Fisher’s Five Tines Fork and other Quantum Theories of Index Numbers
Yrjo O. Vartia · 1978
Fisher’s (1922) perhaps most interesting contributions concern the biases of index number formulas. Weighted index numbers (omitting modes and medians) seem to cluster into five groups according to the type of the average and the weights used. Fisher explains this using the concepts of ‘type bias 1 and ‘weight bias 1 interacting with each other, see Fisher (1922, p. 83–117, 352–6). His theory is condensed in a graphical representation, called the Five-tined Fork, each tine representing index numbers having the same ‘dose of bias’, i.e., 2+, 1+, 0, 1- or 2-. For instance the group 2+ consists of weighted index numbers (except modes and medians) having a double upward bias, see Fisher (1922, p. 202–5). Fisher concludes on p. 204–5: “Thus, barring ‘simples’ and ‘modes’ and their derivates (and possibly medians if we wish to have our results very close), we find that, although we have numerous formulae, they all fall under only five clearly defined heads, namely, those without bias, those with single bias up or down, and those with double bias up or down. The five tines include all the arithmetic, harmonic, geometric, and aggregative weighted index numbers and their derivates which we have obtained.” These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.