I don’t understand. Anthony already addressed Claude’s 4th point above:
Following (3): There are positive epistemic motivations for imprecise credences. So yes, Elga is asking the impreciser to override what they consider locally (epistemically) rational.
More explicitly:
So “adopt sharp credences” means “have a state that doesn’t need forcing” — which is the opposite of forcing.
For someone who finds imprecise credences locally (epistemically) rational, “have a state that doesn’t need forcing” requires forcing themself into that state, and overturning the verdicts that would be implied (or allowed) by imprecise credences.
I fear what’s going on here and in the EA Forum thread is that you’ve picked a position and you’re prompting Claude in a way that will defend the position even if the arguments are weak, applied unfairly or ignore important context, and then pick and present any remaining argument that seems plausible to you. But Claude can generally quite easily make plausible-sounding arguments that are actually bad, and it can keep doing so ad nauseum.[1] This can mean being more exhaustive of the space of arguments and making sure each one is addressed, but it’s also exhausting and frustrating to deal with, because it seems like it will never end and it’s indistinguishable from motivated reasoning.
So, I think answering these would help:
What exactly is the position you’re defending? Has it changed throughout these discussions (in this thread or on the EA Forun post)?
Are there any cases in these discussions where you think an argument you made or endorsed turned out wrong, or a counterargument was correct? And if so, how has that affected your credences in the position you’ve been defending?
After all of these discussions, in your own words, what are your reasons for believing in sharp credences (or whatever position you’re defending)?
And this is why I recommend you filter through a round of exhaustive critique in another session, including checking if the arguments are being applied unfairly or have been already addressed, and for counterarguments. Better yet to do this with an LLM from another family.
Hi Michael. I believe in sharp credences because they follow from 3 premises I find very intuitive. From the abstract of Hammond (1988):
Behaviour norms are considered for decision trees which allow both objective probabilities and uncertain states of the world with unknown probabilities. Terminal nodes have consequences in a given domain [unrestricted domain]. Behaviour is required to be consistent in subtrees [dynamic consistency]. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree [consequentialism]. It implies that behaviour reveals a revealed preference ordering [“a complete [sharp], transitive, binary relation”] satisfying both the independence axiom and a novel form of surething principle.
Can you spell out these 3 premises explicitly? I’m not sure what you’re referring to.
I had in mind these 3 sentences from the abstract of Hammond (1988).
Terminal nodes have consequences in a given domain [unrestricted domain]. Behaviour is required to be consistent in subtrees [dynamic consistency]. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree [consequentialism].
I have not read the paper, but I understand the 3 premises above lead to completeness and independence as defined in the premises of Von Neumann–Morgenstern utility theorem.
It implies that behaviour reveals a revealed preference ordering [“a complete, transitive, binary relation”] satisfying both the independence axiom and a novel form of surething principle.
I wrote “a complete [sharp]” in my last comment. I do not think completeness alone implies sharp probabilities. One can collapse unsharp probabilities to sharp ones using something like the midpoint rule discussed in Adam Elga’s paper. However, assuming one rejects rules like this, completeness leads to sharp probabilities?
And did you know about and endorse these 3 premises when you posted Elga’s paper on the EA Forum?
I did not know about Hammond (1988) before linkposting Adam’s paper. I found it thanks to this comment from Simon on my linkpost. I would still have endorsed the premises if I had read about them before publishing the post.
What exactly is the position you’re defending? Has it changed throughout these discussions (in this thread or on the EA Forun post)?
I mostly want to defend completeness, which I understand is a key premise of Anthony’s unawareness argument. However, I have been defending sharp probabilities (and by this I have meant sharp probability distributions, which imply their expected values are sharp too).
Are there any cases in these discussions where you think an argument you made or endorsed turned out wrong, or a counterargument was correct? And if so, how has that affected your credences in the position you’ve been defending?
I do not feel like I have been making arguments. My recollection is that I have mostly been quoting Claude, and asking questions.
I lightly endorsed Adam’s claim that “Sharp does not entail Uniqueness” before linkposting the paper. I did not think much about it before linkposting. A comment from Jim Buhler prompted me to think a bit more about it, and come to the view that “I endorse sharpness and uniqueness. As far as I can tell, the issues of unsharp probabilities would apply in the same way to non-unique probabilities”. There is more context about my views about uniqueness in my reply to Jim.
