In game theory, a lottery is a probability distribution over outcomes. Lotteries occur all the time in games because mixed strategies randomize the outcomes that occur. Thus, while many utility representations preserve linear orderings, not all utility representations preserve the relative intensity of the preferences.
To even manipulate preferences in this manner, we first need some rules for how weigh one lottery versus another. This is where independence and continuity come into play, which we will cover later.
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