The basic analytical theory of politics uses assumptions to simplify an impossibly complex world. But assumptions limit the external applicability of the model. The assumptions we have used so far include: Candidates know the distribution of voter preferences; voters know where candidates will locate in the policy space; candidates have no goals other than winning the election; finally, all enfranchised citizens vote.

In this section, some important extensions of the basic model are introduced. The extensions represent applications of more realistic assumptions to the problems we have discussed in earlier chapters:

• Candidates with policy preferences

• Candidate uncertainty about voter location

• Voter uncertainty about candidate location

• Abstention out of indifference or alienation

• Voting is a collective action problem

These extensions make the model more complex, but dramatically improve the model's ability to explain real-world politics. Interestingly, the main prediction of the basic classical model, that there is a fundamental centralizing tendency in political competition, is robust with respect to alternative assumptions.