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The Mathematical Intelligencer 24 (2002) 2-3 (Letters to the Editor)

Condorcet Splitting and Point Criteria

Sir, At my age I don't write many Letters to the Editor any more. But when I read Crespo Cuaresma's article on «Point Splitting and Condorcet Criteria,» in the Summer 2001 issue of your esteemed journal (pp. 23-26), I sat up straight, circumstances permitting.

First of all, I was delighted to see the name of my distinguished colleague Condorcet hitting the headlines yet again [1]. Of course, the voting system carrying his name is really mine. In fact when, some hundreds of years after me, my system was named after him, this only anticipated that yet another few hundreds of years later, Stigler [2] came up with Stigler's Law of Eponomy. This states, as you know as well as I do, that a decent manner in which to properly indicate that a scientific result is not yours is to have it named after you. The only catch is that the world is not told it's mine. That's why I am so grateful to Iain McLean and John London [3], and others as detailed in [4], who recently took pains to put the facts on record. While initially missing out on my very first paper on the subject [5], they nevertheless recognized my achievements just on the grounds of the two later papers [6, 7]. That first paper got buried away in the catacombs of the Vatican Library and was excavated only in October 2000 [4]. Which, incidentally, teaches the practical lesson that even when your paper remains unread for over seven hundred years, it's still not too late for it to resurface at the turn of the next millenium and drive home its point. Your readers may find this comforting.

Speaking of practicality, I notice that I should come to why I am writing this letter. It's because I was intrigued by the eminently practical solution that Crespo Cuaresma has for his friends Alan and Charles. As the two fellows don't know what to do with their money, they distribute not it, but infinitely divisible points. I particularly appreciate the ingenious mathematization of those mundane monetary mishaps because, as a philosopher, I am thrilled by the philosophical implications. When I was active we worried much about contemplating an infinitely expansible universe, but an infinitely divisible point was unthinkable. A point was a point. An indivisible unity. Or, as I said in [5], unus punctus. I apologize for changing the dialect, it's just that I don't know what you folks would say these days, a pixel?, which makes me chuckle since, once you are on file with as many publications as I am, close to three hundred, you can be used as the intellectual originator of almost anything. Some people have even turned me into one of the fathers of Computer Science [8], though simultaneously picturing me as «one of the most inspired madmen who ever lived» does not do me justice. All through my life one of my concerns was communication, and if communication is promoted not only by my combinatorial aids but also by Computer Science, then I would hail it loudly and instantly work it into my general art. As a first attempt I have had my three electoral papers rapidly prototyped at, to assist your contemporaries in the correct attribution of my ideas.

Yours truly,
Ramon Llull (1232-1316)
Left Choir Chapel
San Francisco Cathedral
Palma de Mallorca
Catalonian Kingdom


[1] H. Lehning: «The birth of Galois and the death of Condorcet.» Mathematical Intelligencer 13 (1991), 66-67.
[2] S.M. Stigler: «Stigler's law of eponomy.» Transactions of the New York Academy of Sciences, Series II 39 (1980), 147-157.
[3] I. McLean: «The Borda and Condorcet principles: Three medieval applications.» Social Choice and Welfare 7 (1990), 99-108.
[4] G. Hägele and F. Pukelsheim: «Llull's writings on electoral systems.» Studia Lulliana 42 (2002), 3-38.
[5] R. Llull (before 1283): «Artifitium electionis personarum.» Codex Vaticanus Latinus 9332, 11r-12v.
[6] R. Llull (about 1283): «En qual manera Natanne fo eleta a abadessa.» Codex Hispanicus 67, 32v-34r.
[7] R. Llull (1299): «De arte eleccionis.» Codex Cusanus 83, 47v-48r.
[8] M. Gardner: Logic Machines and Diagrams, Second Edition. Harvester Press, Brighton, 1983.

by the good offices of
Friedrich Pukelsheim
Inst. für Mathematik, Univ. Augsburg
D-86135 Augsburg, Germany
e-mail: Pukelsheim@Math.Uni-Augsburg.De

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