Terminal nodes have consequences in a given domain [unrestricted domain]. Behaviour is required to be consistent in subtrees [dynamic consistency]. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree [consequentialism].
Why do you believe behaviour should be consistent in subtrees? Why can’t just the fact that the trees are different be enough to permit (but not necessarily require) different behaviour? I think this premise is basically assuming away our responses, so it’s doing a lot of work.
There could be specific differences we could point to to justify different behaviour, like the argument I made here, which does not apply to each bet on its own.
EDIT: Actually, I’m not sure how the premises relate to my argument, since IIUC, Hammond’s model is that outcomes are in the terminal nodes, and those differ between the isolated bets and the two bets in sequence.
I wrote “a complete [sharp]” in my last comment. I do not think completeness alone implies sharp probabilities. One can collapse unsharp probabilities to sharp ones using something like the midpoint rule discussed in Adam Elga’s paper. However, assuming one rejects rules like this, completeness leads to sharp probabilities?
The space of potential rules could be huge, so that could be assuming quite a lot.
Completeness is one of Savage’s axioms, which together imply sharp probabilities. Completeness probably does a lot of the work, but other parts may be important, too. (I’m not that familiar with Savage’s axioms or theorem, though, so I wouldn’t be able to explain much more with reading more myself.)
I did not know about Hammond (1988) before linkposting Adam’s paper. I found it thanks to this comment from Simon on my linkpost. I would still have endorsed the premises if I had read about them before publishing the post.
Why did you believe in sharp credences when you linkposted Elga’s paper? Do you no longer endorse those reasons as important for your beliefs?
I do not feel like I have been making arguments. My recollection is that I have mostly been quoting Claude, and asking questions.
I lightly endorsed Adam’s claim that “Sharp does not entail Uniqueness” before linkposting the paper. I did not think much about it before linkposting. A comment from Jim Buhler prompted me to think a bit more about it, and come to the view that “I endorse sharpness and uniqueness. As far as I can tell, the issues of unsharp probabilities would apply in the same way to non-unique probabilities”. There is more context about my views about uniqueness in my reply to Jim.
So when you’ve quoted Claude to us (including the summary post of Elga’s paper itself), say the answer “makes sense” and/or ask for our reactions, you didn’t endorse any of what it says?
Why do you believe behaviour should be consistent in subtrees? Why can’t just the fact that the trees are different be enough to permit (but not necessarily require) different behaviour? I think this premise is basically assuming away our responses, so it’s doing a lot of work.
I just have a strong intuition that what matters are the consequences of my actions given the current state of the world regardless of how I arrived at the current state.
I think my thoughts are compatible with the premises.
Why did you believe in sharp credences when you linkposted Elga’s paper? Do you no longer endorse those reasons as important for your beliefs?
Elga’s paper supports my belief in sharp expected values (EVs), including EVs of distributions describing probabilities. However, my belief in completeness is supported more by Hammond (1988), and I understand lack of completeness matters more than unsharp EVs for Anthony’s unawareness argument for “no impartial altruistic justification for preferring any action over another”.
So when you’ve quoted Claude to us (including the summary post of Elga’s paper itself), say the answer “makes sense” and/or ask for our reactions, you didn’t endorse any of what it says?
If I say something like “Claude’s objections make sense to me”, or “I endorse Claude’s objections”, I mean it based on the conventional meaning of the words involved. However, the meaning of “I endorse X” depends on the context. All else equal, the endorsement is stronger if I have thought more about the topic, and have written about it more.
I just have a strong intuition that what matters are the consequences of my actions given the current state of the world regardless of how I arrived at the current state.
This seems completely consistent with the backward induction argument I made in the second half of my comment here.
I think my thoughts are compatible with the premises.
Conditional on being in town, you wouldn’t pay, because this is lower EV. It doesn’t matter how you got there (by your own claim). By consistency in subtrees (which you claim), this means outside of town, ahead of time, you won’t pay even if you get to town (unless you can force yourself to override your later local choice). So you will be predicted not to pay, and you will be left stranded, which is worse than getting into town and paying.
If it helps, build the decision tree.
