I can give a counter-example to the Modesty Argument as stated: “When you disagree with someone, the Modesty Argument claims that you should both adjust your probability estimates toward the other, and keep doing this until you agree.”
Suppose two coins are flipped out of sight, and you and another person are trying to estimate the probability that both are heads. You are told what the first coin is, and the other person is told what the second coin is. You both report your observations to each other.
Let’s suppose that they did in fact fall both heads. You are told that the first coin is heads, and you report the probability of both heads as 1⁄2. The other person is told that the second coin is heads, and he also reports the probability as 1⁄2. However, you can now both conclude that the probability is 1, because if either of you had been told that the coin was tails, he would have reported a probability of zero. So in this case, both of you update your information away from the estimate provided by the other. One can construct more complicated thought experiments where estimates jump around in all kinds of crazy ways, I think.
I’m not sure whether this materially affects your conclusions about the Modesty Argument, but you might want to try to restate it to more clearly describe what you are disagreeing with.
I can give a counter-example to the Modesty Argument as stated: “When you disagree with someone, the Modesty Argument claims that you should both adjust your probability estimates toward the other, and keep doing this until you agree.”
Suppose two coins are flipped out of sight, and you and another person are trying to estimate the probability that both are heads. You are told what the first coin is, and the other person is told what the second coin is. You both report your observations to each other.
Let’s suppose that they did in fact fall both heads. You are told that the first coin is heads, and you report the probability of both heads as 1⁄2. The other person is told that the second coin is heads, and he also reports the probability as 1⁄2. However, you can now both conclude that the probability is 1, because if either of you had been told that the coin was tails, he would have reported a probability of zero. So in this case, both of you update your information away from the estimate provided by the other. One can construct more complicated thought experiments where estimates jump around in all kinds of crazy ways, I think.
I’m not sure whether this materially affects your conclusions about the Modesty Argument, but you might want to try to restate it to more clearly describe what you are disagreeing with.