If Thompson appeals to moderates, his most ardent supporters will desert him and he will not have enough votes to win the election  However, if he does not appeal to moderates, these moderates will vote for his opponent and he will not have enough votes to win the election
Either way, Thompson is bound to lose the election
If Chen supports building a new art center, the center will be built. If Chen opposes building a new art center, the center will not be built. So whether or not a new art center will be built depends on Chen's decision.