Abstract
Aggregating the preferences of a group of experts is a recurring problem in several fields, including engineering design; in a nutshell, each expert formulates an ordinal ranking of a set of alternatives and the resulting rankings should be aggregated into a collective one. Many aggregation models have been proposed in the literature, showing strengths and weaknesses, in line with the implications of Arrow's impossibility theorem. Furthermore, the coherence of the collective ranking with respect to the expert rankings may change depending on: (i) the expert rankings themselves and (ii) the aggregation model adopted. This paper assesses this coherence for a variety of aggregation models, through a recent test based on the Kendall's coefficient of concordance (W), and studies the characteristics of those models that are most likely to achieve higher coherence. Interestingly, the so-called Borda count model often provides best coherence, with some exceptions in the case of collective rankings with ties. The description is supported by practical examples.
Highlights
A problem that is common to a number of fields, including engineering design, is that of aggregating multiple ordinal rankings of a set of alternatives into a collective ranking
There is a substantial agreement on the design criteria, the selection of design alternatives is generally driven by the different personal experience of designers (Dwarakanath and Wallace 1995)
Arises the need to aggregate preference rankings of design alternatives that reflect the opinions of individual experts, using appropriate aggregation models (Fishburn 1973b; Franssen 2005; Cook 2006; Hazelrigg 1999; Frey et al 2010; Katsikopoulos 2009; Ladha et al 2003; Reich 2010; Nurmi 2012)
Summary
A problem that is common to a number of fields, including engineering design, is that of aggregating multiple ordinal rankings of a set of alternatives into a collective ranking. A passionate debate on the effects of the Arrow’s impossibility theorem in engineering design is still going on (Arrow 2012; Reich 2010; Hazelrigg 1996, 1999, 2010; Scott and Antonsson 1999; Franssen 2005; Yeo et al 2004; McComb et al 2017) This theorem establishes the impossibility of a generic aggregation model to provide a collective ranking that always satisfies several desirable properties, known as fairness criteria, i.e., unrestricted domain, non-dictatorship, independence of irrelevant alternatives (IIA), weak monotonicity, and Pareto efficiency (Arrow 2012; Fishburn 1973a; Nisan et al 2007; Saari 2011; Saari and Sieberg 2004; Franssen 2005; Jacobs et al 2014).
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