 Since it can also be shown that, for every lottery \(P\) in \(\mathcal{P}\), there exists an act \(f\) such that \(P_f=P\), the important upshot of this result is that one can effectively simplify the representation of the agent’s preferences over acts, recasting them as preferences over the smaller set \(\mathcal{P}\) of so-called subjective lotteries, i.e., subjective probability distributions over outcomes. To simplify notation, the preference relation over \(\mathcal{P}\) will be denoted by the same symbol, \(\succeq\), allowing context to disambiguate.