Ranked-weighted utilities and qualitative convolution

For gambles-non-numerical consequences attached to uncertain chance events- analogues are proposed for the sum of independent random variables and thei r convolution. Joint receipt of gambles is the analogue of the sum of rando m variables. Because it has no unique expansion as a first-order gamble ana logous to convolution, a definition of qualitative convolution is proposed. Assuming ranked, weighted-utility representations (RWU) over gains (and, s eparately, over losses, but not mixtures of both), conditions are given for the equivalence of joint receipt, qualitative convolution, and a utility e xpression like expected value. As background, some proper-ties of RWU are d eveloped.