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 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?