesting mesh of Lijphartian ideas (proportional representation in the legislature) and Horowitzian ones (an executive electoral system which incentivises cross-ethnic coalition-forming).

Musings on electoral systems: proportional representation, Swiss-style

Switzerland adopted proportional representation for federal elections in 1919, after a ballot initiative passed on the third attempt. The system used is a variation on the open-list proportional system common in Europe; but whereas most such systems allow the voter to cast one vote for either a party or an individual candidate, Switzerland adds complexity to maximise voter choice.

In a Swiss federal election, parties present one or more lists of candidates, ideally comprising as many candidates as there are seats to be filled (up to thirty-four in Zurich, the largest canton). Lists can be combined together, forming an apparentement, the result of which is that their vote totals are counted together, and thus their remainders over their original quota of seats can be combined to earn another seat. The apparentements also give voters an idea of which other parties a party can work with; for example, elections in Geneva are dominated by a Socialist/Green/Labour bloc and a Liberal/Radical/Christian Democrat bloc. Lists presented by the same party can also form a sous-apparentement within an apparentement. For example, parties can nominate all-female and all-male lists, a separate list for their youth branch, a list of candidates appealing to expatriate voters, or different lists for different regions of a canton.

The Swiss voter has as many votes as there are seats to be filled; for this example I will use eleven, Geneva’s representation in the National Council. She can cast a straight-ticket vote (vote compact), giving eleven party votes to the party of her choice and one personal vote each to its candidates. She can cross out (latoisage) the name of a disfavoured candidate on her party’s list, giving eleven party votes to the party but only ten personal votes to each of the non-eliminated candidates. She can cross out one candidate on her party’s list and give a second vote (cumul) to a favoured candidate; this gives eleven party votes and eleven personal votes (two to one candidate, one to nine, and none to one). She can replace a crossed-out candidate on her party’s list with a candidate from a different list (panachage); thus casting ten party votes for her original party and one for the party of the written-in candidate. And she can combine all these three methods on one ballot.

A list’s vote is the sum of personal votes received for its candidates and unused personal votes on its ballots (for example, when a voter crosses out a name but doesn’t replace it with any other candidate or a second vote for another candidate). The seats are distributed proportionally between all stand-alone lists and apparentements, and then between sous-apparentements and between their component lists, all without any electoral threshold. The seats won by each list are given to the candidates with the most personal votes.

The Swiss system allows the voter maximum freedom of choice: she can cast votes for candidates on different lists and cast double votes for candidates she particularly wants to see elected, and her influence on the ordering of the candidates on a list is in proportion to how many votes she cast for that list. By ensuring that a personal vote cast for a different party’s candidate means a party vote is cast for that list, the system prevents a voter from influencing another party’s candidate selection without throwing their lot in with that party. This stands in contrast to open primaries in the United States, where independents and supporters of other parties can vote in a party’s primary, then vote against it in November. (This can be the source of mischief, as when some Democrats tried to boost Rick Santorum’s chances against Mitt Romney this year.)

The system of apparentements means that voters can support a small party which is unlikely to win seats without wasting their vote, provided it is allied to larger parties. In the 2011 federal poll in Geneva, for example, the Greens retained their seat despite polling a lower percentage of the vote than in the previous election. The reason was the surge in support for smaller left-wing parties, who won no seats themselves but who helped the Socialist/Green bloc to increase its vote share. Perhaps the most fascinating aspect of Switzerland’s electoral system, however, is the way in which parties run multiple lists. The youth branches’ lists seem a good way to get more young people into elected office and would give the young activists valuable experience in running an election campaign. The expatriate lists look like a better way to ensure expatriate representation than the French and Italian experiments with (heavily gerrymandered) overseas constituencies, and the concept of sous-apparentements could be useful for promoting cross-ethnic parties in divided societies (for example, a party in Northern Ireland pooling the votes of a Protestant list and a Catholic list).

How would the Swiss system work if exported to the United States? Let’s assume a larger House of Representatives – I like the idea of one thousand members. The seats would be allocated to the states: Wyoming, the smallest, would have two; California would have over one hundred and twenty, and might need to be broken down into smaller regions. Primaries would become unnecessary, as all party factions and interest groups could be accommodated either by places on the main party ticket, or by the use of the sous-apparentement system – a list of establishment Republicans and a list of Teabaggers could pool their votes while retaining a certain distance from one another. In any case, the ability to replace candidates on lists and to cast double-votes for others would replicate the effect of primaries by allowing a party’s voters to determine which of its candidates are elected. With Duverger’s Law beaten, the Democratic-Republican duopoly could be replaced by a two-bloc system (for example, a Democratic-Green coalition might face off against a Republican-Libertarian-Constitution entente, and unhappy members of the current major parties could gravitate towards new or currently marginalised parties). And without wasted votes or the spoiler effect, no American voter need worry that casting a third-party vote will do a Ralph Nader to their preferred major party.