The Fine Gael parliamentary party will select a new leader to replace Mr Michael Noonan next week, although efforts are still under way to reduce the number of candidates.
The runners, as of now, are the Dublin North Central TD, Mr Richard Bruton, Mr Phil Hogan of Carlow-Kilkenny and Mr Enda Kenny from Mayo. Dublin South Central's Mr Gay Mitchell may yet enter.
The decision to hold a vote was taken by TDs, senators and MEPs at the end of a two-day gathering, although they rejected suggestions that it marked a failure to agree on a consensus choice.
The first three candidates should already have some idea of their chances after colleagues expressed their preferences in a secret straw poll before lunchtime yesterday.
"The ballot papers were done on a 1, 2, 3 basis and were handed in to Bruton, Hogan and Kenny, who then met afterwards to discuss matters," said one TD.
Mr Mitchell did not want his name to be included in the straw poll, although he told colleagues that he "reserved the right" to submit a nomination by the Tuesday noon deadline.
The Longford-Roscommon TD, Mr Denis Naughten, has confirmed that he will not stand. "I have thought long and hard about it and have decided against," he told The Irish Times.
The other youthful possibility, Mr Simon Coveney from Cork South Central, also confirmed that he would not go before next Wednesday's meeting, beginning at 2 p.m.
Last week Mr Coveney had been one of those who believed that the party should take some considerable time to decide on its way forward before selecting a leader.
However, he said he had been persuaded that they had to move more quickly, partly because a vacuum would cause problems and also so that they would have someone to nominate for the post of Taoiseach when the Dáil resumes.
Talks will now be held to see if an agreement can be reached whereby one or two of the candidates will step aside so that a consensus leader can emerge, according to a number of sources.
The formal resignation of Mr Noonan, who had already announced his intention to quit, was submitted to the chairman of the parliamentary party, Mr Padraig McCormack, yesterday. Mr Noonan did not attend yesterday's sessions.
Announcing that he will stand, Mr Richard Bruton said he believed that Fine Gael should occupy the political centre ground and campaign strongly on economic and social issues.
Delighted by the harmonious tone of the gathering, Mr McCormack said: "We came to reach consensus on how we would appoint a leader. And we have achieved that." A leader could not have emerged from the meeting since, under the party's rules, seven days' notice has to be given and the outgoing leader must have already resigned.
Seven of the 49 parliamentary party members were absent, although a number, including Ms Mary Banotti MEP, have offered detailed views by letter on the way forward.
One of the absentees, Mayo TD Mr Michael Ring, who is ill, said: "There was never going to be a consensus leader. We should have set about electing one last week." Contrary to yesterday's report, Mr Coveney made clear that he had never said that he would only stand if Mr Gay Mitchell looked like getting the top job, even though some colleagues were left with that impression.
Concerned that he had caused Mr Mitchell upset, Mr Coveney said: "I said that I would only run if I believed that somebody unacceptable was going to get the post."