A distance-based theory of lottery complexity

This paper proposes a metric approach to measuring the complexity of lotteries. Starting by observing that degenerate lotteries are the simplest choice alternatives, the complexity of a lottery is evaluated by its distance from the closest degenerate lottery. Equivalently, a lottery is complex when it is difficult to approximate it by a single outcome. Given a metric over outcomes, the complexity index we consider is the minimum average distance between the lottery and one of its best degenerate proxies.