Bayes Optimal Classifier

So far we've sought the most probable hypothesis given the data $D$ (i.e., $h_{MAP}$)
Given new instance $x$, what is its most probable classification?
$h_{MAP}(x)$ is not the most probable classification!
For example, given three possible hypotheses: \[ P(h_{1}\,|\,D)=.4, P(h_{2}\,|\,D)=.3, P(h_{3}\,|\,D)=.3 \] ($h_1$ is the MAP hypothesis) and given a new instance $x$, \[ h_{1}(x)=\oplus, h_{2}(x)=\ominus, h_{3}(x)=\ominus \] what is the most probable classification of $x$, $\oplus$ or $\ominus$?