Eight weeks after polling day, the political options have narrowed to either a Fine Gael minority government supported grudgingly by Fianna Fáil for an uncertain timespan , or else another general election.

There is, however, a third option: power-sharing. It would require a major change to the political culture, and would not necessarily be a panacea for good governance, but some political theorists say it would provide more stable administration and also be more democratic than the current model of governing by way of an operational majority.

But how would it work? As a contribution to public debate in the wake of the general election, The Irish Times is co-hosting a public voting experiment with the De Borda Institute, DCU and CiviQ, demonstrating how a national unity government might be elected.

Members of the public have been invited to join political scientists to take part in a role play exercise. They will first be split into “party groups”, and will be charged with representing those parties in negotiations.

Groups will then discuss which TDs they wish to nominate, and for which ministries. Here tactics kick in - because parties can’t hold all ministries. They must work out who they think will be elected, and how best to cooperate with other party groups.

The ballot paper itself requires a shift in mind-set. Instead of having a list of candidates which you number in preference 1, 2, 3, etc you have a “matrix” ballot with candidates on one axis and cabinet positions on the other.

Using this grid, voters first fill in the candidates they wish to see elected to cabinet in order of preference. Then, opposite each name, they put a tick in the column identifying the ministry to which they want the individual appointed.

A 15-member cabinet representing the 32nd Dáil might well consist of five ministers from Fine Gael, four from Fianna Fáil, two from the Independents, two from Sinn Féin and two from the remaining parties of Labour, AAA/PBP, Social Democrats and the Greens.

However, the exact complexion would depend on how effective parties are in negotiations. Under the matrix system, parties do better if they vote all the way down the ballot paper and not just for their own candidates.

In practice, "it forces politicians of different persuasions to cooperate", says Peter Emerson, director of the Belfast-based De Borda institute, and a veteran of power-sharing initiatives in conflict zones in Europe and the developing world.

It also avoids the risk of producing a government that is led by a minority faction - “the tail wagging the dog” - as has happened in previous coalition talks. Moreover, says Emerson, a matrix vote better reflects the nature of electoral opinion.

“What we have at the moment is the politics of the pendulum - left-wing/right-wing, or republican/democrat. But the human species is evolving. So if society at the moment is x per cent left wing and y per cent right wing the ratios will be slightly different at the next election.”

Using power-sharing, “the democratic process actually evolves” instead of being reset with each new administration.

But does it always work out for the best?

Dr Dawn Walsh, who has studied power-showing arrangements internationally, says the design and implementation of such "forced coalitions" determines their effectiveness.

“The devil is in the detail,” she remarks.

“In Northern Ireland there have been concerns over the accountability of ministers and accusations that ministers focus on their own community. This is a specific problem related to how power-sharing is applied in Northern Ireland as ministerial portfolios are allocated on the basis of a mathematical formula [known as d’Hondt].

“There is no agreed programme for government which can lead to individual ministers not being accountable. However the relatively strong oversight provided by the committee system somewhat negates this.”

Emerson accepts electing a power-sharing government would only be a partial solution: getting it to govern more inclusively and democratically would be the next step. Here he sees a broader role for multi-option voting, or “preferendums”, where politicians decide on policy by ranking preferences rather than a binary “Tá/Níl”.

The controversy over the introduction of water charges could have been avoided, he says, had all parties taken part in a “preferendum” on how best to manage the national water supply.

But will politicians only accept power-sharing under duress?

“Power-sharing is generally used to manage inter-group conflict caused by the permanent exclusion of groups from decision-making,” says Dr Walsh.

“External issues can also play a large role in when power-sharing is used. External threats which would negatively affect all communities in a country can encourage them into a power-sharing government to defend against this.”

The likes of Brexit, or a major economic shock, might have such an effect here.

Emerson was involved in the New Ireland group in Belfast during the 1980s and ran a people’s convention in 1986 which saw nationalist and unionist politicians vote - by way of preferendum - on ten options. The winning choice was a tripartite devolution and power-sharing arrangement between London, Dublin and Stormont - “a mini Belfast agreement 12 years ahead of its time”, notes Emerson.

He believes Saturday’s event could have a similar historic quality. For the first time, he points out, a government of national unity will be elected in the Republic, at least in theory.

* The public voting experiment on power-sharing government will take place at Ballymun Civic Centre on Saturday, April 23rd from 9.30 am to 1.30 pm.

Participants will be asked to assume the identity of a TD for the morning and to negotiate a government as though representing the 32nd Dáil.

The role play ballot will be run by a team of political scientists led by the de Borda Institute and political analysts CiviQ. It will be followed by panel discussion on whether power-sharing is either feasible or desirable in the Republic, with Stephen Collins, Political Editor of The Irish Times; Roisin Shortall, Social Democrats TD for Dublin North West; and Jane Suiter, director of the Institute for Future Media and Journalism, DCU.

To register to participate please email marketing@irishtimes.com and put “Politics” in the subject line.

For more information on the event see: www.deborda.org