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Society, Politics & Law

Straight talking collides with cyclical preferences

Updated Tuesday, 2nd January 2018

Alan Shipman wonders if an 18th Century French aristocrat foresaw a twist in the Brexit vote that will trip up UK negotiators.

The pro-EU march from Hyde Park to Westminster in London on March 25, 2017 Creative commons image Icon Ilovetheeu under CC-BY licence under Creative Commons BY-SA 4.0 license The pro-EU march from Hyde Park to Westminster in London on March 25, 2017

One of the few things economists agree on is that preferences should not be ‘cyclical’. If I prefer option A to B, and B to C, I should logically also prefer A to C. If I don’t, someone who trades in A, B and C would soon have all my money. And if lots of others share my inconsistency, a market-based system won’t be as economically efficient or socially just as the theories suggest.

Yet sometimes in practice, cyclical preference seems perfectly rational. When choosing among election candidates, I might prefer Gottabee Wright to Hardy Lefte, and think both of them more worthwhile than third candidate Strickland Centre. But if confronted with the binary choices, I prefer Wright over Centre and Centre over Lefte.

Or, when choosing an exhibition match opponent for my snooker playing cousin, I may prefer Joe Perry (a middle-ranking professional) over the unknown Harry Cueless (because beating Perry is possible on a bad day and would be much more impressive), and Harry Cueless over Ronnie O’Sullivan (against whom my cousin would have little chance). But forced to choose between Joe and Ronnie, I go for Ronnie, because a victory over either is unlikely and one over Ronnie would get bigger headlines – even though, to stay non-cyclical, I should be choosing Joe.

Forget bent bananas, here’s the straight loop

Cyclical preference emerges more readily when more than one person is involved in the choice. The 18th Century philosopher, Condorcet, showed the paradox that can arise when three voters make binary choices among three candidates. Suppose voter A, a convinced conservative, prefers Wright to Centre and Centre to Lefte. Voter B, a socially conscious liberal, prefers Centre to Lefte and Lefte to Wright. Voter C, who likes radicalism in all its forms, prefers Lefte to Wright and Wright to Centre.

If Wright and Lefte stand for election, B and C both vote for Lefte, and Wright (preferred only by A) is eliminated). If Lefte and Centre are the candidates, A and B both vote for Centre, eliminating Lefte (who is preferred only by C). But if the contest is between Wright and Centre, Wright gets the votes both of A and C, eliminating Centre.

We could try to resolve these inconsistent results by staging a second-round runoff between the two candidates who get two votes in the first two contests. But all three candidates could emerge as the winner, depending on which choices are offered first. Condorcet’s demonstration of cyclicity in some voting patterns reappears in the contemporary Arrow Impossibility Theorem, which shows that it may be impossible to combine individual preferences into a coherent collective preference without violating one of three rules that all seem self-evidently fair. 

The referendum cycle

Why does any of this matter now, when Brits have had a national vote each year since 2015 and are at risk of election fatigue? Because, it seems, those who voted for Brexit on 23 June 2016 may have been expressing a cyclical preference – one now propelling career-threatening pirouettes among the politicians trying to fulfil their wish.

It seems that for most of the 17.4m who voted to leave the EU, Brexit must guarantee that the UK can negotiate its own trade treaties (which means leaving the customs union) and exert more control over immigration (which means leaving the single market). In short, a Hard Brexit was what they asked for, as Theresa May acknowledged in her hard-line cabinet statement in August 2016. Given a choice between Hard and Soft versions, most voters want Hard. Given a choice between Hard and Remain, they obviously also want Hard.

But what if the Hard option is ruled out – economically by the damage (even if only short-term) incurred while stuck between old and new trade arrangements, or politically by the need to keep an open border round Northern Ireland?

The pro-EU march from Hyde Park to Westminster in London on March 25, 2017 Creative commons image Icon Ilovetheeu under CC-BY licence under Creative Commons BY-SA 4.0 license The pro-EU march from Hyde Park to Westminster in London on March 25, 2017

It’s becoming uncomfortably clear that in this case – given only the choice between Soft Brexit and Remain – many Hard Brexit enthusiasts would prefer to Remain. They suspect that Soft Brexit will leave the UK with most of the present costs of membership (including a large financial contribution, conformity to single market rules and common external tariffs) without all the benefits, and prevent the radically different approach to domestic and external trade policy that would be possible with a cleaner break.

Leave champion Boris Johnson put it succinctly in December 2017: too Soft a Brexit would leave the UK like an EU vassal state, still obeying all the rules having lost its seat at the table that sets them. It would be like climbing out of a window but then refusing to move further than the ledge, in case the next step reveals a sharp drop instead of a marvellous escape route. If the UK is to gain anything from leaving, it must (to satisfy most Leavers) swing decisively away from Europe’s way of doing things. This makes a ‘soft’ approach worse than no change at all.

So is a Hard Brexit ruled out?

Such insidious cyclicity among Leave voters won’t trouble their political leaders provided a sufficiently Hard Brexit option remains on the table. But that’s been rendered highly uncertain by the Withdrawal Agreement struck with the EU on 8 December, to ensure ‘sufficient progress’ and enable talks to start on post-membership arrangements.

That agreement effectively commits the UK to stay in the customs union and single market for two years after ‘leaving’, agree reciprocal protection of existing EU citizens’ rights, and keep Northern Ireland in “full alignment with those rules of the Internal Market and the Customs Union” for the foreseeable future.

This opens the door to Scotland, London and other Remain-voting regions to demand their own special deals, including ‘full alignment’, so as to maintain full access to the single market and to migrant workers. Since special rules could not be applied to parts of the UK without breaking up the whole, this points to the softest of soft Brexits, which to many amounts to not really Brexiting at all.

Condorcet among the Conservatives

So many who voted Leave in the referendum may prefer to Remain if the Hard Brexit option has turned irreparably Soft. This unsquareable circularity threatens to scupper Theresa May’s designs for a satisfactory departure on 29 March 2019, even if her shaky parliamentary majority stays intact till then.

The prime minister must draw three unpalatable lessons. First, Hard Brexit is the only option that most Leavers will settle for. Second, if Hard Brexit does too much social, economic and political damage, Soft Brexit is the only alternative that in some way honours the referendum verdict. Third, Soft Brexit – while averting the economic and social damage risked by the Hard – gives the UK comparable costs to existing membership while sacrificing many of the advantages, and is very unlikely to leave us better off than staying fully in.

Most prime ministers steer clear of such dangerously contradictory preferences, but May – who once spoke cogently for Remain – stepped into the role when the contradictory demands were already on display. If she can keep this vexatious cycle moving forward, she will have joined the magic circle and deserve a second term.





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