“I suspect that as soon as you specify some scheme, it will be clear that assigning probability 1⁄3 to Heads gives the right decision when you apply standard decision theory, and that you don’t get the right decision if you assign probability 1⁄2 to Heads and use standard decision theory.”—I’ve already explained that you make a slight modification to account for the number of times you are asked. Obviously, if you don’t make this modification you’ll get the incorrect betting odds.
But I’m not looking to set things on a solid foundation in this post, that will have to wait to the future. The purpose of this post is just to demonstrate how a halver should analyse The Beauty and the Prince given foundations.
“I suspect that as soon as you specify some scheme, it will be clear that assigning probability 1⁄3 to Heads gives the right decision when you apply standard decision theory, and that you don’t get the right decision if you assign probability 1⁄2 to Heads and use standard decision theory.”—I’ve already explained that you make a slight modification to account for the number of times you are asked. Obviously, if you don’t make this modification you’ll get the incorrect betting odds.
But I’m not looking to set things on a solid foundation in this post, that will have to wait to the future. The purpose of this post is just to demonstrate how a halver should analyse The Beauty and the Prince given foundations.