The biggest question that emerged at last week’s conference on referendums at New York University was how to understand what people meant when they voted.

Professor Larry Wolff, Director of the Center for European and Mediterranean Studies, opened the conference with a survey of the history of modern referendums, starting with that on the constitution of 1793 in revolutionary France. The outcome seemed unambiguous, 99.4 per cent in favour, but it was on a turnout (on male suffrage) of less than 30 per cent and the constitution never came into effect.

Professor Wolff then surveyed the referendums in Upper Silesia, Danzig, Schleswig and elsewhere after the First World War. US President Woodrow Wilson was keen on them as a way to apply his principle of self-determination, but almost immediately had second thoughts as the difficulties became apparent. How do you define the area to be polled? Who should supervise the ballots – David Lloyd George, the British Prime Minister, pointed out that the only alternative to German military supervision was Allied invasion and occupation of disputed territories? Should there be a turnout threshold?

In those cases, the question itself was simple: do you want to be a citizen of Germany or Poland, Germany or Denmark, and so on.

But the wording of questions is usually controversial. Jane Jenson, Professor of Political Science at Montreal University, looked at the 1980 and 1995 referendums on independence for Quebec. In the second referendum the question was: “Do you agree that Quebec should become sovereign after having made a formal offer to Canada for a new economic and political partnership… ?” It was lost by 50.6 to 49.4 per cent.

The Quebecois issue has receded since then, but controversy has raged on, so much so that a Clarity Act was passed in 2000. This provides that, in a future referendum, the question must say the province will cease to be part of Canada, and cannot promise association or partnership with the rest of Canada “before the fact”. This seems prescient about our EU referendum, as the biggest question now is what kind of relationship with the EU Leavers thought they were voting for.

EU referendum - in pictures Show all 18 1 /18 EU referendum - in pictures EU referendum - in pictures A woman in a wheelchair with British and European Union flags shows her support for the United Kingdom to remain in the European Union on the day of the EU Referendum in Gibraltar Getty Images EU referendum - in pictures A polling station being used in the EU referendum at Batley Town Hall in the constituency Labour MP Jo Cox PA EU referendum - in pictures People arrive to vote in the EU Referendum at the Library where British MP Jo Cox was shot and fatally wounded last week in Birstall EPA EU referendum - in pictures A man arrives to vote at a polling station for the Referendum on the European Union in north London REUTERS EU referendum - in pictures Voters queue to enter a polling station at Trinity Church in Golders Green in London Getty Images EU referendum - in pictures British Prime Minister David Cameron and his wife Samantha Cameron leave after voting in the EU Referendum at Central Methodist Hall, Westminster Getty Images EU referendum - in pictures Labour Party leader Jeremy Corbyn cast his vote at a polling station at Pakeman Primary School in Islington Getty Images EU referendum - in pictures Chelsea pensioners arrive at a polling station near to the Royal Chelsea Hospital PA EU referendum - in pictures A woman wearing an "I'm In" t-shirt, promoting the official "Remain" campaign, leaves a polling station in London AFP/Getty Images EU referendum - in pictures People queuing outside a polling station on Amott Road in London PA EU referendum - in pictures Scotland's First Minister and Leader of the Scottish National Party (SNP), Nicola Sturgeon and her husband Peter Murrell, react as leave after casting their votes at a polling station at Broomhouse Community Hall in east Glasgow AFP/Getty Images EU referendum - in pictures A man wearing a European themed cycling jersey leaves after voting at a polling station for the Referendum on the European Union in north London REUTERS EU referendum - in pictures Ukip leader Nigel Farage arrives to cast his vote at Cudham Church of England Primary School in Biggin Hill, Kent PA EU referendum - in pictures Justice Secretary and prominent 'Vote Leave' campaigner Michael Gove poses with his wife Sarah Vine after voting in the European Union referendum at their local polling station in Kensington Getty EU referendum - in pictures Nuns leave a polling station after voting in the EU Referendum in London EPA EU referendum - in pictures People arrive to cast their ballots in the EU Referendum in Gibraltar. The United Kingdom and its dependant territories are going to the polls to decide whether or not the the United Kingdom will remain in the European Union Getty Images EU referendum - in pictures A man driving a van covered in stickers urging people to vote for the United Kingdom to remain in the European Union drives outside a polling station on the day of the EU Referendum in Gibraltar Getty Images EU referendum - in pictures A sign on a gable wall in Belfast's, Loyalist Tigers Bay urging voters to leave the EU using scripture from Revelation 18:4, as voters head to the polls across the UK in a historic referendum on whether the UK should remain a member of the European Union or leave PA

However, the Clarity Act produced no clarity about the size of majority required: the Canadian House of Commons is to decide that at the time, “taking into account the participation rate and other matters it considers to be relevant”.

The trouble is, as Joan Pau Rubiés of the Catalan Institute for Research and Advanced Studies pointed out, that anything other than a simple majority is arbitrary. But he thought a referendum was “not the best option” in Catalonia, because the people are divided and a referendum makes it “difficult to generate a consensus”. In the 2014 referendum organised by the Catalan government but not recognised by the national government, 81 per cent voted for independence, but on a turnout of only about 40 per cent.

John Nicolson, the Scottish National Party MP, spoke about the Scottish referendum in 2014. There were no doubts about its legitimacy, or even about the question, which was probably biased slightly in favour of independence (Yes rather than No), because David Cameron sought to minimise grievance-mongering.

Nicolson said he never expected the Yes campaign to win, but thought the result could be different if there is another vote. He pointed out that Brexit changed how Scotland was seen by the rest of the EU. Previously Scottish nationalism had been regarded as a disruptive force threatening to break up an EU nation-state: “Now Scotland is seen as a good European wanting to remain in the EU while its big brother stomps off in a huff.”

