## Response to spoil-proofing elections by Julie Rehmeyer in the New Scientist 12 March 2008

A. The title "spoil-proofing elections" was not very appropriate because the article mainly concentrated on Borda voting. Spoilers still occur in Borda voting. (And the article never defines "spoiler"...)

B. The claim "69 percent of the time, an election result can be changed by changing the voting rules" is meaningless without a more precise definition (and none is provided). I assure you I can change the election result 100% of the time by changing the rules! Actually, there is a meaning behind this, namely a paper D.G.Saari & M.M.Tataru: The probability of dubious election winners, Economic Theory 13 (1999) 345-363 claimed the 69% figure for weighted positional voting systems only. But even as such, the claim is still wrong because this paper was erroneous. My computer simulations revealed the 69% figure was in error, and then it turned out the same error was also detected (independently confirming my computer) by William V. Gehrlein & Dominique Lepelley: The probability that all weighted scoring rules elect the same winner, Economic Lett. 66,2 (2000) 191-197. See puzzle #46.

C. The quote:

Suppose, [Saari] argues, that voters prefer candidate A to candidate B to candidate C and candidate B then drops out. The voters should still prefer A to C, right? Saari found that for three-candidate elections, the Borda count is the method most likely to ensure that.
is simply false. With range voting (which is not mentioned in the article) if B drops out, then A is still preferred to C, 100% of the time. No exceptions whatever. [But with Borda, there are exceptions.] This Borda=best statement by Saari would become true if we restrict attention to a very small subclass of election methods that does not include range voting. But as a statement about all election methods, it is just false.

D. The quote:

In a system like the Borda count, a candidate dropping out wouldn't change the rankings of the other candidates.
is even more false! – counterexample here where a candidate dropping out totally reverses the rankings of the others.

[Not to put too fine a point on it, but these errors would have been spotted if I had been sent the article for a preview. Also as is rather commonplace, the systems discussed did not include range voting, despite the fact that range voting is superior to them in every way that is discussed in the article. The article also cites previous Science News pieces by Klarreich – that one wasn't bad but criticism of/response to the Klarreich piece is available here – and by Peterson. The Peterson piece is discussed here very briefly.
An amazing commonality is that all 3 pieces would have been better if they'd included range voting and range voting appears to be superior or equal to every method they did discuss, in every way they discussed, in all 3 pieces.]