Elga’s paper supports my belief in sharp expected values (EVs), including EVs of distributions describing probabilities.
Are you saying you believed in sharp credences primarily because of Elga’s arguments?
This [why I (Vasco) believe in dynamic consistency] seems completely consistent with the backward induction argument I made in the second half of my comment here.
I agree. Claude says your argument breaks what I referred to as consequentialism. “Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree [consequentialism]”. Here is what Claude said.
The structure of the tree must be irrelevant [for consequentialism to hold] — only the set of achievable consequences at the root matters. (And Hammond proves in §5 that this forces the revealed preference relation to be a complete, transitive ordering.) The way to show Michael violates this is to build two trees with the identical feasible consequence set and show his rule behaves differently in them.
Tree 1 — the one-shot (normal-form) version: a single choice among the four consequences directly. Apply maximality to the static menu. Only NEITHER is dominated (BOTH beats it statewise); every other pair crosses. So the acceptable set is {BOTH, A-only, B-only}.
Tree 2 — the sequential version we’ve been working with, which has the same four consequences reachable at the root (accept-accept → BOTH, accept-reject → A-only, reject-accept → B-only, reject-reject → NEITHER), so F [the set of feasible consequences] is identical. But Michael’s backward induction pruned reject-A. Reaching B-only requires rejecting A, so with reject-A gone, B-only is now unreachable. The acceptable set collapses to {BOTH, A-only}.
Now put the two verdicts against the shared feasible set. Same F, different Φ [set of consequences from following a given behaviour] — and the culprit is B-only, admissible in the one-shot menu but excluded once the same consequences are reached through sequential structure.
Conditional on being in town, you wouldn’t pay, because this is lower EV.
If the driver is able to predict what I will do in town with perfect accuracy, and they will only drive me to town if I pay, then I will pay in town. Not paying would go against the perfect accuracy of the driver, and therefore the thought experiment would not be coherent, as the driver cannot have and not have perfect accuracy? As far as I understand, if I was driven to town, paying would be the only option I would consider.
Are you saying you believed in sharp credences primarily because of Elga’s arguments?
I already believed in sharp expected values before knowing about Elga’s paper. My intuition has been that it makes a lot of sense to represent uncertainty with distributions, but that only a single distribution is right in principle, even if I believe many different ones are reasonable in some sense.
Fair that my proposal violates Hammond’s conception of consequentialism, and that conception is at least a very plausible-at-first-glance conception of consequentialism: only the consequences matter, not the structure of the decision tree.
However, my proposal and argument seem compatible with a broader conception of consequentialism, and indeed your “what matters are the consequences of my actions given the current state of the world regardless of how I arrived at the current state”. We accept bet A (rule out rejecting bet A) and rule out the non-dominated option [reject A, accept B] for entirely consequentialist reasons: to prevent ourselves from rejecting both bets, which would be dominated in terms of consequences by accepting both bets. The ends, i.e. avoiding consequence-dominated sequences, justify the means, i.e. ruling out both a dominated option and an undominated option together. In the alternative where we just pick one of the 4 options directly in one step, ruling out [reject A, accept B] doesn’t help us avoid rejecting both bets, the dominated option.
If the driver is able to predict what I will do in town with perfect accuracy, and they will only drive me to town if I pay, then I will pay in town. Not paying would go against the perfect accuracy of the driver, and therefore the thought experiment would not be coherent, as the driver cannot have and not have perfect accuracy? As far as I understand, if I was driven to town, paying would be the only option I would consider.
Yes, you can’t not pay if you got a ride, assuming perfect accuracy. But this doesn’t solve the problem (guarantee a ride to town, which is presumably better). Before the driver decides whether or not to drive you, they predict that if they drove you, you paying would be worse to you once you got into town and feasible, so you wouldn’t pay. So, they don’t drive you, and you end up in the worst case.
That is unless unless you change how you think about the utilities of each option, give up consequentialism or otherwise find a way to commit to preventing yourself from not paying in town. And then all of these kinds of solutions are available to those with unsharp credences in the two bet problem by Elga.
Yes, you can’t not pay if you got a ride, assuming perfect accuracy. But this doesn’t solve the problem (guarantee a ride to town, which is presumably better).
