A choice function is a mathematical concept used in decision theory and economics to describe how individuals or groups select options from a set of alternatives. It assigns a specific choice to each possible set of options, reflecting preferences or priorities. For example, if given a menu of dishes, a choice function would identify which dish a person prefers based on their tastes. In formal terms, a choice function can be represented as a mapping from sets of alternatives to a single selected option. This concept is crucial in understanding consumer behavior and is often applied in fields like game theory and social choice theory.