Definitions
Veto players are political actors whose approval is necessary but not sufficient to
alter the policy status-quo. They should be distinguished from decisive players, whose
approval is sufficient but not necessary to change existing policies, and from dictators,
whose approval is both necessary and sufficient to impose new policies (Strom and
Swindle 2002). Models of veto players seek to predict the probability of policy change
rather than the specific policies that will emerge in equilibrium. The theory assumes that
any proposal representing an improvement over the status-quo for all veto players will
not face resistance and thus will defeat the existing equilibrium. The set of policy
positions thus capable of defeating an existing policy is known as the winset of the status-
quo, W(SQ). The larger W(SQ), the greater the probability of policy change and hence
the lower policy stability (Tsebelis 1995). Following this standard approach, we model
the size of the winset (the proportion of policy space able to defeat the status-quo) as our
dependent variable.
In order to explore the role of veto players in presidential regimes, we construct a
two-dimensional policy landscape represented by a 50x50 lattice. Political actors in our
model (whether individuals or institutions) locate themselves in one of the 2,500 discrete
policy positions and seek to minimize the distance between their ideal points and the
policy implemented. Figure 1 illustrates a simple case of executive-legislative relations
in this policy-scape. A president with veto power is located to the right and to the north
of the status-quo, while the House and the Senate are located to the left and south. Let us
call the preferred set V
i
(SQ) to the set of policy positions contained within the
indifference curve of any given actor, i. In the absence of decisive actors or dictators, the
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Convention