10% of the population sunburns easily.
90% of people who sunburn easily wear sunscreen.
10% of the people who don’t sunburn easily wear sunscreen.
Regardless of whether or not you sunburn easily, wearing sunscreen will reduce the chances of getting sunburn.
You don’t know if you sunburn easily or not.
EDT looks at this data and says, “It’s better to be a randomly chosen member of the group of people who don’t wear sunscreen than a randomly chosen member of the group of people who do. Therefore, don’t wear sunscreen.” And that seems like the wrong answer, because your decision whether or not to wear sunscreen doesn’t actually affect whether or not you sunburn easily. In other words, the problem with EDT is that it can’t handle “Simpson’s Paradox”.
Evidential decision theory is a school of thought within decision theory according to which the best action is the one which, conditional on your having chosen it, gives you the best expectations for the outcome.
This is not the same as “being a randomly chosen member of a group of people...” and I’ve explained why. The information about group membership is contained in the filtration.
Here’s an intuition pump:
10% of the population sunburns easily. 90% of people who sunburn easily wear sunscreen. 10% of the people who don’t sunburn easily wear sunscreen. Regardless of whether or not you sunburn easily, wearing sunscreen will reduce the chances of getting sunburn. You don’t know if you sunburn easily or not.
EDT looks at this data and says, “It’s better to be a randomly chosen member of the group of people who don’t wear sunscreen than a randomly chosen member of the group of people who do. Therefore, don’t wear sunscreen.” And that seems like the wrong answer, because your decision whether or not to wear sunscreen doesn’t actually affect whether or not you sunburn easily. In other words, the problem with EDT is that it can’t handle “Simpson’s Paradox”.
According to wikipedia, the definition of EDT is
This is not the same as “being a randomly chosen member of a group of people...” and I’ve explained why. The information about group membership is contained in the filtration.