The theories one uses needs to be explicit, especially when the issue is as complicated as Brexit or Trump.

Two of my intellectual mentors, Maynard Keynes and Karl Popper, give broadly the same advice. Be aware that you are using theories; be sensitive to their assumptions, to their limitations. Very often our public discussions involve no awareness of the underlying theoretical constructs, let alone their weaknesses (as well as their strengths).

Keynes’ and Popper’s dictum was reinforced by my training as an applied mathematician, because modelling involves theorisation. Within weeks of beginning to study economics, I read Kenneth Arrow’s famous doctoral thesis on social choice, which has troubled economists ever since. In essence it says that under plausible assumptions, a group may not be able to make rational social choices (ones that gives consistent rankings) other than by a dictatorship.

Economists have unsuccessfully hunted around for a resolution that does not require a dictator. My practical conclusion is that often outcomes are not some simple ideal but depends on the decision-making process.

Perhaps to make good quality social decisions we need a dictator; that seems a very depressing conclusion when one thinks of, say, Hitler, Mao and Stalin. A decade later I came across the aphorism of Quintin Hogg, later Lord Hailsham, that parliamentary government involved ‘elected dictatorships’.

That seemed oh so true, when were under Rob Muldoon who ruled with an iron will. Or so it appeared. Later, reading accounts of the inner workings of the Muldoon government I saw a different story. There is a moving description by Muldoon’s head of department, Gerald Hensley, of him learning of the Rugby Union refusal to call off the 1981 Springbok Tour: ‘he stared down at his desk for some time and then said gloomily “I see nothing but trouble in all this, nothing but trouble”.’ The ‘elected dictator’ had to make a bloody compromise; he went with the pro-tour group – presumably for electoral reasons – and so we had internal strife, even within families.

The relevant analysis comes from game theory (look it up if you dont know) which says that in such conflict situations there is a ‘core’ of policy choices which no group or coalition of groups can veto. A benign interpretation of an elected dictator in a democracy is that they are restricted to choosing policies from a democratically determined core, but that they have absolute discretion about which policy within it to choose. In that way society gets consistent policy decisions.

The role of MMP is for the people to choose their dictator. (Perhaps I should add that this game-theory model is static; political leadership may be about the dynamic version; see what I mean by being sensitive to the assumptions?)

I have briefly sketched an account underlying the principles of cabinet government as melding dictatorship and democracy. But what happens if there is no core, that every option can be vetoed? Ask Theresa May, for we are seeing a breakdown of cabinet government in today’s Britain.

May started off her pursuit of Brexit with a set of ‘redlines’, which, I take, she interpreted as the implicit demands of those who voted ‘Leave’ in the referendum. When I went hunting for them I found the lines very fuzzy and numerous. (See here and here for some lists.)

But two key ones for an economists’ purposes are

1 The UK was to have an independent trade policy to allow it to negotiate its own free trade agreements (starting with the US, Australia and New Zealand)

2. Ending the free movement of people from the EU

That led to the May-deal with the EU. If she wanted to maintain some special relationship with the EU, there was not a lot of choice, given the redlines.

Recently the British Parliament voted overwhelmingly against the May-deal, some 432 to 202. (The equivalent in the New Zealand Parliament would be the government losing a vote by 82 to 38.) But this did not lead to the defeat of the May Government. The ruling Conservative Party do not want a Corbyn-led Labour Party in government, while they cannot agree on an alternative leader.

May thinks she can get a majority by fudging the deal, but given her redlines, I am sceptical. Her other strategy seems to be to threaten an even more unacceptable ‘no-deal’, which would probably lose by about 530 to 100. (Say 100 to 20 here.)

Normally, negotiating theory would say go back and review your redlines. But there are two understated ones which seem to preclude this. One is that the Conservative Government is dependent upon a small Northern Ireland party which is fearful of deals which could see a united Ireland. The land border between them is crucial here. The effect of the first implicit redline is that there needs to be a controlled border. Relaxing it to make the border more permeable would probably mean a customs union, which would rule out FTAs with others countries.

An even bigger veto comes from the hundred-odd ‘no-dealer’ Conservative MPs who are comfortable with the explicit redlines but their logic is for Britain to pull out of any deal with the EU. Implicitly, May is committed to maintaining the unity of the Conservative Party; that may be her biggest single redline. (An unkind remark is that she is willing to sacrifice Britain for her party.) So she is absolutely jammed without any core options to choose from.

Once I thought that parliament might be able to resolve the impasse. But the Arrow theorem kicks in, rather savagely. One assessment of the main parliamentary factions is

• No Deal (Hard Leavers) 100

• May-deal (No freedom of movement) 200

• Corbyn loyalists 30

• Soft Brexit (Customs union) 150

• People's Vote (Hard Remainers) 150

The figures are not precise but, even if Corbyn makes up his mind, there are still four factions, none of which can dominate any of the others.

It is hard to see a solution. For instance, there just might be among the second choices a majority for a customs union, breaching some of May’s redlines. But that requires negotiation with the EU and parliament does not have the executive authority. I assume that would mean another prime minister and that might mean agreement between some Conservatives and Labour.

The British Parliament may vote for a delay of the March 29 implementation date, although that is not without its complications including that there is an election for Members of the European Parliament in May. Anyway, a delay is not a resolution.

I could speculate on what happens after. (I note an interesting proposal to have a referendum at the time of the elections for the European Parliament. Arrow says that how its questions are structured may be crucial.) But I leave you to speculate instead, with the hope that the analytic frame I have set out is of some use.

After, you might apply it to the US. Trump is of the view he is an elected dictator with absolute authority. Nancy Pelosi may, or may not, have taught him that he is one subject to democratic checks and balances, and that he needs to think about the core. Not the minority follow him irrespective of how badly he does, but that he should look for core policies that no coalition can veto.