Yeah. It wouldn’t be as strong in practice (neither nature nor people are in the habit of offering two-sided bets) but as a theoretical constraint it seems to work as well.
Not with the payoffs given by de Finetti. For example, there’s no way to play the roulette so it becomes an “anti-roulette”, giving you a slight edge instead of the casino. Nature usually gives you a choice between doing X (accepting a one-sided bet as is) or not doing X. You don’t always have the option of doing “anti-X” (taking the other side of the bet, with the risks and payoffs exactly reversed).
Yeah. It wouldn’t be as strong in practice (neither nature nor people are in the habit of offering two-sided bets) but as a theoretical constraint it seems to work as well.
Isn’t nature always in the habit of offering two-sided bets? Like, you can do one thing or the other.
Not with the payoffs given by de Finetti. For example, there’s no way to play the roulette so it becomes an “anti-roulette”, giving you a slight edge instead of the casino. Nature usually gives you a choice between doing X (accepting a one-sided bet as is) or not doing X. You don’t always have the option of doing “anti-X” (taking the other side of the bet, with the risks and payoffs exactly reversed).