This article may contain spoilers.
This dilemma can occur whenever your survivors are in a building surrounded by a large number of zombies.
When this dilemma occurs, a picture of a truck will show with context to the situation on the left and options on the right.
The options are displayed on the far right side and are as follows:
Let the group sacrifice the least popular member.
Find some valuable items to offer.
If you choose the first option, the member with the most prejudices against them/the lowest relationship score will be chosen. Following text about the survivor in question being dragged unwillingly into the truck's cage, the truck will drive off and nearly all the zombies will be lured in a random direction. The survivor in question will also show up as 'killed' with a bloodied portrait.
Choosing the 'Find some valuable items to offer' option will randomly pick items in your inventory and they will be given to the piper (The items are lost essentially). The piper will fire his horn and leave, taking a good portion of the zombies with him. If an addequate supply of valuable items is not available, then the outcome is the same as trying to ignore the piper.
If you decide to ignore the piper, he will get mad and blare his siren, luring more zombies to your location. This is equivilant of creating a distraction in the building.