Going back to the main variable in this book, policy stability: as we will see, it is defined
by the size of the winset of the status quo.
6
Why do I use this concept instead of the widely
accepted notion of (Nash) equilibrium? The absence of equilibrium analysis is due to the fact
that in multidimensional policy spaces equilibria rarely exist. In fact, while in a single dimension
equilibria of voting models are guaranteed to exist, Plot (1967) has demonstrated that in multiple
dimensions the conditions for the existence of equilibrium are extremely restrictive. McKelvey
(1976) and Schofield (1977) followed up the study by demonstrating that in the absence of
equilibrium any outcome is possible.
On the other hand, the winset of the status quo has the self-imposing quality that it is the
intersection of restrictions that each participant imposes on the set of outcomes. No rational
player given the choice would accept any outcome that he does not prefer over the status quo.
7
In
this sense my analysis is much more general than any other model (like bargaining, exclusive
jurisdictions of ministers, or prime-minister) that introduces a series of additional restrictions in
order to produce a single equilibrium outcome.
8
produce low deficits if the country is familiar with low deficits (Switzerland or Germany).
6
The more appropriate expression would be: “winset of the default outcome.” However, most of the time the default
solution is the status quo. For example, Rasch (2000) has identified countries that a formal rule specifies that a vote
has to be taken on the floor of the parliament whether a proposal as modified by amendments is accepted. Even in
cases where there is no such a formal rule votes comparing the status quo with the emerging alternative are taken on
the floor of parliament. For example, in Herbert Doering’s study of 18 Western European countries in the 1981-91
period out of 541 bills a final vote had been taken 73% of the time (Doering http://www.uni-
potsdam.de/u/ls_vergleich/research). In all these cases the final outcome is by definition within the winset of the
status quo. In the cases where a final vote comparing the alternative with the status quo is not taken, the default
alternative is specified either by rules or by a vote in parliament. If a majority in parliament can anticipate an
outcome that they do not prefer over the status quo they can take steps to abort the whole voting procedure. So, from
now on I will be using the expression “winset of the status quo” instead of “winset of the default alternative.”
7
Here I am excluding cases where a player receives specific payoffs to do so For example, he may receive promises
that in the future his preferences on another issue will be decisive. I do not argue that such cases are impossible, but
I do argue that if they are included they make almost all possible outcomes acceptable on the basis of such logroll,
and make any systematic analysis impossible.
8
Huber and McCarty (2001) have produced a model with significantly different outcomes depending on whether the
prime minister can introduce the question of confidence directly, or has to get the approval of the government first.