Impossible by design? Fairness, strategy, and Arrow’s impossibility theorem

Abstract

The design process often requires work by teams, rather than individuals. During teambased design it is likely that situations will arise in which individual members of the team have different opinions, yet a group decision must still be made. Unfortunately, Arrow's Impossibility Theorem indicates that there is no method for aggregating group preferences that will always satisfy a small number of "fair" conditions. This work seeks to identify methods of combining individual preferences that can come close to satisfying Arrow's conditions, enabling decisions that are fairer in practice. First, experiential conjoint analysis was used to obtain individual empirical utility functions for drinking mug designs. Each empirical utility function represented individual members who were part of a design team. Then, a number of functions for constructing group preference were analysed using both randomly generated preferences and empirical preferences derived from the experiential conjoint survey. The analysis involved checking each of Arrow's conditions, as well as assessing the potential impact of strategic voting.Based on the results, methods that should be used to aggregate group preference within a design team in practice were identified and recommended.2

Aggregating multiple ordinal rankings in engineering design: the best model according to the Kendall’s coefficient of concordance

“…Returning to the context of the early-design stage, design alternatives are often not very well defined and there are doubts about how) to prioritize them (Weingart 2005;Kaldate et al 2006;McComb et al 2017. Although 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).…”

“…Alongside this, a passionate debate on the effects of the Arrow's impossibility theorem in engineering design is still going on (Arrow 2012;Reich 2010;Hazelrigg 1996Hazelrigg , 1999Hazelrigg , 2010Scott and Antonsson 1999;Franssen 2005;Yeo et al 2004;McComb et al 2017). In short, this theorem establishes the impossibility of a generic aggregation model to provide a collective ranking that always satisfies several desirable properties, also 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).…”

“…For a given set of m expert rankings concerning n alternatives, different aggregation models may obviously lead to different collective rankings (Saari 2011;McComb et al 2017). Identifying the model that best reflects the m rankings is not easy, also because it may change from case to case.…”

“…For example, several authors attempted to measure the coherence (or consistency) between the expert rankings and the collective one (Chiclana 2002;Maisano 2015, 2017;Franceschini and Garcia-Lapresta 2019). Other authors hypothesized a relationship between the so-called implicit agreement of the expert rankings and the Arrow's fairness (McComb et al 2017). Moreover, Katsikopoulos (2009) expressed the need for greater clarity in the discussion ofengineering design methods to support decision making.…”

Designing Improved Teams for Crowdsourced Competitions

“…This may indicate that optimal team size is task-dependent. In addition, computational work has demonstrated that smaller teams are capable of making decisions that have better axiomatic characteristics [22].…”