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Are Liberal Democrats the ‘Condorcet Party’?

The Shakespeare Report.

This is an unusually difficult election for pollsters to feel confident about, because the strength of the LibDems changes the very nature of the polling question. We ask people who they will vote for. Well, that’s unambiguous question, you might think, but the reality of voting in a marginal seat creates a genuine ambiguity. Imagine you are a Labour supporter in a LibDem-Conservative marginal, and you know you will vote LibDem, tactically, to stop the Tories in that seat. What should you answer? “LibDem” would be factually correct. But you actually want Labour to win. You don’t want to ‘vote’ for LibDem in a poll, you want to indicate the real nature of your support, which is for Labour. There isn’t a simple ‘honest’ answer.

This can play havoc with the voting intention figures, once more and more seats are perceived as marginal, and the Liberal Democrats become the 'Condorcet Party'.

The conventional model of voter choice imagines, for each issue, individuals placing their preference along a line running from one extreme to another. For example, one line may run from complete pacifism to neo-Con interventionism. The views of the public are spread along this line, with a peak somewhere near the middle. Imagine a multi-dimensional area defined around these peaks, each weighted according to the relative importance of the issue to the voters, and you have the ‘centre ground’. Parties generally try to place themselves very close to that centre ground in order to give themselves the best chance of winning.

The French mathematician Marie-Jean-Antoine-Nicolas Caritat de Condercet proposed an alternative model (just before being condemned to the guillotine by the French Revolution): what if there is not a single peak, but a double peak along the line? For example, take attitudes to the EU: we may find two peaks, one towards the ‘full integration’ end, and the other near the ‘get out now’ end, and not much in the middle.

The LibDem policy of a referendum to settle the ‘in or out’ question appeals to both peaks simultaneously, and legitimately. And across the whole policy arena, the LibDems prefer to appeal to a distribution of ‘peaks’ of opinion. This often leads to accusations of duplicity from rivals, but in fact many individuals happily maintain apparently contradictory positions perfectly reasonably. Weighing up the advantages of full integration into a truly democratic European Union and exit from an unreformable one, you can easily prefer both options to hovering at some unsustainable mid-way point.

In choice theory, a party which is in third place but beats or ties with each of its rivals is called the ‘Condorcet winner’. You can imagine the LibDems in such a position: they are not the number one choice, but in a straight LibDem-Conservative race, Labour supporters prefer the LibDems, while they are also preferred by Conservatives in a straight Labour-LibDem fight. This, of course, is what can happen in the marginals. What holds them back is the perception that they cannot win overall. That’s why the debates (and the polls) have become so important and fraught.

Condorcet argued that in some situations, majority rule is inherently unstable, and a very narrow majority or hung parliament may well demonstrate that: locating government at some carefully-orchestrated middle-position that few actually support may not be the optimal option.

Stephan Shakespeare is CEO of YouGov.


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