Independence of Irrelevant Alternatives in Engineering Design

Abstract

When discussing Arrow’s Impossibility Theorem (AIT) in engineering design, we find that one condition, Independence of Irrelevant Alternatives (IIA), has been misunderstood generally. In this paper, two types of IIA are distinguished. One is based on Kenneth Arrow (IIA-A) that concerns the rationality condition of a collective choice rule (CCR). Another one is based on Amartya Sen (IIA-S) that is a condition for a choice function (CF). Through the analysis of IIA-A, this paper revisits three decision methods (i.e., Pugh matrix, Borda count and Quality Function Deployment) that have been criticized for their failures in some situations. It is argued that the violation of IIA-A does not immediately imply irrationality in engineering design, and more detailed analysis should be applied to examine the meaning of “irrelevant information”. Alternatively, IIA-S is concerned with the transitivity of CF, and it is associated with contraction consistency (Property α) and expansion consistency (Property β). It is shown that IIA-A and IIA-S are technically distinct and should not be confused in the rationality arguments. Other versions of IIA-A are also introduced to emphasize the significance of mathematical clarity in the discussion of AIT-related issues.