Something like that. Geoffrey Brennan and Lomasky indeed present the binomial formula and suggest using it in their earlier work, but I haven’t found a case of them using it in any particular way (which could get results like Jason Brennan’s or results like Banzhaf’s), so didn’t want to pin this on them. So I cited Jason Brennan whose uses it to produce these crazily low probabilities in his book. It is possible that Jason Brennan didn’t do the calculations himself and that someone else did (either Geoffrey Brennan and Lomasky or others), but I don’t know and haven’t found an earlier source for the crazy numbers.
Something like that. Geoffrey Brennan and Lomasky indeed present the binomial formula and suggest using it in their earlier work, but I haven’t found a case of them using it in any particular way (which could get results like Jason Brennan’s or results like Banzhaf’s), so didn’t want to pin this on them. So I cited Jason Brennan whose uses it to produce these crazily low probabilities in his book. It is possible that Jason Brennan didn’t do the calculations himself and that someone else did (either Geoffrey Brennan and Lomasky or others), but I don’t know and haven’t found an earlier source for the crazy numbers.
Jason Brennan discusses the background on it a bit here—https://bleedingheartlibertarians.com/2012/10/on-the-probability-of-being-decisive/
Gelman responds in the comments