Illustration of point a): “Infinity is low but not zero.” This does not seem to make sense as written. Plausibly you missed out a “the probability of” or “on the curve” somewhere; which goes back to needing proofreading.
Illustration of b): “I’m trying to map it to a probability on my indifference curve of utility value versus probability (0 to 1) and pick the the highest expected value (probability * utility).” What is the difference (if any) between this, and just picking the highest expected value with no curve involved? (If the curve isn’t constant in expected value, are you not vulnerable to Dutch-booking?) What work is the curve doing in this argument, what rent does it pay? And it is really very unclear how you would plot “infinity” on such a curve.
b) Thinking about how to plot this on graphs is helping me to clarify thinking and I think adding these may help to reduce inferential distance. (The X axis is probability. For the case where we consider infinite utilities as opposed to the human case, the graph would need to be split into 2 graphs. The one on left is just an infinity horizontal line but there is still a probability range. The one on the right has an actual curve and covers the rest of the probability range but doesn’t matter since its utility values are finite. Considering only the infinite utilities is a fanatical decision procedure but doesn’t generally lead to weird decisions. Does that make sense?)
I believe you are thinking of infinity as a number, and that’s always a mistake. I think that what you’re trying to say with your left-hand graph is that, given infinite utility, probability is a tiebreaker, but all infinite-utility options dominate all finite utilities. But this treats “infinity” as a binary quality which an option either has or not.
Consider two different Pascal’s muggers: One offers you a 1% probability of utility increasing linearly in time, the other, a 1% chance of utility increasing exponentially with time. Clearly both options “are infinite”; equally clearly, you prefer the second one even though the probabilities are the same. They occupy the same point on your left-hand graph. But by your suggested decision procedure you would choose the linearly-increasing option if the first mugger offered even an epsilon increase in probability; and this is obviously Weird. It gives you a smaller expected utility at almost all points in time!
This needs
a) proofreading and
b) unpacking for inferential distance.
Illustration of point a): “Infinity is low but not zero.” This does not seem to make sense as written. Plausibly you missed out a “the probability of” or “on the curve” somewhere; which goes back to needing proofreading.
Illustration of b): “I’m trying to map it to a probability on my indifference curve of utility value versus probability (0 to 1) and pick the the highest expected value (probability * utility).” What is the difference (if any) between this, and just picking the highest expected value with no curve involved? (If the curve isn’t constant in expected value, are you not vulnerable to Dutch-booking?) What work is the curve doing in this argument, what rent does it pay? And it is really very unclear how you would plot “infinity” on such a curve.
Give it an editing pass, and post again.
Thanks for the response! I really appreciate it.
a) Yes, I meant “the probability of”
b) Thinking about how to plot this on graphs is helping me to clarify thinking and I think adding these may help to reduce inferential distance. (The X axis is probability. For the case where we consider infinite utilities as opposed to the human case, the graph would need to be split into 2 graphs. The one on left is just an infinity horizontal line but there is still a probability range. The one on the right has an actual curve and covers the rest of the probability range but doesn’t matter since its utility values are finite. Considering only the infinite utilities is a fanatical decision procedure but doesn’t generally lead to weird decisions. Does that make sense?)
In a word, no.
I believe you are thinking of infinity as a number, and that’s always a mistake. I think that what you’re trying to say with your left-hand graph is that, given infinite utility, probability is a tiebreaker, but all infinite-utility options dominate all finite utilities. But this treats “infinity” as a binary quality which an option either has or not.
Consider two different Pascal’s muggers: One offers you a 1% probability of utility increasing linearly in time, the other, a 1% chance of utility increasing exponentially with time. Clearly both options “are infinite”; equally clearly, you prefer the second one even though the probabilities are the same. They occupy the same point on your left-hand graph. But by your suggested decision procedure you would choose the linearly-increasing option if the first mugger offered even an epsilon increase in probability; and this is obviously Weird. It gives you a smaller expected utility at almost all points in time!
Thanks @RolfAndreassen. I’m reconsidering and will post a different version if I get there. I’ve marked this one as [retracted].