On fair countable lotteries
Two reverse supertasks—one new and one invented by Pérez Laraudogoitia (Philos Stud 168:619–628, 2014)—are discussed. Contra Kerkvliet (Log Anal, 2016) and Pérez Laraudogoitia, it is argued that these supertasks cannot be used to conduct fair infinite lotteries, i.e., lotteries on the set of natural numbers with a uniform probability distribution. The new supertask involves an infinity of gods who collectively select a natural number by each removing one ball from a collection of initially infinitely many balls in a reverse omega-sequence of actions.
KeywordsReverse supertasks Uniform probability distributions Countable additivity axiom
The reverse supertask of Sect. 1 is, essentially, of my invention. I first presented it in an unpublished paper, from which Timber Kerkvliet learned about it. In my original version, each god halved the number of balls in the collection. Timber Kerkvliet found it simpler to work with the version in which each god just removes a single ball. I also realized that the formalism of this paper would be more elegant with that version, and I therefore adopted it. I have benefitted from discussions about this supertask with Jon Pérez Laraudogoitia, Øystein Linnebo, Martin Jullum, Phil Chodrow, Laureano Luna, Carl Baker, Federico Luzzi, Thomas Brouwer, Andreas Fjellstad, Crispin Wright, John Norton, and Timber Kerkvliet.