# Lotteries = probability distribution?

Are "lotteries" in the model for choice under uncertainty not just probability distributions?

• Usually, yes. Details may vary (finite support or not, countable vs finite additivity...) – Michael Greinecker Jun 24 '20 at 20:22
• Alright, thank you. – Xenusi Jun 24 '20 at 20:40

The starting point for the model is a set $$X$$ of possible prizes or consequences. In many economic problems (and for much of this class), $$X$$ will be a set of monetary payoffs. But it need not be. If we are considering who will win Big Game this year, the set of consequences might be: $$X=\lbrace\text{Stanford wins}, \text{Cal wins}, \text{Tie}\rbrace.$$ We represent an uncertain prospect as a lottery or probability distribution over the prize space. For instance, the prospect that Stanford and Cal are equally likely to win Big Game can be written as $$p=(1/2,1/2,0)$$. Perhaps these probabilities depend on who Stanford starts at quarterback. In that case, there might be two prospects: $$p$$ or $$p'=(5/9,3/9,1/9)$$, depending on who starts.