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Will a vote for Theresa May strengthen her bargaining hand?

As the run-up to the UK's snap general election continues, the Conservative party appear content to talk about one thing and one thing only - strong and stable leadership for Brexit negotiations. Throughout the campaign Theresa May has been particularly keen to claim that 'every vote for me strengthens my hand in the Brexit negotiations'. This claim seems to be going down well with voters. But does it make any sense?
          In bargaining theory the disagreement point is of critical importance. In the Brexit negotiations we can think of the disagreement point as the outcome if no deal is done between the UK and the EU and so the UK simply leaves the EU in March 2019 and starts from scratch. Most experts seem to agree that no deal would be bad - very bad for the UK and bad for the EU. That means that a deal is essential. It also means that the UK starts from a bad negotiating position. 
        To put some analysis to this consider the figure below. This plots the payoff of the EU and payoff of the UK depending on what deal is done. The blue line captures all the possible outcomes from a deal - some deals better for the UK and some for the EU. The bottom red dot captures the outcome if no deal is done. Note that if no deal is done then payoffs are well below the blue line - an agreement is good. Also, if no deal is done then the UK loses more than the EU - this puts the UK in a bad negotiating position. 

  
           In a world of calm deliberation the EU and UK could easily come to an agreement that is better than no deal. But, unfortunately, some Brexiters seem to have got over excited by the referendum win and started to believe their own rhetoric. In  particular, they are claiming that no deal is not that bad. This is encapsulated by Theresa May's claim that 'no deal is better than a bad deal'. This statement is either a tautology or a claim that no deal may be relatively good. Brexiters are also fond of claiming that no deal would be worse for the EU than the UK. So, returning to the figure, let the red Eurosceptic dot represent the 'optimistic' stance of Brexiters.
            Before she called an election, Theresa May had a small majority in parliament. That means it was going to be difficult to get anything through parliament that the eurosceptics did not like. And there is not much room for maneuver if you want do a deal better than the eurosceptic initial belief. Note, however, that this strengthened Theresa May's hand quite a lot. In particular, European politicians seemed keenly aware that it was going to be difficult to get any deal through the UK parliament. This means that they might have reluctantly had to make some concessions.
          What if Mrs May has a huge majority in parliament? Well, then anything will get through parliament and so we revert back to the actual disagreement point. The bigger the majority, therefore, the weaker is the UK's position. Ultimately, things are not so bad, because a Conservative majority makes it more likely a deal can be done. Indeed, Theresa May presumably called an election because it was becoming increasingly clear that Conservative backbenchers were going to make life very tough. This made no deal more likely.
         The trouble is, the rhetoric of the Brexiters seems to have no bound. This rhetoric is not convincing anyone in Europe but is being lapped up by much of the British press and public. If we go into these negotiations with a public who think the initial position is the top eurosceptic red dot then it may be difficult for any prime-minister, no matter how big the majority, to sell a deal. In other words, Britain seems to be walking into a cul-de-sac of disaster. The only crumb of comfort is that the UK economy seems to be showing the signs of Brexit. That may concentrate minds.     

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