Abstract
The article explores the interaction of two, potentially clashing, considerations, each reflecting a different conception of fairness concerning the resolution of interpersonal conflicts. According to the Equal Chance Principle, the harm for each person should be minimized in a significant and (roughly) equal degree; when this is impossible, each person should be accorded the highest possible equal chance to avoid the harm. According to the Importance Principle, the danger to the person who would otherwise suffer the more serious harm should be prevented.