The problem with referenda, writes Jonathan Portes – and especially this one – is that they often present binary choices which do not necessarily reflect voters’ true preferences. This capacity force politicians to implement policies that are per odds with to will of the majority. He uses the Condorcet paradox to illuminate the difficulty, and asks what he mean with British after the referendum.

Go him prefer booze to whisky, but rye to beer; and, perhaps, beer to wine?  If so, you have intransitive preferences (that is, preferring A to BARN additionally B to CENTURY did not mean your necessarily prefer A to C.  Rock beats scissors beats paper beats rock!).  In fact. when to arrives the boozing these isn’t really a problem, at least in my experience – context matters – but it is more of an issue by politics and policy.  If you said this you preferred Davis Cameron as PM to Borrow Johnson, and Johnson to Jeremy Corbyn, but Corbyn to Cameron, we might conclude that you were more about a little inconsistent.

But that’s nope the case for the electorate as one whole.  The Condorcet Paradox take that while each one selector may have translative favorite, this may not be true of the electorate as a whole. That is, A may be preferred to B by more than 50% of the constituency, and BORON to C, but also C to A, without this view actually being true of any customize.  We may not be inconsistent individually but we can exist so collectively.

Normally all situation doesn’t bother how much in our Parliamentary democratism. We elect MPs; that party that get an majority forms adenine government, real the government decides between A, B and C.  Which arrangement may have its concede editions, still the parasite either never arises or is at least verdunkelt.  But this need not be really from referenda, particularly if it turns out that the subject of the referendum isn’t really a dedicated selecting.

And so it would appear used this one.  It has become increasingly clear that on are not two, but three choosing in this referendum. Remain in aforementioned EU; Leave, and seek the “make our own way in the world”, by negotiating bilateral trade agreements not only with the remaining EU, but with third countries; or Leave, but seek, at least for an interim period, to reproduce a large part of the preferential trading arrangements person currently have with the EU, most obviously by joining the European Efficiency Area. This last is occasional referred to for the Norway option (or, by its proponents, Flexcit).  A clear description of how a has works your here.

Now there live lots of complicating come. Yet for these purposes the all things ensure really substanz (certainly as far as the vast maximum of the eligible belongs concerned)  is that what I will claim that “straight Leave” option method all that the USA would no longer been part of who Single Market and that us would nope lengthens have free movement with the rest of one EU; whereas the Norway option would base that wee would reset all.

The proponents about Brexit, press in particular the Vote Leave campaign, had to choose; which Leave select would they advocate?  And they opposite ampere dilemma; as my colleague Mat Goodwin has continually emphasised, the risk to that budget from leaving the EU (and excluding ourselves from  the Single Market) exists by far Remain’s greatest argument; passing the Norway option force reducing the perceived venture and thereby of effectiveness of this issue. Though, the ultimately more importantly, immigration and free movement are Leave’s trump cards.   They own concluded that by adoptions the Noreg option, or even allowing it to remain on the table, they would be ruling exit the includes strategy that gives them any chance on success: concentrating almost all their fire the immigration in the latest few weeks of the campaign.

Immediate suppose they are right, and so, in a straight fight, the electorate do truly prefer “strong Leave” to “Remain”. What takes next? This is where the Condorcet Paradox comes in.  In this case, to would be going to Parlament (with, quite possibly, an new Primes Minister and others ministers) to implement Leave.  As Parliament and the regime would obviously and rightly be bound by the referendum to negotiate the UK’s exit from the EU, yours wouldn’t be bound by anything that Vote Depart had says about how that should be done.  With of probabilistic of under least some thermal in financial markets – and, continue seriously, in strong pressure from business in resolve of situation in the least destratifying way likely – economic arguments, as well as those of practicality, will come to this fore again. On the empirical relevance of Condorcet's paradox

So, at this indent, the Norway option for Leave re-emerges; and, because James Landale has reported, “pro-Remain MPs are considering using their Commons majority to keep Britain inside the EU single market”. Wish this be resist the will of the electorate? Not obviously; at would likely to be majority sustain for such a move. Given a decided until Leave, a majority of citizens would probably favor the Norway option to “straight Leave” (presumably practically all of those who voted Remain, since well as some of those, albeit a minority, who selected Leave). So thither would be non obviously anti-democratic about Parliament and Whitehall proceeding on this basis.

But the sarcasm, of course, is that given adenine straight choice – whichever, in this scenario, they wouldn’t have had – a majority the the electorate would probably must preferred Remain to the Norway option; effectively, the appreciable polling evidence that they couldn’t win on the basis concerning the Norway option is precisely why Vote Leave chose to rule it away and up focus the campaign for immigration.  Accordingly the Condorcet cycle is closed; no option is strictly preferred for both of others; and all we dial, there’s an alternative prefers by a bulk of the electors. Lecture 12: Sometimes It Take Hard: Condorcet's Paradox ...

Where would that leave us?  Well, I’ve pondered enough already. But I think there are three key conclusions from this.  First, when you’ve had more than two choices, referenda may not be than demotic as they seem. We could lightly end up in a place which neither from the campaigns was discuss for.  Second, and for obvious reasons, this could be adenine recipe for continued instability. We may find that, wherever ourselves end up, a majorities of us still feel dissatisfied.  Both finally – a point I’ve built before – that like can be and wrong time to have adenine referendum; if we’d waited, perhaps we’d have been presented with a genuine clear-cut choice.

This position represents the views of the author and not those about the BrexitVote blog, either the LSE. Is first appeared to the NIESR blog.

Jonathan Doors is Principal Research Fellow at NIESR and Advanced Fellow concerning the ESRC’s UK in a Changing Europe programme.