Consequentialism (as defined by Hammond) does not guarantee me a ride to town, but I see this as a problem for me, not consequentialism. Why should one expect consequentialism to save the person in the desert? In general, consequentialism recommends actions compatible with bad outcomes for some people, and good outcomes for others.
For me the upshot of the thought experiment is that I am basically certain to stay in the desert. I will never be able to commit 100 % to paying in town. The simple fact that I would have to think about commiting is a sign that the chance of not paying would be above 0. So a driver who only drove me to town if they were certain I would pay would certainly leave me in the desert. So, regardless of how much I commit, I think I would be certain to end up in the desert.
Consequentialism should guarantee the best (expected) outcomes for the consequentialist. That’s the whole point. If Hammond’s version doesn’t do that, then it seems like a bad version. That being said, his kind of consequentialist can work, you just need to be willing to assign higher value to actually paying in town, say by caring about keeping promises even if you’d predict with your current values you’d rather break them later.
For me the upshot of the thought experiment is that I am basically certain to stay in the desert. I will never be able to commit 100 % to paying in town. The simple fact that I would have to think about commiting is a sign that the chance of not paying would be above 0. So a driver who only drove me to town if they were certain I would pay would certainly leave me in the desert. So, regardless of how much I commit, I think I would be certain to end up in the desert.
Let’s assume the driver will drive you if they predict you’re at least 80% likely to pay. Maybe you can’t fully guarantee a ride, but you can increase the probability by at least temporarily modifying how you make decisions, e.g. by caring more about keeping promises.
Anyway, here are my takeaways from Parfit’s hitchiker:
If sticking to your generally preferred decision rule leads to worse outcomes in some cases, you should consider modifying your rule, e.g. by caring about keeping promises for their own sake.
If you’re okay accepting that your rule will sometimes lead to predictably worse outcomes than another rule, then this at least partly undermines all dominance based arguments, including money pumps.
1 and 2 undermine Elga’s arguments against unsharp credences.
Consequentialism should guarantee the best (expected) outcomes for the consequentialist. That’s the whole point. If Hammond’s version doesn’t do that, then it seems like a bad version.
I think being left in the desert is the best and only outcome if the driver only takes me to town if they are certain I will pay them there.
Let’s assume the driver will drive you if they predict you’re at least 80% likely to pay. Maybe you can’t fully guarantee a ride, but you can increase the probability by at least temporarily modifying how you make decisions, e.g. by caring more about keeping promises.
I do not understand why this poses a problem to consequentialist reasoning. If I want to maximise my chances of survival, I should just constrain myself as much as possible to pay the driver in town. I would most likely be wrong if I found myself in town thinking there is only 10 % chance of paying if the driver is calibrated. I could try not to pay, but I would end up paying 80 % of the time. Reliably not paying would not be a live option if the driver is calibrated?
I don’t understand. Anthony already addressed Claude’s 4th point above:
More explicitly:
For someone who finds imprecise credences locally (epistemically) rational, “have a state that doesn’t need forcing” requires forcing themself into that state, and overturning the verdicts that would be implied (or allowed) by imprecise credences.
I fear what’s going on here and in the EA Forum thread is that you’ve picked a position and you’re prompting Claude in a way that will defend the position even if the arguments are weak, applied unfairly or ignore important context, and then pick and present any remaining argument that seems plausible to you. But Claude can generally quite easily make plausible-sounding arguments that are actually bad, and it can keep doing so ad nauseum.[1] This can mean being more exhaustive of the space of arguments and making sure each one is addressed, but it’s also exhausting and frustrating to deal with, because it seems like it will never end and it’s indistinguishable from motivated reasoning.
So, I think answering these would help:
What exactly is the position you’re defending? Has it changed throughout these discussions (in this thread or on the EA Forun post)?
Are there any cases in these discussions where you think an argument you made or endorsed turned out wrong, or a counterargument was correct? And if so, how has that affected your credences in the position you’ve been defending?
After all of these discussions, in your own words, what are your reasons for believing in sharp credences (or whatever position you’re defending)?
And this is why I recommend you filter through a round of exhaustive critique in another session, including checking if the arguments are being applied unfairly or have been already addressed, and for counterarguments. Better yet to do this with an LLM from another family.
