a note on "a note on nanson's rule"
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A Note on "A Note on Nanson's Rule"Author(s): P. C. FishburnSource: Public Choice, Vol. 64, No. 1 (Jan., 1990), pp. 101-102Published by: SpringerStable URL: http://www.jstor.org/stable/30025209 .
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Public Choice 64: 101-102, 1990. © 1990 Kluwer Academic Publishers. Printed in the Netherlands.
A note on "A note on Nanson's rule"
P.C. FISHBURN A T& T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974-2070
Niou's note (1987) on Nanson's rule for determining a winner from voters' pre- ference rankings accuses several people, including Fishburn (1977), of missta- ting Nanson's rule. He says, for example, that I (1977: 473) describe the rule thus:
Nanson's function is a Borda elimination procedure. At each stage in a sequential process we delete all candidates who have the lowest Borda count at that stage unless all have the same Borda count. The process continues until no more candidates can be deleted. Those that remain constitute the choice set.
What this passage describes is indeed not Nanson's rule, but something I defi- ned earlier in the paper as "Nanson's function" and designated as C2. In ex- plaining the name chosen for C2, I (1977: 474) added that:
In using Borda counts at each stage of a sequential elimination procedure, Nanson proposed that all candidates whose Borda counts in that stage are less than or equal to the average count be deleted (unless all remaining candidates have the same Borda count). The C2 function deletes only the lo- west Borda count candidates at each stage but is similar in spirit to Nanson's original method.
By choosing not to acknowledge this subsequent passage, Niou may convey the impression that I had not done my homework. Indeed, Nanson (1883) continu- es to make fascinating reading more than a century after its publication, and I would be happy to send a copy of my annotated copy of his paper to anyone who is interested in the original.
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References
Fishburn, P.C. (1977). Condorcet social choice functions. SIAM Journal on Applied Mathematics 33: 469-489.
Nanson, E.J. (1883). Methods of election. Transactions and Proceedings of Royal Society of Vic- toria 19: 197-240.
Niou, E.M.S. (1987). A note on Nanson's rule. Public Choice 54: 191-193.
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