Politicians from Fianna Fáil, Fine Gael and Sinn Féin have said they support the principle of a simple majority determining the result of any vote on a United Ireland.
Jim O'Callaghan of Fianna Fáil and Neale Richmond of Fine Gael said, however, that those supporting an effort to bring about a United Ireland should strive for a larger majority than 50 per cent plus one in any Border poll.
Sinn Féin’s Eoin Ó Broin meanwhile insisted that if there is a majority “most people will accept the outcome” once there is a “thoughtful” and “evidenced-based debate”.
Their remarks come after Labour Party chairman Jack O'Connor raised concern at the prospect of a narrow result in a poll on a united Ireland and its implications.
Mr O’Connor also said there would have to be a guarantee that there will be a significant number of unionist ministers in any government that is formed in the event of a united Ireland.
In a speech to the trade union section of his party, he appealed to Labour to follow the republican tradition and principles of the 1916 leader James Connolly.
“It is imperative that we, who are informed by the legacy of Connolly, intervene to counsel against any proposition that a vibrant sustainable democracy can be constructed on the basis of a sectarian headcount, most especially one which results in a ‘50 per cent plus one’ conclusion.
“Such a result would present the very real danger of a reversal into the ‘carnival of reaction’, which he correctly predicted would accompany partition, to the power of 10,” he said.
Fianna Fáil TD Mr O'Callaghan outlined his position on such a narrow result saying: "Bunreacht na hEireann, the British Constitution and the Good Friday Agreement are all clear on what is required for change to take place in the constitutional position of Northern Ireland.
“They all provide and require that this change will and can only take place if the majority of people in Northern Ireland make that decision.
“None of those fundamental legal documents require a weighted majority. In fact, such a requirement would be contrary to our constitution and the British constitution.”
He added: “Nonetheless, it should be the desire and intention of all people who seek unity to try to ensure that there is as large a majority of people in Northern Ireland as possible who would support establishing a new unified country.”
Separately, Mr Richmond said: "One of the great failings of the Brexit Referendum and the convulsed process that followed wasn't laced in the margin of victory but the fact that Brexit was an ill-defined concept with no tangible meaning.
“If and when we have a border poll, we should be voting on a clear vision of what a united Ireland would look like, including provisions that respect the equal status and concerns of unionists.”
He said the terms of the Good Friday Agreement are “quite clear” and “if the Secretary of State for Northern Ireland deems a border poll necessary then 50 per cent plus one in a Referendum is sufficient and that shouldn’t be changed.”
Mr Richmond added: “However, the challenge and the aim for those of us who seek a United Ireland is to achieve much more than that, in terms of a large electoral mandate as well as charting a vision for an inclusive and dynamic New Ireland.”
Mr Ó Broin responded to the concern raised by Mr O’Connor saying: “My preference is, as with all referenda, 50 per cent plus one is the norm.
“It was good enough for Repeal, it was good enough for marriage equality, it’s good enough for EU treaties so it should be good enough for this.”
More complex
He said that if the debate is conducted in a “reasoned, measured, evidence-based way” he thinks such a narrow result would be “more complex” than a sectarian headcount.
Mr Ó Broin argued that people will also consider what a united Ireland means for healthcare, education, housing and taxation.
“There’s a lot of people, including people in the North, who have an open mind and we’ve seen that in some of the recent polls in the North,” he said.
“So I think the debate is good, and I think the more our media and our political system - including comments from Jack who is a seasoned politician and trade unionist who deserves to be listened to - the more that debate happens the better.”
He was asked about the recent riots in the North, blamed in part on the Northern Ireland Protocol in the Brexit deal and it was put to him that a narrow majority for a United Ireland would make for a more dangerous situation.
He said: “I’m not so sure that the small number of people involved in some of these riots would take into account whether it’s [the result of a vote on a United Ireland] 51 per cent or 60 per cent or 70 percent.
"Those issues on the ground, particularly in Belfast, are best dealt with through dialogue, best dealt with through people working together and thankfully a lot of that work has been ongoing over the last number of weeks, which is why we haven't seen those scenes repeated."
“I think if we have the right kind of public debate over a period of time, then I think, most people will accept the outcome of that and we’ll deal with that as it happens,” he said.