We develop comparative results for ratio-based efficiency analysis (REA) based on the decision-making units' (DMUs') relative efficiencies over sets of feasible weights that characterize preferences for input and output variables. Specifically, we determine (i) ranking intervals, which indicate the best and worst efficiency rankings that a DMU can attain relative to other DMUs; (ii) dominance relations, which show what other DMUs a given DMU dominates in pairwise efficiency comparisons; and (iii) efficiency bounds, which show how much more efficient a given DMU can be relative to some other DMU or a subset of other DMUs. Unlike conventional efficiency scores, these results are insensitive to outlier DMUs. They also show how the DMUs' efficiency ratios relate to each other for all feasible weights, rather than for those weights only for which the data envelopment analysis (DEA) efficiency score of some DMU is maximized. We illustrate the usefulness of these results by revisiting reported DEA studies and by describing a recent case study on the efficiency comparison of university departments. This paper was accepted by Teck-Hua Ho, decision analysis.efficiency analysis, data envelopment analysis, preference modeling

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A multiattribute additive value function that has been built from a complete specification of the decision maker's (DM's) preferences gives scale-independent decision recommendations, which do not depend on how the value function is normalized. In this paper, we show that if the preference specification is incomplete, many widely employed decision rules for comparing alternatives give scale-dependent decision recommendations in which the relative ranking of alternatives depends not only on the DM's preferences but also on the normalization of the value function. But because normalization does not involve preference statements, the recommendations should be scale independent so that they do not depend on the chosen normalization. To provide such recommendations, we propose ranking intervals, which show how a given alternative compares with all other alternatives for all value functions that are consistent with the stated preference information. These intervals can be computed from mixed integer linear optimization problems that are constrained by inequalities implied by the DM's preference statements. We illustrate the use of ranking intervals by analyzing university rankings and discuss their uses in project portfolio selection.