There is one voting dimension, 2. preferences are single-peaked, 3. and politicians have no uncertainty about voter preferences. Recall that efficiency requires the maximization of total social surplus. In general, no. The efficient outcome is for politicians to cater to the mean preference.
Total surplus equals average surplus multiplied by the number of people.
If the number of voters is fixed, then, total surplus reaches its maximum when you maximize average surplus. Imagine running a store democratically, when there are many more customers than employees. The Coase Theorem implies that log-rolling can take care of the divergence between median and mean preferences. The Coase Theorem similarly implies that log-rolling allows people to bargain to efficiency on multiple dimensions. B. Even if median and mean preferences are identical for each issue, if a single election handles multiple issues, democracy need not yield the efficient result.