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 a person is given a menu of dishes, the choice function determines which dish they will select based on their tastes. In formal terms, a choice function can be represented as a mapping from sets of alternatives to a single chosen element from each set. This concept is important in understanding consumer behavior and can be applied in various fields, including game theory, social choice theory, and market analysis.