The terrible tyranny of the majority

"Democracy is a pathetic belief in the collective wisdom of individual ignorance. No one in this world [...] has ever lost money by underestimating the intelligence of the great masses of the plain people. Nor has anyone ever lost public office thereby." - H.L. Mencken

I continue to plough through 'Numbers Rule'. Regular readers will not be surprised to learn that my original grasp of the higher mathematics involved has been found wanting. Condorcet's Paradox is indeed apposite, but unsurprisingly there have been further theoretical developments since the late eighteenth century. What we in the UK are living through is actually a worked example of Kenneth Arrow's Independence of Irrelevant Alternatives condition. The really bad news is that this condition appears in a paper proving that it is impossible to design a system of voting which can correctly choose between multiple alternatives. I think we all knew that empirically, but it's good to see a mathematical proof.

Citoyen Condorcet

Arrow won a Nobel Prize, but Condorcet didn't fare so well. He was in many ways a man after your bloggist's own heart - mathematician, accountant, revolutionary, married to a beautiful woman twenty years his junior - and in addition he was a friend of Thomas Jefferson and Adam Smith. On the downside he made the mistake of falling out with Robespierre and, well, that was that. One of the book's conclusions seems to be that the only method of government that does away with manipulations, paradoxes and inconsistencies is a dictatorship; in this case it certainly did away with Condorcet.

Citoyen Arrow

As a by-product of all this I have discovered that in dealing with the common problem of dividing a fixed amount unevenly such that each subset is an integer and they add back to the original number (come on, don't pretend you've never had to do it) that the best way to proceed is by rounding on the geometric mean. All these decades I have been rounding on the arithmetic mean. I feel foolish.