Tuesday, 28 March 2017

Brexit and the Condorcet Paradox

Tomorrow the government will trigger Article 50 and start the formal process of getting the UK out of the EU. So, how did we get in this mess in the first place? I think the Condorcet Paradox provides an interesting angle on the problem. In particular, I want to look at preferences for Remain versus Soft Brexit, i.e. leave the EU but still remain in the single market or other collaborations centered on the EU, and Hard Brexit, i.e. walk completely away from the EU. 
          The one thing we know for sure is that in the referendum last June around 52% of people voted Leave and 48% voted Remain. What does that tell us? In my recollection the referendum campaign primarily focused on the question of Soft Brexit versus Remain. No doubt some would disagree with that. But things like the customs union only started being talked about after the vote. Instead we heard a lot during the campaign about the Norway or Swiss model of Soft Brexit. True the Leave camp made promises like 'take back control of our borders' that inevitably mean hard Brexit. But, the Leave camp was far less pro-active in actually joining the dots and saying what hard Brexit would mean. The referendum vote tells us, therefore, that the British people prefer Soft Brexit to Remain.
         Once Theresa May took power the discussion very quickly turned to focus on Soft Brexit versus Hard Brexit. Now, the Brexiters were keen to join the dots and argue that 'taking back control' inevitably meant Hard Brexit. Soft Brexit, they argue, is essentially Remain in different clothes - if we are going to leave then it has to be Hard Brexit. We have no idea how the country would vote on this issue but I think there is a fair chance the country would prefer Hard Brexit to Soft Brexit
        If the country prefers Hard Brexit to Soft Brexit and prefers Soft Brexit to Remain then you might expect they would prefer Hard Brexit to Remain. But, I would be surprised if that was the case. If the original referendum campaign had been a tussle between Hard Brexit and Remain then Remain may well have won. The vote was close enough as it was and opinion polls have consistently shown that people want to remain part of the single market. Overall, therefore, we end up with a Condorcet Paradox:

Hard Brexit beats Soft Brexit
Soft Brexit beats Remain
Remain beats Hard Brexit.

          If there is a Condorcet Paradox then it is impossible to say which option is the most preferred. Note, however, that we are set to end up with an outcome, namely Hard Brexit, that is worse than we started with, namely Remain. That does not look like a good deal! Plaudits should, however, go to the Brexiteers for their strategic opportunism. In particular, we know that whenever there is a Condorcet Paradox the outcome depends on the voting procedures. The only way those favoring Hard Brexit were going to get what they wanted was to play off Soft Brexit versus Remain and Hard Brexit versus Soft Brexit. By design or good fortune that is exactly what has happened. 
          And are we going to get a vote on the final deal, pitting Remain versus Hard Brexit? Of course not. And how long before the UK votes to rejoin the EU because Join is better than Hard Brexit? Probably, a long, long while. 


  1. Good post, exposing the underlying problem. I wrote a piece on the same subject a few months ago—do have a look! https://medium.com/nodust-on-brexit/the-trouble-with-referendums-9afedcd499ea?source=linkShare-d706161a485e-1491164273

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