2. The model
• Two parties, A and B, are competing for a
single political position.
• There are a continuum of voters uniformly
distributed on the interval[ 0, 1], with
density function f(x).
• We assume that all voters in the interval
[0,b] are registered as members of party B,
where 0 < b < 1/2
Focus on the smaller party
• Two candidates of party B, I and 2, are
competing for nomination in the primary,
and the winner of which is to compete with
the nominee of party A in the final election.
The positions of the candidates are x1 and
x2 respectively, with xl < X2 < b.
Stochastic element
• The position of party A's nominee, XA, is
still unknown at the time of party B's
primary, and is assumed to be a random
variable uniformly distributed on (b, 1].
• Let g(.) be the probability density of XA
Utility of voter x