Importance of reading widely and choosing the right terminology

I couldn't help smile when I read the following passage from a short note in GEB. It shows how not being extra careful about the terms one uses can lead to massive confusion down the road.

A possible cause of Echenique’s oversight might be the confusing state of the terminology regarding SUB and IIA (not to mention Arrovian IIA in social choice, which is a different concept). As pointed out by Echenique, the substitutability property is also Sen’s condition α (Sen, 1969) and the so-called Chernoff’s condition. But it has also been called axiom C3 in Arrow (1959), the Heritage property H in Aizerman and Aleskerov (1995) or in Moulin (1985), and the Heredity property in Aleskerov and Monjardet (2002) or in Aleskerov et al. (2007). On the other hand, IIA is Postulate 5 in Chernoff (1954), Axiom 2 in Fishburn (1975), the strong superset’s axiom in Bordes (1979) and the Outcast Property O in Aizerman and Aleskerov (1995) or in Aleskerov (1999). Moreover, IIA was introduced in famous Nash’s (1950) paper where Nash only used single-valued choice functions. In this case the substitutability property H coincide with IIA (or O), and so one finds sometimes the expression “Nash’s IIA” used for “SUB”; a bit confusing . . . isn’t it? 


Hat tip: Felix Brandt for pointing out the article.

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