A guest post by Daniel Bochsler:
In yesterday’s referendum vote, Swiss voters have decided to expel foreign delinquents automatically. One year after the minaret ban, this new referendum further fuels the discussion whether direct democracy endangers minority rights. But the new referendum is also a rare observable occurrence of Condorcet’s paradox of majority cycles.
Majority cycles, which have been described by the French mathematician Marquis de Condorcet, are well known to students of political science and economics. However, they remain a phantom, as the literature is widely theoretically driven, and there empirical evidence remains scarce.
Let us define first what we speak about. Majority cycles can occur in any situation where voters have the choice between three (or more) options: Different groups of voters have their preference ordering about those propositions. Imagine that we have a first group of partisans of a reform, which however do not like an alternative counter-proposal, so that their preference order would be Reform > Status Quo SQ > counter proposal CP. A second group of voters is reform-friendly, but between both reforms they favour the counter proposal [CP > Reform > SQ]. A third group of voters does not like either of both reforms, but they would still prefer the counter-proposal to the reform proposal [SQ > CP > Reform]. Each group of voters has rationally plausible, transitive preferences. Jointly, the collective preference order results to be intransitive. Two out of three groups of voters favour Reform over SQ. Two groups, again, favour CP over Reform. Finally, two groups (although not the same), favour SQ over CP. Hence, (if none of the three groups counts an absolute majority of voters,) the collective preference order is intransitive, SQ > CP > Reform > SQ. Each of the three options is defeated by exactly one other option, as this table shows:
|Reform vs SQ||CP vs SQ||Reform vs CP|
|Voter 1||Reform||Status quo||Reform|
|Voter 3||Status quo||Status quo||Counter-proposal|
In yesterday’s referendum, the Swiss decided between two alternative reform proposals – the radical popular initiative by the Swiss People’s Party, a more moderate counter-proposal of the government, and the status quo. And they voted for the most radical option. While we lack information about the individual ballots, the result looks like a Condorcet cycle, as we see in this table:
|Yes||No||% for first option|
|Reform vs SQ||1,398,360||1,243,325||52.9|
|CP vs SQ||1,189,186||1,407,743||45.8|
|Reform vs CP||1,252,625||1,270,831||49.6|
The occurrence of a majority cycle could be anticipated in the pre-referendum campaign, as a combination of the voting preferences of different groups of voters. Indeed, the referendum results shows that a majority of Swiss voters would have preferred the governmental counter-proposal (which respects international law and fundamental rights) to the radical initiative – but they voted instead for the initiative. This opens quite a few questions:
1) The counter-proposal contained many of the claims of the radical initiative. Having this in mind, why did a respectable number of those voters who voted in favour of the initiative reject the counter-proposal?
2) Public choice teaches us that in single-dimensional decisions, where we can rank all options on one axis, having two extreme poles and a solution between the two (more precisely, this implies that we should have single-peaked preferences), as in the present case, majority cycles should not occur. Apparently, it did, nevertheless.
The theory of majority cycles also teaches us how to vote strategically in multi-option decisions. Usually, committees or parliaments employ the amendment procedure for multi-option decisions. If there is more than one option for an amendment, then the proposed amendments are voted on in pairs. Acting strategically, a chair that anticipates a cycling preference order, can schedule his/her favourite option in the last round of voting, in order to make it pass.
In multi-option referendums in Switzerland, all pair-wise decisions appear on the same referendum ballot. In this situation, voters can strategically create artificial cyclic majorities in order to make their favourite proposal pass. In yesterday’s referendum, the Swiss People’s Party was probably inspired by this idea. The counter-proposal might have served as a compromise between the radical initiative and the status quo, and it was probably the most popular of the three referendum options. Also, it fulfilled a lot of the Swiss People’s Party’s requests. Nevertheless, the party encouraged its supporters to reject the counter-proposal. Lacking sufficient votes from anti-immigrant voters, the counter-proposal failed narrowly to win a majority of votes, and only the more radical initiative passed. According to the (reform-friendly) rules for multi-option referendums in Switzerland, the optional question (reform versus counter proposal) does not count in such cases, and the popular initiative is accepted.
Anticipating the outcome, the acceptance of the initiative might have easily been avoided. Indeed, in Condorcet cycles, one strategic vote can neutralise another. Radical anti-immigrant voters around the Swiss People’s Party probably rejected the counter-proposal for strategic reasons. Opponents of special laws for immigrants (equal-right-voters) might have applied a simple counter-strategy, and have hindered the radical initiative to pass: voting strategically in favour of the counter-proposal would have secured a majority of votes (and cantons) in favour of the less radical counter-proposal. This would have blackmailed the Swiss People’s Party campaign for the more radical option. Indeed, a group of Social Democratic MPs and several of their cantonal branches have given such a strategic voting recommendation. But the national party branch, along with the Green party, which campaigned for equal rights, decided against any strategic voting.
Switzerland appears like a dream world for the study of majority cycles. There is very little evidence of directly observable Condorcet paradoxes. In parliaments and committees, usually two consecutive simple majority decisions are made, so that MPs do not express their full preference orders, and majority cycles do not become visible. Swiss voting institutions, however, appear as quite unique in the world, as no other country, to our knowledge, applies multi-option referendums where voters can fully rank three options. After a change of the rules in 1987, Swiss voters have a short experience with multi-option referendums where they can fully rank-order all three proposals. Precisely six years before the referendum of yesterday, a majority cycle occurred in a multi-option referendum in the canton of Bern on 28 November 2004.
This new (supposed) Condorcet cycle might not only speak to Public Choice specialists. It might also speak to scholars who are concerned about minority rights in direct democracy. And the same Condorcet cycle also carries a message to equal-right-voters, who are now very concerned about the new slap of the Swiss voters in the face of the immigrant community: No, the referendum result is not only the expression of xenophobic values among many Swiss voters. It is also a consequence of the refusal of many equal-right-voters to vote strategically.