AND SO WE ENTER the middle ground. Ireland’s new TDs have met, decided not to elect a Taoiseach, and go away again.

Four candidates were put forward for election as Taoiseach, a job which (usually) requires the winner to have the support of 78 colleagues. The closest anyone came yesterday was Enda Kenny, who has just 56 backers in his corner.

Micheál Martin only has his 42 Fianna Fáil colleagues; Gerry Adams has his 22 fellow TDs and one independent; Richard Boyd Barrett mustered just two independents to leave a total of 8 in his favour.

Nobody expected a Taoiseach to be elected yesterday – and Enda Kenny’s formal resignation is little more than a box-ticking exercise in constitutional protocol. But the outcome of yesterday’s votes does give us a clear indication of where the loyalties in the Dáil will lie – and whether there is any prospect of Enda Kenny wrestling back his job, or someone else forging a coalition to take it from him.

After those votes, it is difficult to see how anyone could do so.

To get a better sense of the lay of the land, I’ve put together a breakdown of exactly how each of our 158 TDs voted in yesterday’s ballots:

The Oireachtas has updated (corrected?) the record of who voted for whom in yesterday's #Dail votes for Taoiseach: pic.twitter.com/XghtFsjk2t

— Gavan Reilly (@gavreilly) March 11, 2016

Realistically from this we can draw a couple of conclusions:

• The TDs from Fine Gael, Fianna Fáil or Sinn Féin are not likely to support any Taoiseach from a party outside their own. (I’ll come back to the issue of a ‘grand coalition’ in a moment.)
• As Labour campaigned for the return of its coalition with Fine Gael, but is now ruling itself out of government, it’s not likely to support anyone outside of a FG nominee (if, indeed, it supports anyone at all).
• Given their political leanings, the Anti-Austerity Alliance, People Before Profit and Independents4Change TDs will not support a nominee from FG or FF. We can also add left-leaning independents Catherine Connolly and Seamus Healy to this list.

This leaves us with 17 independents (including the 6 of the Independent Alliance, who we can treat as if they were a party), the three Social Democrats, and the two Greens – a total of 22.

This 22 would, hypothetically, bring Enda Kenny to 79 – the bare minimum number he needs for a majority.

But this sort of majority would require the backing of four parties (FG, Labour, SD and the Greens), and the pseudo-party of the Independent Alliance, and another 11 independent TDs – a patchwork quilt of a coalition that would fall apart without an unprecedented level of plate-spinning. (Among the 11 TDs are Thomas Pringle and Maureen O’Sullivan, who are also quite left-leaning, and Michael Lowry who has become a persona non grata in Fine Gael ranks.)

In the opponents’ column, Kenny might face Fianna Fáil, Sinn Féin, the AAA-PBP, Independents4Change, and the left-wing independents Connolly and Healy – a total of 78.

This hypothetical majority is wafer-thin and utterly unsustainable – and also assumes the unquestioning loyalty of Labour, which knows it has no political future if it becomes simply lobby fodder for Fine Gael. It is, in short, not a runner.

Fianna Phoenix

We then turn to the only other leader with any potential viability – Fianna Fáil’s Micheal Martin, who faces the same battle... only harder.

Let’s assume all the wheels fall into place – however unlikely that might seem – and Martin gets the support of the Social Democrats, Greens (yes, another FF-Green partnership!), the six in the Independent Alliance and the seven in Labour.

This brings him to 61 – leaving Martin 18 votes short of a cast-iron majority. We can assume Fine Gael and Sinn Féin would oppose him, putting 73 votes in the opposition category.

Simply add the six AAAPBP and four Independents4Change – neither of whom, it’s fair to say, would support Fianna Fáil on anything contentious – and the opponents have an insurmountable majority of 83. No amount of independents could save him.

That leaves only two options...

The above calculations, of course, are based on the idea that a minority coalition is off the table. But the measure of a government is that it has to be able to legislate in accordance with its own desires – and a minority government with so many legs would face the permanent risk of collapse if something contentious (say an unexpected political scandal, or a new EU treaty) were ever to arise.  

To view it another way: shift your timeline forward to October and a FG minority government’s first budget. FG wants to abolish the Universal Social Charge; the first incremental step in doing so would be opposed by FF, SF and the ten TDs on the further-left. That’s 76 TDs already and only needs three more to provide a veto.

All of the arithmetic and the fractured landscape means only some kind of partnership between Fine Gael and Fianna Fáil would have the numerical strength to work.

A full-blown coalition is Fine Gael’s preferred option at this point, but Fianna Fáil leader Micheál Martin seems to have hardened his opposition to it. (His comments outside Leinster House yesterday, to that effect, were his first public remarks in 11 days – and ended the idle speculation that a deal could be in the offing.)

If Martin were to backtrack on this and negotiate a programme for government, he would then have to seek its approval at a special FF Ard Fheis – which again, it appears, has little appetite to become a junior partner to Fine Gael. Defeat for a Martin-led proposal would also herald the end of Martin’s political career and is a risk he is unlikely to take.

The grand marriage

The only remaining option then is a Fine Gael minority government with Fianna Fáil’s tacit support. If grand coalition is FF’s no-go area, minority government is FG’s – and many in the blue side would rather commit political hari-kiri than form a government that wilfully required Fianna Fáil’s approval for any major act.

Such a government would also collapse at Fianna Fáil’s whim, as it could table a motion of no confidence in Kenny that would be guaranteed to pass.

There is one curious possibility in this area, but it's not a recipe for long-term government.

When the Dáil next meets, and if Enda Kenny is put forward as Taoiseach for a second time, Fianna Fáil could abstain. If they did so, and everyone else voted just as they did last time, Kenny would be elected by 57 votes to 51 – and be bounced into a minority government he doesn’t want to lead.

This wouldn’t last terribly long, though. Even with FF’s support for legislation, a FG minority government would take a battering in the weekly sessions where opposition TDs can table bills and motions of their own. Within a month of taking office, for example, a FG minority’s water charges would been abolished. Its USC-scrapping Budget would collapse it. It would be inevitable that such a government would pull the rug on itself and another election would follow.

It all points to a single outcome. Unless Irish politics changes fairly drastically, and everyone agrees to start supporting each others’ budgets, we’ll be heading to the polls a second time before the year is out – and potentially even before the summer.

Gavan Reilly is Today FM's Political Correspondent. http://twitter.com/gavreilly