Dilemma

A situation in which one must choose only one of two or more – usually undesirable, but sometimes desirable – alternatives. The predicament involves alternatives which are ostensibly incompatible and seems to defy a satisfactory solution;

also: a conflict comprised of opposing values or motives.

(see also:  decision-making, decision analysis, judgement, decision, counterfactual reasoning, attitude, decision-making under uncertainty, statistical decision-making, Decisions – some questions probing ethical dimensions of, definition, language, ethics)