Hi Michael. I believe in sharp credences because they follow from 3 premises I find very intuitive. From the abstract of Hammond (1988):
Could you answer my other questions, too?
Can you spell out these 3 premises explicitly? I’m not sure what you’re referring to.
And did you know about and endorse these 3 premises when you posted Elga’s paper on the EA Forum?
I had in mind these 3 sentences from the abstract of Hammond (1988).
I have not read the paper, but I understand the 3 premises above lead to completeness and independence as defined in the premises of Von Neumann–Morgenstern utility theorem.
I wrote “a complete [sharp]” in my last comment. I do not think completeness alone implies sharp probabilities. One can collapse unsharp probabilities to sharp ones using something like the midpoint rule discussed in Adam Elga’s paper. However, assuming one rejects rules like this, completeness leads to sharp probabilities?
I did not know about Hammond (1988) before linkposting Adam’s paper. I found it thanks to this comment from Simon on my linkpost. I would still have endorsed the premises if I had read about them before publishing the post.
I mostly want to defend completeness, which I understand is a key premise of Anthony’s unawareness argument. However, I have been defending sharp probabilities (and by this I have meant sharp probability distributions, which imply their expected values are sharp too).
I do not feel like I have been making arguments. My recollection is that I have mostly been quoting Claude, and asking questions.
I lightly endorsed Adam’s claim that “Sharp does not entail Uniqueness” before linkposting the paper. I did not think much about it before linkposting. A comment from Jim Buhler prompted me to think a bit more about it, and come to the view that “I endorse sharpness and uniqueness. As far as I can tell, the issues of unsharp probabilities would apply in the same way to non-unique probabilities”. There is more context about my views about uniqueness in my reply to Jim.
Why do you believe behaviour should be consistent in subtrees? Why can’t just the fact that the trees are different be enough to permit (but not necessarily require) different behaviour? I think this premise is basically assuming away our responses, so it’s doing a lot of work.
There could be specific differences we could point to to justify different behaviour, like the argument I made here, which does not apply to each bet on its own.
EDIT: Actually, I’m not sure how the premises relate to my argument, since IIUC, Hammond’s model is that outcomes are in the terminal nodes, and those differ between the isolated bets and the two bets in sequence.
And what do the premises together imply for Parfit’s hitchhiker and this decision problem with St Petersburg lotteries? Are those acceptable conclusions to you?
The space of potential rules could be huge, so that could be assuming quite a lot.
Completeness is one of Savage’s axioms, which together imply sharp probabilities. Completeness probably does a lot of the work, but other parts may be important, too. (I’m not that familiar with Savage’s axioms or theorem, though, so I wouldn’t be able to explain much more with reading more myself.)
Why did you believe in sharp credences when you linkposted Elga’s paper? Do you no longer endorse those reasons as important for your beliefs?
So when you’ve quoted Claude to us (including the summary post of Elga’s paper itself), say the answer “makes sense” and/or ask for our reactions, you didn’t endorse any of what it says?
I just have a strong intuition that what matters are the consequences of my actions given the current state of the world regardless of how I arrived at the current state.
I think my thoughts are compatible with the premises.
Elga’s paper supports my belief in sharp expected values (EVs), including EVs of distributions describing probabilities. However, my belief in completeness is supported more by Hammond (1988), and I understand lack of completeness matters more than unsharp EVs for Anthony’s unawareness argument for “no impartial altruistic justification for preferring any action over another”.
If I say something like “Claude’s objections make sense to me”, or “I endorse Claude’s objections”, I mean it based on the conventional meaning of the words involved. However, the meaning of “I endorse X” depends on the context. All else equal, the endorsement is stronger if I have thought more about the topic, and have written about it more.
This seems completely consistent with the backward induction argument I made in the second half of my comment here.
Conditional on being in town, you wouldn’t pay, because this is lower EV. It doesn’t matter how you got there (by your own claim). By consistency in subtrees (which you claim), this means outside of town, ahead of time, you won’t pay even if you get to town (unless you can force yourself to override your later local choice). So you will be predicted not to pay, and you will be left stranded, which is worse than getting into town and paying.
If it helps, build the decision tree.
