You don’t get tired at all… there is no cost at all...
So you have deliberately constructed a scenario, then defined “winning” as something forbidden by the scenario. Unhelpful.
That’s multiple solutions.
You have specified multiple games. I have defined a finite set of solutions for each Actor that can all be stated as “use the stopping function”. If your Actor has no such function, it is not rational because it can get stuck by problems with the potential to become unbounded. Remember, the Traveling Salesman must eventually sell something or all that route planning is meaningless. This sort of thing is exactly what a stopping function is for, but you seem to have written them out of the hypothetical universe for some (as yet unspecified) reason.
A reader can’t go to the author and demand volume 2...
Incorrect. People do it all the time, and it is now easier than ever. Moreover, I object to the comparison of your essay with a book. This context is more like a conversation than a publication. Please get to the point.
My objective is to convince people of this abstract theoretical point...
You have done nothing but remove criteria for stopping functions from unbounded scenarios. I don’t believe that is convincing anybody of anything. I suspect the statement “not every conceivable game in every conceivable universe allows for a stopping function that does not permit somebody else to do better” would be given a non-negligible probability by most of us already. That statement seems to be what you have been arguing, and seems to coincide with your title.
Friendly Style Note: I (just now) noticed that you have made some major changes to the article. It might be helpful to isolate those changes structurally to make them more visually obvious. Remember, we may not be rereading the full text very often, so a timestamp might be nice too. :)
You’ll be pleased to know that I found a style of indicating edits that I’m happy with. I reaslised that if I make the word edited subscript then it is much less obnoxious, so I’ll be using this technique on future posts.
There is no need to re-read the changes to the article. The changes just incorporate things that I’ve also written in the comments to reduce the chance of new commentators coming into the thread with misunderstandings I’ve clarified in the comments.
“So you have deliberately constructed a scenario, then defined “winning” as something forbidden by the scenario. Unhelpful.”—As long as the scenario does not explicitly punish rationality, it is perfectly valid to expect a perfectly rational agent to outperform any other agent.
“Remember, the Traveling Salesman must eventually sell something or all that route planning is meaningless”—I completely agree with this, not stopping is irrational as you gain 0 utility. My point was that you can’t just say, “A perfectly rational agent will choose an action in this set”. You have to specify which action (or actions) an agent could choose whilst being perfectly rational.
“You have done nothing but remove criteria for stopping functions from unbounded scenarios”—And that’s a valid situation to hand off to any so-called “perfectly rational agent”. If it gets beaten, then it isn’t deserving of that name.
There is no need to re-read the changes to the article...
I have been operating under my memory of the original premise. I re-read the article to refresh that memory and found the changes. I would simply have been happier if there was an ETA section or something. No big deal, really.
As long as the scenario does not explicitly punish rationality, it is perfectly valid to expect a perfectly rational agent to outperform any other agent.
Not so: you have generated infinite options such that there is no selection that can fulfill that expectation. Any agent that tries to do so cannot be perfectly rational since the goal as defined is impossible.
Exactly, if you accept the definition of a perfectly rational agent as a perfect utility maximiser, then there’s no utility maximiser as there’s always another agent that obtains more utility, so there is no perfectly rational agent. I don’t think that this is a particularly unusual way of using the term “perfectly rational agent”.
And it would still get beaten by a more rational agent, that would be beaten by a still more rational agent and so on until infinity. There’s a non-terminating set of increasingly rational agents, but no final “most rational” agent.
If the PRA isn’t trying to “maximize” an unbounded function, it can’t very well get “beaten” by another agent who chooses x+n because they didn’t have the same goal. I reject, therefore, that an agent that obeys its stopping function in an unbounded scenario may be called any more or less “rational” based on that reason only than any other agent that does the same, regardless of the utility it may not have collected.
By removing all constraints, you have made comparing results meaningless.
Might be. Maybe that agent’s utility function is actually bounded at 1 (it’s not trying to maximize, after all). Perhaps it wants 100 utility, but already has firm plans to get the other 99. Maybe it chose a value at random from the range of all positive real numbers (distributed such that the probability of choosing X grows proportional to X) and pre-committed to the results, thus guaranteeing a stopping condition with unbounded expected return. Since it was missing out on unbounded utility in any case, getting literally any is better than none, but the difference between x and y is not really interesting.
