Looking for Brexit consensus? You won’t find it – and this Nobel-winning economist can tell you why

Should pure blue sky research be funded?

Certainly, the answer from government-backed research councils seems to be “no”. The emphasis is increasingly on research which has immediate practical applications.

Yet seemingly esoteric research can shed light in quite unexpected areas. For example, a PhD thesis written by a then obscure research student 70 years ago helps us understand the difficulties encountered today in resolving the current Brexit problem with a series of votes.

The number of alternatives suggested as the outcome of the Brexit process has been bewildering.

During the past week alone there has been: Theresa May’s deal; her deal plus a customs union; her deal plus a customs union and the Single Market; a Canada-style free trade agreement; another referendum; revoking Article 50 and cancelling Brexit; and leaving without a deal at all.

Little wonder that MPs have struggled to produce an overall majority in favour of any particular option.

So now we come to the idea of so-called “indicative votes”. MPs are due to vote on each of a large range of options to see which, if any, command a majority.

A variant would be to get MPs – or the electorate as a whole if there were another referendum – to rank explicitly the alternatives in order of preference. When we elect the London mayor, we have to express our preferences rather than just cast one vote, as we do in a General Election.

All of these approaches seem plausible. They share the same basic idea: test the options with a voting system based in some way on preferences among the alternatives, and see which comes out top.

It seems common sense. But unfortunately, as is often the case, common sense is not a very good thing to rely on.

The PhD thesis mentioned above was written by Kenneth Arrow, who went on to win the Nobel Prize in economics. He demonstrated the inherent problems of preference-based voting systems.

Arrow, who died in early 2017 at the age of 95, is virtually unknown to the general public. He spent his life in the sheltered groves of American Ivy League universities. But he made some of the most profound contributions to economic theory in the whole of the second half of the 20th century.

One of these was his so-called Impossibility Theorem. He proved that, whenever voters have three or more alternatives, no system of ranked voting can convert the ranked preferences of individuals into a set of preferences at the aggregate level which is guaranteed to be consistent.

Arrow’s result applies not just to a given practical example, but to all systems of this kind. Paradoxes abound. For example, even if all voters prefer X to Y, it is entirely possible that at the group level the result may not reflect this.

When once asked about the practical implications, Arrow himself said: “Most systems are not going to work badly all of the time. All I proved is that all can work badly at times.”

Brexit is an excellent example not just of this, but of the value of high quality, blue sky research.