How not to be wrong on voting methods

On page 419, Jordan Ellenberg in his 2014 book  How Not To Be Wrong, the power of mathematical thinking,  writes:
One voting system to which Arrow's Theorem doesn't apply is "approval voting," in which you don't have to declare all your preferences, you just vote for as many of the people on the ballot as you want, and the candidate who gets the most votes wins.  Most mathematicians I know consider approval voting or its variant to be superior to both plurality voting and IRV;  it has been used to elect popes, secretaries-generals of the United Nation, and the officials of the American Mathematical Society, but never yet government officials in the United States.

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