Lotteries and expected utility The preference of lotteries Continuous: LL'L"e@ the set is closure {a∈[0,1]:aL+(1-a)L%L"}c[0,1 {a∈[0,1]:L"%aL+(1-a)L}c[0,1 Independence axiom aL+(1-a)L”%aL+(1-a)L”冷→L%L 连续性和不相关性Lotteries and expected utility • The preference of lotteries: – Continuous: the set is closure – Independence axiom: L L L , ,  L { [0,1]: (1 ) } [0,1]     + −  L L L   % { [0,1]: (1 ) } [0,1]     + −  L L L   %     L L L L L L + − + −  (1 ) (1 )     % % 连续性和不相关性