Various factors. Off the top of my head probably...
Chance. Region population. Unit size. Total army strength in region. Recent looting. Lax/neutral/strict looting. What you loot for. Regional sympathies to your realm.
The biggest thing is proportion of your realm's troops to the regional population, probably followed by Chance.
EDIT:
My strategy with looting when I was Thalmarkin general was in carefully focusing on low pop regions to devastate or conducting more mobile looting where you loot for some hours, then set travel to next region, gather, repeat on way to next region. Those peasants fighting you are now no longer working in the fields to produce food or gold for their lord.
Also, when fighting peasants, pull your forces back and focus on ranged strength. Advanced marshal formations that may be useful are the Delay and Wound, Shall Not Pass, or Strategic Withdrawal.
