Quiggin, J. and van Veelen, C.M. (2007). Multilateral indices: conflicting approaches? Review of income and wealth, 53(2):372--378.

This short paper focusses on an apparent conflict between two results from different approaches to the problem of finding multilateral index numbers. The impossibility theorem of Van Veelen (2002) is an axiomatic result that rules out the existence of a multilateral index that satisfies four modest requirements. This also implies that no bilateral index can consistently be generalized to a multilateral setting. Adopting a revealed preference approach, Dowrick and Quiggin (1997) however construct a multilateral extention of Fisher's ideal index, which preserves a range of desirable properties. This note shows what it is that drives the divergence between those two results. It also gives implications for practical use of results from either approach.