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).