Relatively few politicians willingly forsake center stage, although a touch of _____ on their parts now and again might well increase their popularity with the voting public.

Option C is the correct answer.

Self-effacement is the quality of not claiming attention for oneself.

In this context, it contrasts well with the idea that only a few politicians forsake the centre stage, and a touch of not claiming attention could enhance their popularity.

The other options don't fit the context:
Option A: Garrulity means talkativeness, which wouldn't help with increasing popularity.
Option B: Misanthropy means disliking people, which would likely decrease popularity.
Option D: self-dramatization involves drawing attention to oneself dramatically, which could have the opposite effect of increasing popularity.