Political scientists, along with counterparts in other social science disciplines, have sought a number of theoretical approaches to describing, explaining, and predicting coalitional behavior. Coalitions arise in situations with at least three actors (individuals, groups, countries), wherein no single actor can achieve an optimal outcome on its own; rather, cooperation with one or more other actors is necessary. Coalition theories purport to shed light on why alliances emerge, why they take the forms they do, how they endure, and why they collapse.
Much of coalition theory embraces the basic assumptions of rational political behavior. Faced with dilemmas about how to maximize gains through cooperation with one or more other parties, rational political actors will weigh preferentially ordered alternative strategies and consistently pursue coalition options connected with more preferred outcomes. The game-theoretic tradition, which has dominated coalition research, flows directly from this foundational assumption of rationality. Game theorists view the process of coalition formation as a social interaction in which bargaining behaviors can be modeled by a priori assumptions and deductive propositions about what the negotiators value most.
Conventional coalition theory generally makes four assumptions: relevant players in the coalition game are unified parties, each of which can be considered a single bargaining entity with indivisible motives; the coalition game is zero-sum, with gains by one party constituting losses for another; the universe of possible coalitions is formed by all "winning" combinations of actors; and the game of coalition formation is a single-shot event, independent of previous or future bargaining between the parties to the game. From these baseline assumptions, formal coalition theory has advanced at least two major strands of research: size-criterion studies (the "office-seeking" tradition) and ideological/policy distance (the "policy-seeking" tradition).
In his 1962 book William Riker deduced a "size principle" by which in «-person "games" coalitions of minimum size would be expected to form. Hoping to craft a minimum-winning coalition large enough to win but no larger, rational actors in Riker’s model would, for example, consistently decide to form coalitions of no more than 201 members in a 400-seat parliament. Similarly, in the hypothetical 400-member parliament a coalition of two equally powerful parties combining for 60 percent of the seats would be preferred to a coalition of four equally powerful parties with 60 percent of the seats. The clear assumption is that the overwhelming motivation of rational political actors in coalitional situations is the zero-sum maximization of a fixed prize to be shared among the fewest actors possible. Self-interested actors driven by garnering for themselves the largest share of a fixed-sum prize tend to see the virtues of compromising principles or policies if doing so increases the likelihood of winning.
Advocates of a rival policy-seeking theoretical approach to understanding coalitions countered that actors seek to build alliances with those partners closest to them ideologically and do not simply jump to form alliances with any constellation of "strange bedfellows" that produces victory. In this theoretical camp, articulated most clearly by Abram De Swaan in his seminal 1973 book, the argument is that players in the coalition game seek to minimize the range of policy disagreement and ideological heterogeneity among members of a potential winning coalition. In a legislative context, this anticipates that the most frequent type of coalition found would be those in which members of the winning government would be adjacent or "connected" if placed on an ordinal, single-dimension left-right ideological scale.
Coalition theory has developed considerably since the pioneering works of Riker, De Swaan, and others. Scholars now seek to replace the traditional office-seeking versus policy-seeking dichotomy by borrowing from spatial theories of party competition to model bargaining on the basis of multiple policy dimensions. Still, criticisms of traditional coalition theory abound. Detractors contend that formal theories based on rational choice/game theoretic propositions fail to capture the practice and reality of coalition politics. Models of unconstrained minimalist rationality operating within the context of laboratory-pure "games," say the critics, cannot account for the frequent departures from minimum-winning coalitions (namely, the occurrence of oversized "surplus majority" coalitions or undersized "minority" coalitions). Further, it may be wrong to assume that all coalition actors pursue the same goals, behave as monolithic unitary actors, and engage in the same kind of complex calculus of mathematical alternatives. Whereas some political scientists see the way forward as a choice between formal coalition theory (based on deductive assumptions about rational behavior) and rich description (detailing cases and actor characteristics), others claim such a choice to be a false dichotomy. Advancing knowledge about political coalitions, this latter group contends, will come through systematic and meaningful measurement of structural features that constrain rational behavior.