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This work examines apportionment of multiplicative risks by considering three dominance orderings: first-degree stochastic dominance, Rothschild and Stiglitz&#8217;s increase in risk and downside risk increase. We use the relative <i>n</i>th-degree risk aversion measure and decreasing relative <i>n</i>th-degree risk aversion to provide conditions guaranteeing the preference for &#8220;harm disaggregation&#8221; of multiplicative risks. Further, we relate our conclusions to the preference toward bivariate lotteries, which interpret correlation-aversion, cross-prudence and cross-temperance.