On the 23rd June the UK held a referendum on its membership of the EU and 52% of voters decided we should leave. To put things bluntly - this was the wrong decision. Politicians of all persuasions, however, have been queuing up after the vote to say that we must respect the 'democrat will' of the people. Clearly they do not have much choice, at this stage, given that a majority voted to leave. But, can we really talk of this referendum result as 'democratic'? I don't think so.
To make the case we can start with the impossibility theorems. These theorems, of which Kenneth Arrow's is the most famous prove that there is no voting mechanism that is guaranteed to produce outcomes satisfying some basic desirable properties. For instance, the choice made can be critically influenced by the options on the ballot paper (even if we add options people do not like). There are two basic ways to interpret the impossibility theorems. One is to say that they show there simply is no right decision; if we ask 100 people what they think and we get a 100 different answers then there is no way of determining the optimal thing to do. The other interpretation is to say that a right decision does exist but voting is a very imperfect way of finding it. With either interpretation, democracy does not come out looking particularly good.
There is though one context where voting has been shown to work. It will work, if the decision to be made is a binary one. (This is May's theorem.) The EU referendum was a binary decision - we either remain or leave - and so this surely gives us more faith in the result? Well, the key thing to observe is that framing the question in a binary way does not stop the fundamental issue being non-binary. And this was clearly illustrated in the EU referendum debate. In particular, there was at least three different versions of what would happen if we left the EU: (1) stop immigration, (2) liberalise the economy (meaning more immigration), (3) protect workers right (so de-liberalise the economy). Clearly, these three visions of the future are all incompatible. Which means that many who voted leave are not going to get what they wanted.
Suppose the ballot paper had four options - remain and the three versions of leave. What would the outcome have been then? Indeed, how would the vote have worked. For instance, would voters have been asked to rank choices or just vote for a preferred outcome? We are now firmly in the territory where Arrow's Theorem kicks in. And in all likelihood the outcome, the 'democratic will' of the people, would have been to remain in the EU.
There is a further reason why we should be sceptical of the election results. Standard models of political choice take it as given that voters know what is good for them. That was sadly lacking in this instance. For decades, politicians have found it easier to blame the EU, and then immigrants, for just about every ill that beset the country rather than give the more nuanced truth. This left an open door for leave campaigners to lie and scare. Turkey, for instance, is joining the EU and 17 million Turks are moving to Britain. Etc. If voters are ill-informed then how can we possibly talk of democracy. This is not to slur everyone who voted leave because there clearly are many well-informed people who had good reasons to vote leave. The sad reality, however, is that many of the people who voted leave are those who will suffer most from leaving the EU.
So, what lessons can we take from all this? The main lesson is probably to not have referendums on important issues! Where does that leave democracy? To me, democracy is about electing, in a fair and open way, people to make decisions on our behalf. It is not about ill informed people making decisions for everyone.