[4][5][6] The PAPRIKA method is based on users expressing their preferences with respect to the relative importance of the criteria or attributes of interest for the decision or choice at hand by pairwise comparing (ranking) alternatives.
In MCDM applications, PAPRIKA is used by decision-makers to determine weights on the criteria for the decision being made, representing their relative importance.
In conjoint analysis applications, PAPRIKA is used with consumers or other stakeholders to estimate 'part-worth utilities' (i.e. weights) representing the relative importance of the attributes characterizing products or other objects of interest (i.e., choice modelling, conjoint analysis and discrete choice).
[4][5][6] Examples of areas in which the method is used for multi-criteria decision making or conjoint analysis include (see also 1000minds applications): The PAPRIKA method specifically applies to additive multi-attribute value models with performance categories[33] – also known as 'points', 'scoring', 'point-count' or 'linear' systems or models.
The unweighted points system representation is easier to use and helps inform the explanation of the PAPRIKA method below.
The PAPRIKA method pertains to value models for ranking particular alternatives that are known to decision-makers (e.g. as in the job candidates example above) and also to models for ranking potentially all hypothetically possible alternatives in a pool that is changing over time (e.g. patients presenting for medical care).
For example, for a value model with eight criteria and four categories within each criterion, and hence 48 = 65,536 possible alternatives, there are 65,536 x 65,535 / 2 = 2,147,450,880 pairwise rankings.
The PAPRIKA method resolves this 'impossibility' problem by ensuring that the number of pairwise rankings that decision-makers need to perform is kept to a minimum – i.e. only a small fraction of the potentially millions or billions of undominated pairs – so that the burden on decision-makers is minimized and the method is practicable.
Fundamental to the efficiency of the method is application of the transitivity property of additive value models, as illustrated in the simple demonstration later below.
Pairwise Trade-off Analysis was abandoned in the late 1970s, however, because it lacked a method for systematically identifying implicitly ranked pairs.
The ZAPROS method (from Russian for 'Closed Procedure Near References Situations') was also proposed;[36] however, with respect to pairwise ranking all undominated pairs defined on two criteria "it is not efficient to try to obtain full information".
These eight alternatives and their total score equations – derived by simply adding up the variables corresponding to the point values (which are as yet unknown: to be determined by the method being demonstrated here) – are listed in Table 2.
For many readers, this simple value model can perhaps be made more concrete by considering an example to which most people can probably relate: a model for ranking job candidates consisting of the three criteria (for example) (a) education, (b) experience, and (c) references, each with two 'performance' categories, (1) poor or (2) good.
Thus, which is the better candidate ultimately depends on the decision-maker's preferences with respect to the relative importance of experience vis-à-vis references.
Table 2: The eight possible alternatives and their total-score equations The PAPRIKA method's first step is to identify the undominated pairs.
This simple approach can be represented by the matrix in Figure 2, where the eight possible alternatives (in bold) are listed down the left-hand side and also along the top.
Notationally, undominated pairs in their cancelled forms, like b2 + c1 vs b1 + c2, are also representable as _21 vs _12 – i.e. where '_' signifies identical categories for the identified criterion.
Thus, arbitrarily beginning here with pair (i) b2 + c1 vs b1 + c2, the decision-maker is asked: "Which alternative do you prefer, _21 or _12 (i.e. given they're identical on criterion a), or are you indifferent between them?"
Next, corresponding to pair (ii) a2 + c1 vs a1 + c2, suppose the decision-maker is asked: "Which alternative do you prefer, 1_2 or 2_1 (given they're identical on criterion b), or are you indifferent between them?"
This result can easily be seen by adding the corresponding sides of the inequalities for pairs (i) and (ii) and cancelling common variables.
Simultaneously solving the three inequalities above (i, ii, v), subject to a2 > a1, b2 > b1 and c2 > c1, gives the point values (i.e. the 'points system'), reflecting the relative importance of the criteria to the decision-maker.
Although multiple solutions to the three inequalities are possible, the resulting point values all reproduce the same overall ranking of alternatives as listed above and reproduced here with their total scores: First, the decision-maker may decline to explicitly rank any given undominated pair (thereby excluding it) on the grounds that at least one of the alternatives considered corresponds to an impossible combination of the categories on the criteria.
Of course, most real-world value models have more criteria and categories than the simple example above, which means they have many more undominated pairs.
For such real-world value models, the simple pairwise-comparisons approach to identifying undominated pairs used in the previous sub-section (represented in Figure 2) is highly impractical.
The details of these processes are beyond the scope of this article, but are available elsewhere[1] and, as mentioned earlier, the PAPRIKA method is implemented by decision-making software products 1000minds and MeenyMo.