Decisions with Several Objectives under Uncertainty: Sufficient Conditions for Multivariate Almost Stochastic Dominance Based on Means and Variances

Important business, public policy, and personal decisions typically involve multiple objectives, which in turn can be represented by multiple attributes, and uncertainty. Assessing both multiattribute utility and multivariate distributions for the attributes can be challenging. Moreover, big decisions are often made by boards or committees with members holding divergent views and preferences and facing pressures from different stakeholders. Thus, a full-blown traditional decision analysis that leads to the computation of expected utility is very difficult at best and often not possible. We develop sufficient conditions for multivariate almost stochastic dominance (MASD) based on marginal distributions of the attributes or just on their means and variances. To apply MASD, one only needs to assess bounds on marginal utilities. Alternatively, preferences can be explained and elicited via transfers. Realistic examples illustrate our results, which provide tools for “fast and frugal” screening and evaluation of the available options, while properly accounting for tradeoffs and riskiness. Such tools, consistent with normative decision analysis, are useful when making important decisions in today’s fast-moving and often complex world.