Arrow’s theorem, multi-criteria decision problems and multi-attribute preferences in engineering design

Arrow’s theorem poses limits to the translation of the different preference orders on a set of options into a single preference order. In this paper, I argue, against opinions to the contrary, that Arrow’s theorem applies fully to multi-criteria decision problems as they occur in engineering design, making solution methods to such problems subject to the theorem’s negative result. Discussing the meaning and consequences for engineering design, I review the solution methods to such problems presented in the engineering design literature in the light of the theorem. It appears that underlying such methods is a mix-up of two fundamentally different problem definitions, as the theory of multi-attribute preferences, which is often presented as an adequate approach for engineering design, in fact fails to address the Arrowian multi-criteria problem. Finally, I suggest ways how engineering design might adopt results from discussions of Arrow’s theorem elsewhere in resolving its multi-criteria decision problems.