Potentially All Pairwise RanKings of all possible Alternatives

PAPRIKA (Potentially All Pairwise RanKings of all possible Alternatives) is a multi-criteria decision analysis technique based on pairwise comparisons. Specifically, it is a method for determining the point values (or weights) for additive multi-attribute value models where each criterion (or attribute) is demarcated into mutually-exclusive categories.
PAPRIKA involves the decision-maker pairwise ranking potentially all undominated pairs of all possible alternatives representable by the value model being scored. An ‘undominated pair’ is a pair of alternatives where one is characterized by a higher ranked category for at least one criterion and a lower category for at least one other criterion than the other alternative. Conversely, the alternatives in a ‘dominated pair’ are inherently pairwise ranked due to one having a higher category for at least one criterion and none lower for the other criteria.
The decision-maker begins by pairwise ranking undominated pairs defined on just two criteria at a time (where, in effect, all other criteria’s categories are pairwise identical). This is followed, if the decision-maker chooses to continue, by pairs with successively more criteria, until potentially all undominated pairs are ranked. The number of pairs to be explicitly ranked is minimized because PAPRIKA identifies and eliminates all pairs implicitly ranked as corollaries of the explicitly ranked pairs (via the transitivity property of additive multi-attribute value models).
Thus PAPRIKA identifies potentially all pairwise rankings of all possible alternatives representable by the value model as either dominated pairs (given) or undominated pairs explicitly ranked by the decision-maker or implicitly ranked as corollaries. Because these pairwise rankings are consistent, a complete overall ranking of alternatives is defined. From the inequalities (strict preference) and equalities (indifference) corresponding to the explicitly ranked pairs, point values are obtained via linear programming. Although multiple solutions to the linear program of inequalities and equalities are possible, the resulting point values all reproduce the same overall ranking of alternatives.
Simulations of PAPRIKA’s use reveal that if the decision-maker explicitly pairwise ranks undominated pairs defined on just two criteria at-a-time, the resulting overall ranking of all possible alternatives is very highly correlated with the true ranking.<ref name="article" /> Therefore for most practical purposes decision-makers are unlikely to need to rank pairs defined on more than two criteria. Real-world applications suggest that decision-makers are able to rank comfortably more than 50 and up to at least 100 pairs, and in a short period of time.<ref name="article" />
Notwithstanding the apparent ability of decision-makers to rank this many pairs, PAPRIKA entails a greater number of judgments than most traditional methods for determining point values. Clearly though, different types of judgments are involved: for PAPRIKA, pairwise comparisons of undominated pairs, and for most traditional methods, ratio scale or interval scale measurements of the decision-maker’s preferences with respect to the relative importance of criteria and categories respectively. Arguably, the judgments for PAPRIKA are simpler and more natural and might reasonably be expected to reflect the preferences of decision-makers more accurately.

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