In a plebiscite with a binary choice of options a democracy commits to follow the course of action preferred by the majority of those who choose to vote. The threshold could be arbitrarily set at some level above 50%, meaning that a decision would be deferred if the majority were not of sufficient scale. Many think that this is what Mr Cameron should have done in two of the referenda that he has called, on Scottish Independence and on membership of the European Union. This is a misunderstanding of the significance of a majority vote in such a plebiscite, which is distinct from that in an election where there are more than two options.

Elections where there are multiple choices function to represent the preferences of the majority of individuals, even if that group is nowhere near an absolute majority, as in the First Past the Post electoral system employed in the United Kingdom. It is a peculiar system, and difficult to defend, since it tends give the impression that many votes are ‘wasted’, in other words that they fail to determine the choice of candidate and the information represented in that vote is then lost to the system. There are clearly strong arguments in favour of some sort of proportional representation in the constitution of representative bodies, though they have yet to secure much of a following, more likely because very many could see that it would benefit one party, the Liberal Democrats, that is widely and actively disliked. (The Conservative and Labour parties oppose each other, with vigour, but they don’t find each disgusting, like a bad smell, to use the Chinese test of sincerity. But both are revolted by the Liberal Democrats, and would rather push on with a faulty electoral system than adopt a system that would enlarge the LibDem representation. I share this feeling, as it happens, but recognise that it is a visceral, holistic reaction more than a carefully reasoned one.)

However, it is an error to think that the information recorded in the minority vote during a binary plebiscite is also lost, as it unquestionably is in First Past the Post, or that the views of those voters are unrepresented. Binary plebiscites are exercises in information gathering, allowing the collection of judgements based on data seen from a vast number of perspectives. Voters make errors, and base their votes on false beliefs, but since they do so on both sides, this cancels out, and the proportions represent the population's best assessment of the relative wisdom of the two courses of action. It is a way of balancing the benefits against the disadvantages, and although the choice is binary, the result, the output is not so, it is a descriptive decision which permits those executing the policy to appreciate the degree to which the decision is finely balanced.

Those who voted Remain in the UK independence referendum are not, as a group, stupid or fools; they judged an exit from the EU to be, on balance, and as far as they could tell, harmful to their interests. Those who voted to Leave did the same.

At a national level, the balance 52/48 is substantially in favour of leaving, but not a landslide. Thus any government now carrying out the decision to Leave must operate on the assumption that there are serious hazards to leaving the EU, and that these must be guarded against. Those who voted Leave must avoid the assumption that victory, like a first-past-the-post victory, entitles them to discard the information represented in the Remain vote; on the contrary it is important data, and should inform the way in which the decision to leave is enacted. One might summarise that as “Proceed with Caution”.

But similarly, those those who voted Remain, must accept that the population as a whole, has judged departure from the EU to be net beneficial. To stridently assert that those voting leave are stupid, or selfish, and not entitled to influence a decision is, firstly, inconsistent with the established political principles of this democracy, principles that Remainers would prefer not see abandoned and replaced with an autocracy. Secondly, it is flawed from an information theoretical point of view. It is essential to consult the entire population of minds in order to produce a well-grounded decision. To allocate less weight to the decision of some voters would be to deliberately distort the decision in a prejudicial manner that would defeat the exercise, which, as noted above, is to gather as much information as possible that is relevant to the decision.

At this point, some may say that if breadth of information is desired, why do we only entitle voters over a certain age? This is a reasonable point, and there are arguments for reducing the voting age. But, the same argument in favour of high quality information gathering also supports an age qualification, on the grounds that very young people are insufficiently independent to avoid distorting influences. On this ground there are in fact strong arguments for increasing the voting age, and even denying it to those who are not economically independent. However, the current decision of this democracy is that any citizen, regardless of wealth and over the arbitrary age of 18 can vote (though this was dropped to 16 in the case of the Scottish independence referendum). In other words, as far as this population can tell, this is a reasonable specification to ensure information quality as well as consent to the decision. Seen historically, this a very broad specification, but intelligible in the sense that due to great societal wealth and broad education, there is valuable data available even in the minds of the young (under 20) and those whose economic resources are a small fraction of the whole but, again seen historically, are large in an absolute sense.

Finally, the balance of votes in the EU referendum tells us something of vital consequence about Scotland. In effect, the decision tells us that on balance membership of the EU is probably beneficial to Scotland. Indeed, when we subtract that decision from the UK result we see that the balance of benefits for England and Wales is much more strongly in favour of leaving. This divergence of interest suggests that an independent Scotland is now probable, indeed is de facto already the case. However, it is not inevitable, and the people of England and Wales could decide to change the balance with wealth transfers or other similar considerations. After so much ill-tempered debate, I think this is unlikely to be sufficient, and indeed if I were a Scot I doubt that I would find them remotely adequate.

A similar point can be made with regard to the residential, voting population of London, which was substantially in favour of remaining in the EU. It would probably be wise of the government to examine the character of the population very carefully to determine why they reached this decision, and, in the interests of general harmony, to take steps to adjust the balance for that population.