Asset voting was invented by Lewis Carroll (Charles L. Dodgson)!

Asset voting was invented independently in 2004 by Warren D. Smith and (a somewhat different version somewhat earlier) by Forest W. Simmons. Or so we thought.

The famed children's book author, poet, and wordplay genius Lewis Carroll (Alice's Adventures in Wonderland, Through the Looking-Glass, The Hunting of the Snark, Jabberwocky) was in real life The Reverend Charles Lutwidge Dodgson (1832-1898). He taught mathematics (he invented a remarkable way to evaluate matrix determinants) and also was an early pioneer in photography.

Dodgson was one of the first to examine voting from the standpoint of a mathematician. Indeed, some think he was the best of the early investigators. However, his work was largely forgotten and under-appreciated for about 100 years. It did not help that Dodgson/Carroll did not write down his deeper mathematical thoughts because he wanted to make his voting pamphlets more popular. That caused his thoughts to appear to be pretty shallow and trivial. That changed when Glasglow economist Duncan Black (who, with Kenneth Arrow, initiated the modern revival in mathematical examination of voting) carefully re-examined Dodgson's old works and inferred that Dodgson had to have known a good deal more than he actually said, and in some ways was 50 years ahead of his time. However, Black also unfortunately was under-appreciated during his career.

Dodgson was the first to explore the paradoxes, such as refusing to elect Condorcet winners, suffered by instant runoff voting. He also was one of the first, perhaps even the first, to codify the notion of Proportional Representation and prove "proportionality theorems." If you read page 210 (second column) of Black's re-examination of Dodgson's voting pamphlet (pdf), then you will see that Lewis Carroll invented "Asset Voting" in 1884 and recognized that it enjoyed a proportionality theorem.

The sources below discuss Black & Dodgson. It is claimed that Dodgson was the first person to prove a proportionality theorem for "single nontransferable vote" SNTV. SNTV only is proportional, though, if the voters act cooperatively and strategically, a fact which Dodgson saw using one of the first uses of "game theory." Such cooperative strategy cannot be considered realistic unless all the voters follow "party recommendations" when voting, and those party recommendations are devised by strategists who decide to sacrifice some but not all of their-party's candidates. With "asset voting," Dodgson saw the same proportionality result arises for the same reason, but the unrealistic underlying assumptions are no longer needed.

Asset voting seems by far the simplest voting system with a proportionality theorem. It surely is a very natural system, since it was invented independently by at least three different people, all arriving from different chains of thought, but all recognizing its proportionality theorem. It is surprising it has not gotten more attention. We find that even more surprising now.


Iain McLean, Alistair McMillan, and Burt L. Monroe: Duncan Black and Lewis Carroll, J.Theoretical Politics 7,2 (1995) 107-123. This article was later expanded into this book:

Iain McLean, Alistair McMillan, and Burt L. Monroe (eds.): A Mathematical Approach to Proportional Representation: Duncan Black on Lewis Carroll. Kluwer Academic Publishers (apparently later switched to Springer?) 1996. [Dodgson's pamphlet, "The Principles of Parliamentary Representation," was published in 1884 and republished in this book, as well as other rare historical material. Duncan Black largely-authored but never published this book and after Black died it was reconstructed by the editors.]

Francine F. Abeles (compiler & editor): The Political Pamphlets and Letters of Charles L. Dodgson and Related Pieces, University of Virginia Press 2001 (ISBN 0-930326-14-8)

Duncan Black: Lewis Carroll and the Theory of Games, The American Economic Review 59,2 (May 1969) 206-210. (pdf)

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