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The CAR Method for Using Preference Strength in Multi-criteria Decision Making

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Abstract

Multi-criteria decision aid (MCDA) methods have been around for quite some time. However, the elicitation of preference information in MCDA processes, and in particular the lack of practical means supporting it, is still a significant problem in real-life applications of MCDA. There is obviously a need for methods that neither require formal decision analysis knowledge, nor are too cognitively demanding by forcing people to express unrealistic precision or to state more than they are able to. We suggest a method, the CAR method, which is more accessible than our earlier approaches in the field while trying to balance between the need for simplicity and the requirement of accuracy. CAR takes primarily ordinal knowledge into account, but, still recognizing that there is sometimes a quite substantial information loss involved in ordinality, we have conservatively extended a pure ordinal scale approach with the possibility to supply more information. Thus, the main idea here is not to suggest a method or tool with a very large or complex expressibility, but rather to investigate one that should be sufficient in most situations, and in particular better, at least in some respects, than some hitherto popular ones from the SMART family as well as AHP, which we demonstrate in a set of simulation studies as well as a large end-user study.

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Notes

  1. We will henceforth, unless otherwise stated, presume that decision problems are modelled as simplexes \(S_{w}\) generated by \(w_{1}> w_{2}> \cdots > w_{N}, \Sigma w_{i}=1, \hbox { and } 0=w_{i}\).

  2. To be more precise, a strict ordering is not required since ties are allowed.

  3. In Danielson et al. (2014a) and Danielson and Ekenberg (2014b), ordinal weights are introduced that are more robust than other surrogate weights, in particular. Using steps 1–3 above, cardinal weights can analogously be obtained. This is explained in detail in Danielson and Ekenberg (2015) where the performance of a set of cardinal weights are compared to ordinal weights.

  4. Sometimes there is a limit to the individual numbers but not a limit to the sum of the numbers.

  5. For various cognitive and methodological aspects of imprecision in decision making (see, e.g., Danielson et al. 2007, 2014).

  6. A second success measure we used is the matching of the three highest ranked alternatives (“podium”), the number of times the three highest evaluated alternatives using a particular method all coincide with the true three highest alternatives. A third set generated is the matching of all ranked alternatives (“overall”), the number of times all evaluated alternatives using a particular method coincide with the true ranking of the alternatives. The two latter sets correlated strongly with the first and are not shown in this paper. Instead, we show the Kendall’s tau measure of overall performance.

  7. SMART is represented by the improved SMARTER version by Edwards and Barron (1994).

  8. AHP weights were derived by forming quotients \(\hbox {w}_{i}/\hbox {w}_{j}\) and rounding to the nearest odd integer. Also allowing even integers in between yielded no significantly better results.

  9. The subjects had 2–4 years of university studies with no or little mathematical background. Thus, their level of education corresponds to an average decision making manager in many organisations.

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Acknowledgments

This research was funded by the Swedish Research Council FORMAS, Project Number 2011-3313-20412-31, as well as by Strategic funds from the Swedish government within ICT—The Next Generation.

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Authors and Affiliations

  1. Department of Computer and Systems Sciences, DSV Stockholm University, DSV, Postbox 7003, 164 07, Kista, Sweden

    Mats Danielson & Love Ekenberg

  2. International Institute for Applied Systems Analysis, IIASA, Schlossplatz 1, 2361, Laxenburg, Austria

    Mats Danielson & Love Ekenberg

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  1. Mats Danielson
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Correspondence to Love Ekenberg.

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Danielson, M., Ekenberg, L. The CAR Method for Using Preference Strength in Multi-criteria Decision Making. Group Decis Negot 25, 775–797 (2016). https://doi.org/10.1007/s10726-015-9460-8

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