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⁴ In this article we focus on political actors motivated exclusively by policy preferences. In the coalition literature another common motivational objective is that of office-seeking. We will have more to say about this in the concluding section.

⁵ In what follows, we assume that ministers are policy dictators in their respective jurisdictions. Obviously, this exaggerates ministerial authority in most political systems. However, it is not inaccurate to observe that ministers do have substantial discretion – greater in some polities than in others, to be sure, but significant in all – so that any policy promises that accompany the formation of a government are vulnerable to discretionary ministerial action.

⁶ In the diagrams and discussion to follow, we portray a portfolio jurisdiction as unidimensional. This certainly simplifies the presentation of the argument, but we should underscore that our argument extends without qualification to the more natural setting in which portfolio jurisdictions are multidimensional.

⁷ Laver and Shepsle discuss alternative interpretations of .x⁰ in ‘Coalitions and Cabinet Government’.

⁸ This is a credible proposal since, if the AB government actually forms, party A's (B's, respectively) minister will have every incentive to move towards A's (B's) ideal policy in jurisdiction X (Y). By way of contrast the ‘compromise’ policy, [(AA + BB)/2, (AA + BB)/2)], is not credible. Once ensconced in their respective ministries, coalition partners each have the incentive and, by assumption, the means to ‘backslide’ towards their respective party ideals.

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¹⁰ The win set consists of the points preferred by a legislative majority to BA. This is determined by passing indifference contours through BA for each party (circles centred on each party-ideal point). The interiors of these circles contain the points preferred to BA by each party, that is, points closer to party-ideal points than to BA. Intersections of these circles for collections of parties of majority weight produce the win sets. In Figure 2 (middle panel) there are three ‘petals’ of the win set, associated with the three majority coalitions.

¹¹ Notice, for example, that the midpoint between BB and CC in the middle panel of Figure 1 lies in one of the win set petals. If parties B and C could commit themselves to this point, it would defeat BA and each would be better off. By our argument, however, once portfolios are distributed (say X to party C and Y to party B) there is a tendency for each minister to cheat on the bargain, with policy ultimately gravitating towards the point CB. In this case party B is better off, but more importantly party C is worse off, than at either the bargained agreement or the original status quo BA. Anticipating this, party C would not agree to the bargain in the first place – it is not credible, even though it beats BA.

¹² With the status quo vulnerable, for example, to two credible, invulnerable proposals, it may be established that one is preferred to the other by a legislative majority, while at least one of the participants in the winning proposal actually prefers the losing proposal to it. The ‘standoff’ involves a legislative majority insisting on the proposal it prefers and disenchanted participants in that proposal refusing to give their assent because they would rather have the other proposal.

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¹⁷ Note, as an aside, that as party leader C1 can also refuse to assent to any proposal involving C2 Though this power is not relevant to this particular example, it is clearly an important factor in many possible cases.

¹⁸ Anticipating that the party may get into government, party legislators only take seriously proposals for party policy positions that can be policed by party members who could be nominated for cabinet positions. It is interesting to note that policy bargaining within parties that have no realistic chance of getting into government may well take different forms, since the mechanisms for policing party policy must inevitably be different. It is also important to note that the ‘realistic chance’ of getting into government is endogenous, depending as it does upon the results of intraparty bargaining.

¹⁹ Note that Austen-Smith and Banks, in ‘Stable Portfolio Allocations’, prove that the restricted portfolio core is never empty in a three-party government formation game in which the parties are unitary actors with Euclidean preferences. The above example shows that the availability of more than one credible point within a single party makes cycles possible even in a three-party game.

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