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A veto player is an individual or collective actor who possesses veto power in a political process and behaves strategically. Particular conceptions of the basic concept have to specify, among other things, what the relevant process is, who the veto players are, and what motivates them. The most influential conception of veto players has been developed by George Tsebelis (2002) in his veto player theory. That model has been elaborated in a number of different ways by subsequent scholars.

Tsebelis relies on the concept of the veto player to unify the comparative analysis of political systems. One part of this unification is conceptual. Tsebelis argues that traditional institutional dichotomies such as between unicameral and bicameral parliaments or between presidential and parliamentary systems of government can to a significant extent be replaced by analyzing political systems and situations as particular veto player configurations.

But veto player theory also aims at unifying our causal understanding of politics. The basis of this causal unification is the concept of policy stability—that is, the difficulty of changing the existing policies (the status quo) in a political system. Policy stability is the causal mechanism that links veto player configurations to particular outcomes of substantive importance. Tsebelis argues that in parliamentary systems, in which the cabinet depends on the confidence of the assembly, policy stability leads to cabinet instability. If the cabinet cannot agree on policy change, it will be replaced. For presidential systems, in contrast, veto player theory predicts that policy stability is likely to encourage a coup or some other form of regime instability. Neither of these two arguments is completely new, and they can be criticized, but veto player theory embeds both of them, and many others, in one relatively parsimonious and coherent framework.

Tsebelis distinguishes two types of veto players: (1) Institutional players are those established by a country's constitution. For example, the U.S. Constitution identifies the president as a veto player. (2) Partisan players are established by the way political competition plays out in a given country at a given time. One important analytical strategy of veto player theory is to focus on partisan veto players whenever possible. For example, instead of treating the Finnish parliament as one institutional veto player, the theory treats cabinet parties forming a majority coalition within the parliament as partisan veto players. One advantage of “replacing” institutional with partisan veto players for analytical purposes is that we may be able to ascribe particular policy preferences to the latter. Estimating actors' preferences is crucial for the application of veto player theory.

Tsebelis relies on game theory and a spatial representation of preferences. Actors' preferences are represented by a point—their so-called ideal point—in some one-dimensional or multidimensional policy space, and the actors' main goal is to move the collective decision as close as possible to this point. Based on these formal tools, Tsebelis derives specific hypotheses about the relationship between veto players and policy stability.

A superficial reading of veto player theory often misunderstands it as proving a seemingly trivial point—that a higher number of veto players increases policy stability. Yet one crucial insight of the formal analysis is that the number of veto players alone tells us little about the potential for policy change. What matters is how this number interacts with the distances between the ideal points of veto players' preferences. Moreover, the location of the status quo, the allocation of agenda-setting power, and the internal cohesion of collective veto players may also be of great importance for the outcome of collective decisions. Veto player theory analyses the interplay of these explanatory factors.

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