(humorously) Maybe it just has better things to do than measuring its *ahem* stopping function against the other agents.
So you have deliberately constructed a scenario, then defined “winning” as something forbidden by the scenario. Unhelpful.
You have specified multiple games. I have defined a finite set of solutions for each Actor that can all be stated as “use the stopping function”. If your Actor has no such function, it is not rational because it can get stuck by problems with the potential to become unbounded. Remember, the Traveling Salesman must eventually sell something or all that route planning is meaningless. This sort of thing is exactly what a stopping function is for, but you seem to have written them out of the hypothetical universe for some (as yet unspecified) reason.
Incorrect. People do it all the time, and it is now easier than ever. Moreover, I object to the comparison of your essay with a book. This context is more like a conversation than a publication. Please get to the point.
You have done nothing but remove criteria for stopping functions from unbounded scenarios. I don’t believe that is convincing anybody of anything. I suspect the statement “not every conceivable game in every conceivable universe allows for a stopping function that does not permit somebody else to do better” would be given a non-negligible probability by most of us already. That statement seems to be what you have been arguing, and seems to coincide with your title.
Friendly Style Note: I (just now) noticed that you have made some major changes to the article. It might be helpful to isolate those changes structurally to make them more visually obvious. Remember, we may not be rereading the full text very often, so a timestamp might be nice too. :)
You’ll be pleased to know that I found a style of indicating edits that I’m happy with. I reaslised that if I make the word edited subscript then it is much less obnoxious, so I’ll be using this technique on future posts.
That sounds like it will be much easier to read. Thank you for following up!
There is no need to re-read the changes to the article. The changes just incorporate things that I’ve also written in the comments to reduce the chance of new commentators coming into the thread with misunderstandings I’ve clarified in the comments.
“So you have deliberately constructed a scenario, then defined “winning” as something forbidden by the scenario. Unhelpful.”—As long as the scenario does not explicitly punish rationality, it is perfectly valid to expect a perfectly rational agent to outperform any other agent.
“Remember, the Traveling Salesman must eventually sell something or all that route planning is meaningless”—I completely agree with this, not stopping is irrational as you gain 0 utility. My point was that you can’t just say, “A perfectly rational agent will choose an action in this set”. You have to specify which action (or actions) an agent could choose whilst being perfectly rational.
“You have done nothing but remove criteria for stopping functions from unbounded scenarios”—And that’s a valid situation to hand off to any so-called “perfectly rational agent”. If it gets beaten, then it isn’t deserving of that name.
I have been operating under my memory of the original premise. I re-read the article to refresh that memory and found the changes. I would simply have been happier if there was an ETA section or something. No big deal, really.
Not so: you have generated infinite options such that there is no selection that can fulfill that expectation. Any agent that tries to do so cannot be perfectly rational since the goal as defined is impossible.
Exactly, if you accept the definition of a perfectly rational agent as a perfect utility maximiser, then there’s no utility maximiser as there’s always another agent that obtains more utility, so there is no perfectly rational agent. I don’t think that this is a particularly unusual way of using the term “perfectly rational agent”.
In this context, I do not accept that definition: you cannot maximize an unbounded function. A Perfectly Rational Agent would know that.
And it would still get beaten by a more rational agent, that would be beaten by a still more rational agent and so on until infinity. There’s a non-terminating set of increasingly rational agents, but no final “most rational” agent.
If the PRA isn’t trying to “maximize” an unbounded function, it can’t very well get “beaten” by another agent who chooses x+n because they didn’t have the same goal. I reject, therefore, that an agent that obeys its stopping function in an unbounded scenario may be called any more or less “rational” based on that reason only than any other agent that does the same, regardless of the utility it may not have collected.
By removing all constraints, you have made comparing results meaningless.
So an agent that chooses only 1 utility could still be a perfectly rational agent in your books?
Might be. Maybe that agent’s utility function is actually bounded at 1 (it’s not trying to maximize, after all). Perhaps it wants 100 utility, but already has firm plans to get the other 99. Maybe it chose a value at random from the range of all positive real numbers (distributed such that the probability of choosing X grows proportional to X) and pre-committed to the results, thus guaranteeing a stopping condition with unbounded expected return. Since it was missing out on unbounded utility in any case, getting literally any is better than none, but the difference between x and y is not really interesting.
(humorously) Maybe it just has better things to do than measuring its *ahem* stopping function against the other agents.