A coalition of agents, or a single agent, has an ethical dilemma between several statements if each joint action of the coalition forces at least one specific statement among them to be true. For example, any action in the trolley dilemma forces one specific group of people to die. In many cases, agents face ethical dilemmas because they are restricted in the amount of the resources they are ready to sacrifice to overcome the dilemma. The paper presents a sound and complete modal logical system that describes properties of dilemmas for a given limit on a sacrifice.