2
are more likely to ‘win’ coalition games. The greater the extent to which the left-right dimension
constrains parties, the more likely pivotal and alternational systems are to occur. The greater the
reliability in which a single party can capture the median voter or (in multidimensional space)
occupy the core, the more the system will tend toward a pivotal system than an alternational or
unconstrained system.
2. Unidimensional Models of Opposition Strategy and Coalition Dynamics
All of the models presented below are based on a 3-party parliament. As in Lupia and
Strøm (1995), the parties are labeled 1, 2 and Out. 1 and 2 form the incumbent government, with
Out representing the opposition.
1
Unlike Lupia and Strøm, each of the parties has a status quo
position in a unidimensional policy space P between 0 and 1, where p
2
< p
1
< p
O
. The status quo
is that p
O
- p
1
> p
1
- p
2
. The government formation rule is simply the two closest parties on P
form a coalition together, except when one of the parties has a majority. The model assumes
complete and perfect information. Technical solutions of all models are presented in an
appendix.
2
The models, for analytic simplicity focus on only two terms in players utility functions.
Parties place some value in being in government, though the amount will vary depending on who
they are in government with, but moving positions or introducing new issue dimensions is costly.
The payoff to party i for being in government with party j is labeled g
j
i
, with being in
opposition normalized as 0. The cost of party i moving to position p
*
is labeled as c
i*
, and the
cost is assumed to be 0 when a party does not move and monotonically increase as the absolute
1
The use of three-party models of parliament is quite common, and generalizing from the models to real-world
parliaments with different numbers of parties is discussed in the concluding section.
2
This appendix is available online at http://weber.ucsd.edu/~bnyblade/research.html
Convention