For two-path interferometers, the which-path predictability P and the fringe visibility V are familiar quantities that are much used to talk about wave-particle duality in a quantitative way. We discuss several candidates that suggest themselves as generalizations P of mathcalP for multi-path interferometers, and treat the case of three paths in considerable detail. To each choice for the path knowledge P, the interference strength V -- the corresponding generalization of V -- is found by a natural, operational procedure. In experimental terms it amounts to finding those equal-weight superpositions of the path amplitudes which maximize P for the emerging intensities. Mathematically speaking, one needs to identify a certain optimal one among the Fourier transforms of the state of the interfering quantum object. Wave-particle duality is manifest, inasmuch as P=1 implies V=0 and V=1 implies P=0, whatever definition is chosen. The possible values of the pair $(P,V)$ are restricted to an area with corners at $(P,V)=(0,0)$, $(P,V)=(1,0)$, and $(P,V)=(0,1)$, with the shape of the border line from $(1,0)$ to $(0,1)$ depending on the particular choice for P and the induced definition of V.
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Englert et al. (2007) studied this question.