I'm one of those squishy liberals who thinks that our central banks should focus on lowering the unemployment rate as well as reducing inflation. (And I really don't think we should be gunning for pure price stability.) But Alex Tabarrok makes a good argument for having a "nasty central banker" who cares only about tamping down inflation:

A nasty central banker cares only about reducing inflation and not at all about reducing unemployment (think fat-cat Republican living off fixed income bonds). Precisely because a nasty central banker won't juice the economy to reduce unemployment, the nasty central banker can credibly commit to keep inflation low. The public believes the promise and safely plans for low inflation. Unemployment is the same in both scenarios - because the central bank can never systematically surprise the public with higher than expected inflation - but inflation itself is lower with the nasty central banker and thus the public is better off.

Now I'd be surprised if this was actually true in practice, but it's hard to see a flaw in the logic.