Counting on numbers

Abstract

1. Here is a very simple game. You come up with a number and I come up with a number. If I come up with the higher number, I win; otherwise you win. You go first. Call this ‘The Very Simple Game’. Few would play it if they had to go first and many if they are guaranteed to go second. 2. Here is another one. You come up with a number n and I come up with a number m. If m times 1/n > 1, then I win; if not, then you win. You go first. Call this ‘Still The Very Simple Game’. Since I win just in case m is greater than n, this game collapses into The Very Simple Game. Few people will play it if they have to go first. 3. Here is a third one. Let us call it ‘Looks Like A Tricky Game’. Suppose you have a choice between exactly two actions: Suppose, you are a maximizer of expected utility with an unbounded, aggregative utility function (and with no risk aversion and no temporal discounting). You are perfectly rational. These assumptions are very unrealistic in the case of humans but let that go for the sake of the argument. Let us further assume that for you the expected utility of (A) is 1 (the probability of keeping it, given (A), equals 1, and the utility of having it equals 1). Apart from that, I claim that I can give you things of any value for you I like with no effort or loss on my side. And I want to make you choose (B) (cf. Bostrom 2009: 445).

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