Decision making paradox
Encyclopedia
The word paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

 (parádoxon (παράδοξον) in Greek) comes from the Greek words "para" (meaning against, contrary to) and "doksa" or "doxa" (meaning belief, understanding). A paradox is a seemingly true statement or group of statements that lead to a contradiction
Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...

 or a situation which seems to defy logic or intuition
Intuition (knowledge)
Intuition is the ability to acquire knowledge without inference or the use of reason. "The word 'intuition' comes from the Latin word 'intueri', which is often roughly translated as meaning 'to look inside'’ or 'to contemplate'." Intuition provides us with beliefs that we cannot necessarily justify...

.

This particular paradox relates to decision-making and it was first identified by Triantaphyllou and Mann in 1989. It was further elaborated in the book by Triantaphyllou on multi-criteria decision-making. Since then it has been recognized in the related literature as a fundamental paradox in multi-criteria decision analysis
Multi-Criteria Decision Analysis
Multiple-criteria decision-making or multiple-criteria decision analysis is a sub-discipline of operations research that explicitly considers multiple criteria in decision-making environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria...

 (MCDA) / multi-criteria decision making (MCDM), and decision analysis
Decision analysis
Decision analysis is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner...

, in general. This paradox is related to the quest for determining reliable decision-making methods.

Description of this paradox

The realization for this paradox comes from the rather straightforward observation that there are numerous decision-making methods (both normative and descriptive) each one of which claims to be the "best" one. Furthermore, often these methods may yield different results when they are fed with exactly the same decision problem and data.

Finding the best decision-making method leads to the formulation of a decision problem itself for which the alternatives are the decision making methods themselves. Naturally, one needs to know the best method a-priori in order to select the best method from the available ones.

In the study reported in and an interesting investigation was undertaken. Since in the beginning it was assumed that the best method is not known, the problem of selecting the best method was solved by successively using different methods. The methods used in that study were the weighted sum model
Weighted sum model
The weighted sum model is the best known and simplest multi-criteria decision analysis / multi-criteria decision making method for evaluating a number of alternatives in terms of a number of decision criteria. It is very important to state here that it is applicable only when all the data are...

 (WSM), the weighted product model
Weighted product model
The weighted product model is a popular multi-criteria decision analysis  / multi-criteria decision making method. It is similar to the weighted sum model . The main difference is that instead of addition in the main mathematical operation now there is multiplication...

 (WPM), and two variants of the analytic hierarchy process
Analytic Hierarchy Process
The Analytic Hierarchy Process is a structured technique for organizing and analyzing complex decisions. Based on mathematics and psychology, it was developed by Thomas L...

 (AHP). It was found that when a method was used, say method X (which is one of the previous four methods), the conclusion was that another method was best (say, method Y). When method Y was used, then another method, say method Z, was suggested as being the best one, and so on.

Two evaluative criteria were used to formulate the previous decision-making problem (actually, an MCDM problem). The first criterion was based on the premise that a method which claims to be accurate in multi-dimensional problems (for which different units of measurement are used to describe the alternatives), should also be accurate in single-dimensional problems. For such problems, the weighted sum model
Weighted sum model
The weighted sum model is the best known and simplest multi-criteria decision analysis / multi-criteria decision making method for evaluating a number of alternatives in terms of a number of decision criteria. It is very important to state here that it is applicable only when all the data are...

 (WSM) is the widely accepted approach, thus their results were compared with the ones derived from the WSM. The second evaluative criterion was based on the following situation. Suppose some alternatives are evaluated and one of them is returned as the best alternative (say alternative A). Next, a non-optimal alternative (say alternative B) is replaced by a worse one. Under normal conditions one should expect that the same alternative as before (i.e., alternative A) is the best alternative again. This is also known in the related literature as a ranking reversal. However, this may not happen with some of the methods tested in those experiments. For weights of these two evaluative criteria, all possible combinations were considered such that their sum was always equal to 1.00.

Methods that have been verified to exhibit this paradox

The following is a partial list of multi-criteria decision-making methods which have been confirmed to exhibit this paradox:,

  • The analytic hierarchy process
    Analytic Hierarchy Process
    The Analytic Hierarchy Process is a structured technique for organizing and analyzing complex decisions. Based on mathematics and psychology, it was developed by Thomas L...

     (AHP) and some of its variants.
  • The weighted product model
    Weighted product model
    The weighted product model is a popular multi-criteria decision analysis  / multi-criteria decision making method. It is similar to the weighted sum model . The main difference is that instead of addition in the main mathematical operation now there is multiplication...

      (WPM).
  • The ELECTRE
    ELECTRE
    ELECTRE is a family of multi-criteria decision analysis methods that originated in Europe in the mid-1960s. The acronym ELECTRE stands for: ELimination Et Choix Traduisant la REalité ....

     (outranking) method and its variants.
  • The TOPSIS method.

Looking into the future

Other methods have not been tested yet but it is very likely they may exhibit the same phenomenon. Such methods include the following:
  • The analytic network process
    Analytic Network Process
    The analytic network process is a more general form of the analytic hierarchy process used in multi-criteria decision analysis.AHP structures a decision problem into a hierarchy with a goal, decision criteria, and alternatives, while the ANP structures it as a network...

     (ANP).
  • The PROMETHEE
    Prométhée
    Prométhée is an opera in three acts by the French composer Gabriel Fauré. The libretto, by Jean Lorrain and Ferdinand Hérold, is based on the Greek myth of Prometheus. Although designated a tragédie lyrique, the opera resists easy categorisation. It was intended as a large-scale work with spoken...

     (outranking) method.
  • Multi-attribute utility theory (MAUT).
  • Dominance-based rough set approach
    Dominance-based Rough Set Approach
    Dominance-based rough set approach is an extension of rough set theory for multi-criteria decision analysis , introduced by Greco, Matarazzo and Słowiński...

     (DRSA)
  • Aggregated indices randomization method (AIRM)
  • Nonstructural fuzzy decision support system (NSFDSS)
  • Grey relational analysis
    Grey relational analysis
    Grey analysis uses a specific concept of information. It defines situations with no information as black, and those with perfect information as white. However, neither of these idealized situations ever occurs in real world problems. In fact, situations between these extremes are described as being...

     (GRA)
  • Superiority and inferiority ranking method
    Superiority and inferiority ranking method
    The superiority and inferiority ranking method is a multi-criteria decision making model which can handle real data and provides six different preference structures for the system user. It also incorporates outranking rationale to deal with the 'poor' true-criteria preference structure which...

     (SIR method)
  • Potentially all pairwise rankings of all possible alternatives (PAPRIKA)
  • Value analysis (VA)


What is the best decision making method has always been a highly contested subject. There is always an ongoing debate on this subject. At the same time, a plethora of competing methods exists. A key role in this quest is played by the study of rank reversals in decision making
Rank reversals in decision making
This article describes the role rank reversals play in assessing the merits of decision-making methods. The issue of rank reversals lies at the heart of many debates in decision-making and multi-criteria decision-making, in particular....

.

As stated earlier, it is not uncommon such methods to yield different results when they are presented with exactly the same data. Thus, this decision making paradox is likely to persist for many years to come.
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
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