He referred to the 1953 case brought by the Rector of the University of Glasgow who took exception to the Queen calling herself Elizabeth II, as she is the first of Scotland. Nicolson summarised the court’s decision as being that “she could call herself Ethelred the Unready XXVII if she wanted to”. But the importance today of this ruling was that the Lord President, the highest judge in Scotland, gave his opinion that “the principle of unlimited sovereignty of Parliament is a distinctively English principle and has no counterpart in Scottish constitutional law”. I am not sure how this could be relevant to the SNP’s attempt to keep Scotland in the EU, but it seems to offer scope for more legal fun and games once the UK Supreme Court has disposed of Article 50.

Next in our historical tour was last year’s Greek bailout referendum. Katherine Fleming, Provost of NYU and historian of Greece, expounded on the significance of the word “Ochi”, Greek for “No”, which won 61 per cent of the vote. “No” Day is celebrated in Greece on 28 October. Paradoxically the “No” it commemorates was uttered by Ioannis Metaxas, Greece’s fascist dictator, in 1941, in response to an ultimatum from Mussolini, the Italian dictator. What Metaxas actually said, in a telegram in diplomatic French, was, “Alors c’est la guerre.” Yet this came to be remembered as an assertion of popular resistance, as “Ochi” to the Germans, who invaded Greece shortly afterwards.

This helps to explain the apparent contradiction of the “Ochi” in the referendum, soon after which the Greek government accepted an arguably worse deal. The referendum allowed the Greek people to feel that they had asserted their pride, but then to accept the inevitable terms for staying in the eurozone, which they also want to do.

Next we went to Hungary for this year’s anti-immigration referendum. Istvan Rev, of the Central European University in Budapest, took the conference aback by declaring: “The reason we stuck in the throat of the Soviet empire and the reason it broke a tooth when it tried to bite on us was that we asserted our national ideals, that we stood together and did not surrender the love of our homeland. This is also why we shall not accept the EU’s transformation into a modern-day empire.” Only after several more minutes in similar vein did Rev pause and say, “... thus spoke Viktor Orban on the anniversary of the 1956 Soviet invasion.”

This referendum was on the unusually biased question: “Do you want the EU to be able to mandate the obligatory resettlement of non-Hungarian citizens into Hungary even without the approval of the National Assembly?” But it failed to meet the 50 per cent turnout threshold, a recent change made by Orban, the Hungarian prime minister, because he didn’t like the results of previous referendums. So, although 98 per cent voted Yes, turnout was only 44 per cent. “Sanity – or indifference – defeated the government,” Rev noted. He described Hungary as a country with an “unusually bad and tragic history”.

Finally, we returned to the subject of this year’s British referendum on the EU. I felt that the question was fair (the dull “Remain” option was a little biased against “In”), and the referendum justified. In my contribution I argued that it came about because of democratic pressure, not just because of the demands of Tory party management.

The Remain campaign had problems. James Cronin of Boston College had a good line about the problem of selling a positive case for EU membership. The EU is not the kind of institution about which it is easy to be enthusiastic, he said. “It is like inviting people in America to make a positive case for the Internal Revenue Service.”

Sara Hobolt, of the London School of Economics, backed up Pippa Norris’s finding that class was not much of a factor in Brexit voting. Household income appears to be important, but this is because it tends to reflect level of education, which is a more powerful predictor. In the British Election Study, the most powerful predictor is responses to the question, “Is Britain better than it used to be?” Those who say No tended to vote Leave.

Another finding was that dissatisfaction with the government was not significantly correlated with Brexit voting: the British referendum at least does not seem to have been hijacked as a protest vote against the incumbent government.

I reported yesterday on Ed Miliband’s contribution. As is often the case when you take MPs out of Westminster, there was a lot of common ground between him and Ed Vaizey, the Conservative MP and former Minister of Culture, a Remainer who described himself as “a mainstream centre-right Tory with surprising liberal tendencies”.

Vaizey traced the causes of the Brexit vote from David Cameron’s decision to pull out of the EPP, the EU-wide grouping of centre-right parties, when he ran as leader. The appetite for a referendum was whetted by the supposed betrayal of the promise of one on the Lisbon Treaty (Eurosceptics paid no attention, Vaizey said, to the “small print” of Cameron’s promise: “...unless it has already been ratified”). Plus there was the “relentless blaming of the EU for absolutely everything that went wrong”.

However, Vaizey said that he didn’t think that ultimately a referendum could have been avoided. He drew a parallel with Scotland, where he said that if London had stood against agitation for devolution and then for an independence referendum, it would only have increased the “pressure-cooker” effect.

He said that the 23 June referendum had divided rather than healing, and that he was worried a great deal by the rise of nationalism across Europe. But he concluded that “there has to be some reflection on the part of the EU on its being so distant from the people”.

In answer to a question about whether Britain had enough trade experts to negotiate a good Brexit deal Vaizey said: “I can reassure you about that. We have had, for the past 43 years, a secret team of trade negotiators in sleeper cells in villages around the country. They have been living innocuous lives under assumed identities but they are ready at a moment’s notice to answer the call of duty to serve their country. So there will be no problem about that. These are the best negotiators in the world and they will be able to secure a good agreement within six months.”

To wrap up, Professor Fleming thanked the participants for “the soothing service of distracting us from the dysfunction and toxicity of our politics with the dysfunction and toxicity of British politics”.

The conclusions I took from the conference were that referendums are sometimes justified on big constitutional subjects, such as our membership of the EU, but that politicians should be reluctant to use them and should make sure that the question is as unambiguous as possible.