In this post, I would like to move away from discussion of the rights and wrongs of Brexit but instead concentrate on what outcome people currently prefer. What would be the democratic solution?
Condorcet Paradox
This is a useful part of economic theory that does not get enough attention when discussing democracy. It may seem a little dry but please bear with me because it is very important.
A central concept in economics is preferences:
- I prefer Apples to Bananas (A > B)
- I prefer Bananas to Carrots (B > C)
Given this, you would also expect that:
- I also prefer Apples to Carrots (A > C)
This is called having “transitive” preferences and is a key part of what economists mean for behaviour to be “rational”.
The Condorcet Paradox (https://en.wikipedia.org/wiki/Condorcet_paradox) shows that even if individuals within a group have transitive preferences, the group as measured by majority preference may not have.
In the example above
- A majority of people in a group may prefer Apples to Bananas
- A majority of people also prefer Bananas to Carrots
- However, a majority of people prefer Carrots to Apples
It is entirely possible and logical, even though its it rather counter-intuitive.
Application to Brexit
In Brexit terms, I would have transitive preferences:
- I Prefer Remain to May’s Deal (R > M)
- I prefer May’s Deal to No Deal (M > N)
and completely consistently:
- I also prefer Remain to No Deal (R > N)
For the main groups within the population, let’s imagine 1st, 2nd and 3rd preferences for the various outcomes in the below table:
In my imagined universe:
- Remainers – would prefer May’s Deal to No Deal
- May-Dealers – would prefer No Deal to Remain
- No-Dealers – would prefer Remain to May’s Deal
It may seem an odd choice but, for example, this is Dominic Raab’s expressed view.
It seems for some, defeat is emotionally more acceptable than compromise.
Now let’s have a contest and see who wins if we ran a Referendum on each pair of outcomes:
In this case, the overall population makes these choices:
- Remain is preferred to May’s Deal
- May’s deal is preferred to No Deal
You may think therefore that Remain is preferred to No Deal but this is not the case. Actually:
- No Deal is preferred to Remain
In this imagined case, there is no overall preferred outcome.
What do people actually prefer?
Polling data in the UK is consistent with this problem. Support for the three options is pretty evenly split, and even taking into account second preference, we are no clearer. Each head-to-head matches would be too close to call contests. 
How is this relevant?
If means the UK, as a whole, DOES NOT HAVE A PREFERENCE and therefore there is no single “democratic” correct answer. Representative democracy, with parties and elections, has been our way of dealing with issues like this. Having a referendum on an issue with more than 2 possible answers just leads to nonsense, just as happened in the initial Brexit referendum.
Identity politics vs Pragmatism
The Brexit ultras who want No Deal can be seen as being driven by identity politics. This means that national identity is overwhelmingly important compared to economics. If you are a Remainer for whom Brexit is a matter of identity politics then for you then wanting a referendum is very logical. That is the only feasible route to Remain and anything other than Remain is a loss.
For economic pragmatists supporting a referendum is very dangerous. Remain is by far the best outcome but No Deal Brexit is catastrophically worse than any deal and avoiding a catastrophe is the most important thing.
For political pragmatists supporting a referendum is very dangerous. The result will be close and will not close the issue. There will not be any clearer sense of legitimacy for the outcome and after another 6-month campaign our divisions will be even more entrenched.
Should we have another Referendum?
As an ardent Remainer, you would think that I support another Referendum. But I do not.
Partly given the logic above, I do not think Referenda are consistent with our democratic system and thus a sensible way to resolve a complex issue like this. But also more pragmatically, I think Remain may struggle to win again and there is a good chance No Deal is the eventual winner; or even if Remain were to win, it would not be by a sufficient margin to close the debate.
Applied Macro 