Edited and translated by Iain McLean and Arnold B. Urken
This book consists of a general introduction and the collected works of 1900 years of writers on voting theory and its generalization – social choice. Social choice includes both voting theory and the choice mechanisms inherent in economics. To quote from the book’s jacket: “The writings of Roman lawyer and senator Pliny the Younger are included here as are those of Ramon Lull, a medieval mathematician, missionary, mystic, novelist, and poet; Nicolaus Cusanus, the son of a fifteenth-century winegrower who became a cardinal; Jean-Charles de Borda, a naval engineer; the Marquis de Condorcet, a mathematician, politician, feminist, and economist who died in the French revolutionary Terror of 1794; and Charles L. Dodgson, who became famous as Lewis Carroll. All had fundamental insight into voting and what is now called social choice.”
The introduction makes clear the difference between voting on a binary issue (yes or no) which represents elementary democracy and voting on 3 or more issues which is the domain of social choice. Problems crop up when 3 or more issues are considered. In general the binary issue represents a special case of the more general problem.
Having all these classic papers in one place is indeed a valuable resource. Some of them were unknown previously or unavailable in English. The Golden Age of Social Choice was indeed the period surrounding the French Enlightenment. Borda and Condorcet were contemporaries who came up with the two major voting methods still considered today. Most other methods are variations of these. Condorcet, at one point, was tasked with coming up with a Constitution which he did. It included sophisticated voting methods. However, when Robespierre and the Jacobins took power, they threw out Condorcet’s Constitution and developed one of their own. Condorcet was so outraged that he denounced the Jacobins with the result that he was declared an outlaw whose status was punishable by death. Condorcet hid out for awhile, but left his hiding place when he found out that his hostess could be punished by death for harboring a fugitive. Thus Condorcet became the only person to actually die for Social Choice. Today Condorcet, or what remains of him, resides in the Pantheon in Paris along with Voltaire and Rousseau both of whom, by the way, were uninterested in voting theory.
In the Nineteenth Century the Rev. C. L. Dodgson, a somewhat eccentric figure who wrote “Alice in Wonderland” did some major work on Social Choice without being acquainted with the historical precedents that preceded him. He also was a pioneering person in photography with children as his main subjects. He was a mathematics professor at Christ Church College at Oxford. The impetus for his work was the proverbial faculty meeting at which such issues as whether to construct a belfry were decided. Dodgson had developed a relationship with Dean Liddell’s daughters, one of whose names was Alice, taking them on outings and telling them stories. At some point there was a falling out with the Liddells and Dodgson was forbidden to see the daughters again.
A contemporary of Dodgson’s, E. J. Nanson was a mathematics professor at the University of Melbourne, Australia. Nanson was a Condorcetist, his methods being based on the theories of Condorcet. Nanson’s procedure involved an iterated Borda count, at each stage dropping the candidate(s) with less than the average Borda score until a winner was declared. He showed that his procedure was Condorcet efficient.
Mention also is made of the inventors of proportional representation (PR), a voting method in widespread use today. Two men, Thomas Hill, an Australian, and Thomas Hare, an Englishman, developed this theory which starts from the premise that if there are S seats to fill and V votes are cast, each group is entitled to a number of seats determined by the formula V/S provided a quota is met. Interestingly enough, the predecessor to PR was developed by Thomas Jefferson and Alexander Hamilton who came up with a formula for apportioning House seats according to population.
All in all, this book is a valuable resource although a more in depth interpretation of each paper would have been helpful.