Are you saying you believed in sharp credences primarily because of Elga’s arguments?
I agree. Claude says your argument breaks what I referred to as consequentialism. “Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree [consequentialism]”. Here is what Claude said.
If the driver is able to predict what I will do in town with perfect accuracy, and they will only drive me to town if I pay, then I will pay in town. Not paying would go against the perfect accuracy of the driver, and therefore the thought experiment would not be coherent, as the driver cannot have and not have perfect accuracy? As far as I understand, if I was driven to town, paying would be the only option I would consider.
I already believed in sharp expected values before knowing about Elga’s paper. My intuition has been that it makes a lot of sense to represent uncertainty with distributions, but that only a single distribution is right in principle, even if I believe many different ones are reasonable in some sense.
Fair that my proposal violates Hammond’s conception of consequentialism, and that conception is at least a very plausible-at-first-glance conception of consequentialism: only the consequences matter, not the structure of the decision tree.
However, my proposal and argument seem compatible with a broader conception of consequentialism, and indeed your “what matters are the consequences of my actions given the current state of the world regardless of how I arrived at the current state”. We accept bet A (rule out rejecting bet A) and rule out the non-dominated option [reject A, accept B] for entirely consequentialist reasons: to prevent ourselves from rejecting both bets, which would be dominated in terms of consequences by accepting both bets. The ends, i.e. avoiding consequence-dominated sequences, justify the means, i.e. ruling out both a dominated option and an undominated option together. In the alternative where we just pick one of the 4 options directly in one step, ruling out [reject A, accept B] doesn’t help us avoid rejecting both bets, the dominated option.
Yes, you can’t not pay if you got a ride, assuming perfect accuracy. But this doesn’t solve the problem (guarantee a ride to town, which is presumably better). Before the driver decides whether or not to drive you, they predict that if they drove you, you paying would be worse to you once you got into town and feasible, so you wouldn’t pay. So, they don’t drive you, and you end up in the worst case.
That is unless unless you change how you think about the utilities of each option, give up consequentialism or otherwise find a way to commit to preventing yourself from not paying in town. And then all of these kinds of solutions are available to those with unsharp credences in the two bet problem by Elga.
Consequentialism (as defined by Hammond) does not guarantee me a ride to town, but I see this as a problem for me, not consequentialism. Why should one expect consequentialism to save the person in the desert? In general, consequentialism recommends actions compatible with bad outcomes for some people, and good outcomes for others.
For me the upshot of the thought experiment is that I am basically certain to stay in the desert. I will never be able to commit 100 % to paying in town. The simple fact that I would have to think about commiting is a sign that the chance of not paying would be above 0. So a driver who only drove me to town if they were certain I would pay would certainly leave me in the desert. So, regardless of how much I commit, I think I would be certain to end up in the desert.
Consequentialism should guarantee the best (expected) outcomes for the consequentialist. That’s the whole point. If Hammond’s version doesn’t do that, then it seems like a bad version. That being said, his kind of consequentialist can work, you just need to be willing to assign higher value to actually paying in town, say by caring about keeping promises even if you’d predict with your current values you’d rather break them later.
Let’s assume the driver will drive you if they predict you’re at least 80% likely to pay. Maybe you can’t fully guarantee a ride, but you can increase the probability by at least temporarily modifying how you make decisions, e.g. by caring more about keeping promises.
Anyway, here are my takeaways from Parfit’s hitchiker:
If sticking to your generally preferred decision rule leads to worse outcomes in some cases, you should consider modifying your rule, e.g. by caring about keeping promises for their own sake.
If you’re okay accepting that your rule will sometimes lead to predictably worse outcomes than another rule, then this at least partly undermines all dominance based arguments, including money pumps.
1 and 2 undermine Elga’s arguments against unsharp credences.
I think being left in the desert is the best and only outcome if the driver only takes me to town if they are certain I will pay them there.
I do not understand why this poses a problem to consequentialist reasoning. If I want to maximise my chances of survival, I should just constrain myself as much as possible to pay the driver in town. I would most likely be wrong if I found myself in town thinking there is only 10 % chance of paying if the driver is calibrated. I could try not to pay, but I would end up paying 80 % of the time. Reliably not paying would not be a live option if the driver is calibrated?