Last Saturday, the 27th June, Ireland announced its new coalitional government. It had been a gobsmacking 140 days since its general election. The protracted time it took the coalitional members to agree on a platform testifies of the challenges for decision-making that this coalition will face: both in terms of its internal stability (i.e. sharing the power amongst the members) and its external stability (i.e. withstanding the temptation to form an alternative Government by joining the opposition). Political scientist and commentator have watched enthralled at the gradual formation of this unlikely governing coalition; between Fianna Fáil and Fine Gael – the two large centre-right parties – and the Green party – a much smaller centre-left party.
Ideology aside, the distribution of seats in the 33rd Dáil Éireann, the lower house of Ireland‘s parliament, presents a challenge to the stability of this newly minted coalition. In a world where all parties are driven by acquiring a greater share of the decision power rights, the question that requires answering is straightforward: Can the three coalitional members agree on a power sharing scheme that would ensure that none will decide to defect to the opposition ranks? This question is at the heart of the analysis that my co-authors – Petr Borm, Maria Montero, and Hans Reijnierse – and I explored in our paper “A Bargaining Set for Monotonic Simple Games Based on External and Internal Stability”.
You perhaps would not be surprised to learn that the key to the answer of this question is the degree of unification among the opposition members. Take, as an example, the composition of the current Irish coalitional government. Fianna Fáil has 37 seats in the 160-seat Dáil, thus, 23.13% percent of the votes; Fine Gael has 35 seats, thus, 21.88% percent; and the Green party with 12 votes represents 7.5% percent. Thus, the coalitional government controls 52.5% of the votes in the parliament and the opposition controls the remaining 47.5%. Among the opposition, the biggest party is Sinn Féin with 37 seats (23.13%); both Labour and the Social Democrats have 6 seats each, giving them each 3.75%, Solidarity – People before Profit has 5 seats with 3.13%; Aontú, Independents 4; Change, and Ceann Comhairle have 1 seat (0.63%) each; and there are 19 independent MPs.
Let’s first consider the situation where no alliances are forged among the opposition parties, such that each one acts independently from all the rest. In this case, none of the coalitional partners can threaten to form another government by joining one of the opposition parties. There are no two-party coalitions which can give any two parties more than the 50% required to control the parliament. This is easily seen when you sum up the votes of the largest party in government, Fianna Fáil, and those of the largest opposition party, Sinn Féin, who together would only secure 46.26% of the votes. Our theory predicts that, with a fully fragmented opposition, the current coalitional government will indeed be a stable one. In fact, stability can be sustained under any allocation of decision rights among the three coalitional members.
At the other extreme, we can consider a fully united opposition, where all 7 opposition groups decide to fully coordinate their total vote share of 47.5%. The continued stability of the government can still be ensured. How? In this case any one of the three coalitional parties can threaten to switch sides and join the opposition, effectively forming a new coalitional government. To see that it is enough to consider what would happen if the smallest of the ruling parties, the Greens with 7.5% of the votes, joined the united opposition with 47.5% of the votes: the new coalition would now have control of 55% of the votes. Here, the allocation of decision rights that can render the government stable becomes crucial. In this situation it is one where parties share power equally in reflection of their equally attractive outside option.
Both full cooperation and the absence of any alliance, however, are unlikely scenarios for the opposition. Another possibility where the structure of the opposition complicates government stability is provided where only one of the coalitional partners can join an opposition alliance. For example, suppose Sinn Féin and Labour form an alliance and together they control of 26.88% of the votes. Thus, if Fianna Fáil decided to join their alliance, together they will have just above the necessary 50% to form a new government. Neither Fine Gael nor the Greens, however, would be able to form a new government by forging such an alliance. To maintain stability in the coalitional government, Fianna Fáil would need (almost) all the decision rights.
There are not limitless bargaining opportunities for stable coalitional government. Our theory predicts that when both Fianna Fáil and Fine Gael have the option to form a new government by joining an opposition alliance while the Greens don’t – which is the case when the opposition alliance controls more than 26.87% and less than 42.5% the votes – the government will be unstable. The reason? Either of the larger parties would be able to raise a justified objection against the Greens and the proposed allocation. Their objection will be simple: “I can get more power by forming a government with the opposition than you allow me to have now, so we do not need you.”
These are just early days for the Irish coalitional government. Its future, to a large extent, will be dependent on the coalition’s ability to share power fairly by considering the internal contributions and external opportunities for its members. It is, however, in the hands of the opposition and the formation of their own alliances to set the government on a stable path – or at least so our bargaining theory predicts.
Banner Image by Tommy Kavanagh using CC BY-SA 3.0.