Ever since the UK made the decision to exit the European Union in 2016 there has been a simmering political and public debate on revisiting the outcome in a second referendum. As the Brexit negotiations enter the endgame, a formal campaign for a People’s Vote on the final deal has gathered pace, although the proposition remains contentious. Theresa May claims that a second referendum would be a betrayal of democracy: strong words.

In exploring the legitimacy of holding a second referendum it is worth looking at how and why this has been done in other EU member states. Both Denmark and Ireland held second referendums on EU treaties within 18 months of the first ballot. There is a widespread perception that these second votes were held at the behest of the EU and that these small states were bullied into doing so.

In the second campaign, RTE took to heart its duty to accurately inform and educate

This fundamentally misrepresents the political dynamics involved. In all cases governments, with the support of their parliaments, engaged in a sophisticated political exercise of managing the cross-cutting dynamics of domestic and EU-level politics. The exercise of national political authority was to the fore.

Let’s look at the second Irish referendum on the Lisbon EU treaty. This vote in June 2008 resulted in a decisive defeat for the EU treaty. In a turnout of 53%, 53% voted no, which was a major shock to the government and main opposition parties which had decisively endorsed the treaty. In October 2009 the Irish electorate voted again and returned a very different result. With turnout of 58%, 67% of voters voted yes and just two of the country’s 43 electoral constituencies voted no. A majority of men and women of all age groups and socioeconomic classes endorsed the treaty.

How was this achieved? The Irish government played for time at home. It turned to research to understand voter attitudes, commissioning a comprehensive academic study on the behaviour of the electorate. By September 2008, the government had solid evidence on why voters voted the way they did, and could begin to craft a strategy. Armed with the results, the Irish parliament interrogated Ireland’s future in the EU, and its deliberations led to the publication of a report titled Ireland’s Future in the European Union: Challenges, Issues and Options. While the people had spoken through a referendum, representative democracy reasserted its core role in the Irish political system and the quality of debate underlined the seriousness of the issues at stake.

At the same time, the Irish government engaged intensively with its EU partners. Neither side wanted to lose the Lisbon treaty. By December 2008, the broad outline of a deal was emerging which included the retention of one commissioner per state and legal guarantees on issues such as taxation, security and abortion. Next came the difficult task of translating this into a document. The Irish negotiators met every member state government at least twice and many three or four times between January and June 2009 to achieve agreement. On the eve of the June 2009 European council meeting, the then Irish prime minister, Brian Cowen, wrote to his counterparts saying that without legally binding guarantees he was unwilling to hold a referendum. With such guarantees, the government was prepared to go back to the electorate to ask “is this your final answer?”

Irish voters, particularly “soft” no voters, did not resent voting again because many of them felt that their first vote was uninformed. Lack of knowledge, information and understanding was cited by 42% of those who voted no first time. Unsurprisingly, those voters at the harder end of the no spectrum objected to the second referendum but the majority of voters were willing to revisit the question given the guarantees.

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Three facets of the second campaign contributed to the decisive win. First, the yes campaign mobilised in a different way: political parties and civil society organisations ran an intensive campaign across all media and on the ground. The active involvement of civil society was important, given the government’s unpopularity. A number of highly influential people, including Seamus Heaney, agreed to act as patrons of Ireland for Europe, the largest civil society organisation. Before reciting one of his poems at the launch of the campaign, Seamus said, “There are many reasons for ratifying the Lisbon treaty, reasons to do with our political and economic wellbeing, but the poem speaks mainly for our honour and identity as Europeans.”

Second, the yes campaign was much more effective in framing the agenda. In the first referendum, it was reactive and not particularly persuasive. Second time out, the campaign put the importance of Ireland’s relationship with the EU centre stage while having credible text warriors, who knew the treaty, bat on air and in the print media against the no campaign by taking on inaccurate or exaggerated claims. “Do not believe the lies” became the line on a number of very effective posters.

Third, the coverage of the campaign, particularly by RTE, the national broadcaster, was very different. For the first Lisbon referendum, RTE deployed a conflict frame akin to a Punch-and-Judy contest between yes and no, with little or no editorial intervention to challenge or correct inaccurate claims. Second time around, the conflict frame was accompanied by a responsibility frame, ie that the issue was salient and had to be taken seriously. The broadcaster took to heart its duty to accurately inform and educate.

Was the second vote a travesty of democracy? More people voted in the second referendum and the treaty was carried in urban and rural Ireland and across all socioeconomic groups. Moreover, people felt that they had a much better grasp of the issues. A democracy has the right to change its mind.

• Brigid Laffan chaired the civil society organisation Ireland for Europe in 2009