One thing that came to mind just this morning:
Why is expected utility maximization the most rational thing to do?
As I understand it (and Im a CS, not Econ. major), prospect theory and the utility function weighing used in it are usually accepted as how most “irrational” people make their descisions. But this might not be because they are irrational but rather because our utility functions do actually behave that way in which case we should abandon EU and just try to maximize well being with all the quirks PT introduces (such as loss being more costly than gain and so on)...
Or is this how most people here already do things? Any and all feedback on this idea would be really apreciated (especially links to relevant discussion of this idea as I am sure Im not the first to come up with it).
Sorry. I thought about things a little and realized that a few things about prospect theory definately need to be scrapped as bad ideas.. The probability weighing for instance. But other quirks (such as loss aversion or having different utilities for loss vs gain) might be useful to retain…
It would really be good if I knew a bit more about the different descision theories at this point. Does anyone have any good references from where one would get an overview and good references?
The standard argument against anything other than EU maximization (note that consistent loss-aversion may arise from diminishing marginal utility of money; loss-aversion only is interesting when directionally inconsistent) in economics involves Dutch-booking: the ability to set people up as money pumps and extract money from them by repeatedly offering subjectively preferred choices that violate transitivity. Essentially, EU maximization might be something we want to have because it induces consistency in decision-making.
For instance, imagine a preference ordering like the one in Nick_Tarleton’s adjacent comment, where +10 is different from +20-10. Let us say that +9=+20-10 (without loss of generality; just pick a number on the left side).
Then I can offer you +9 in exchange for +20-10 repeatedly, and you’ll prefer it every time, but you ultimately lose money.
The reason that rational risk aversion (which is to say, diminishing marginal utility of money) is not a money pump is that you have to reduce risk every time you extract some expected cash, and that cannot happen forever.
Ultimately, then, prospect theory and related work are useful in understanding human decision-making but not in improving it.
VNM utility is a necessary consequence of its axioms but doesn’t entail a unique utility function; as such, the ability to prevent Dutch Books is derived more from VNM’s assumption of a fixed total ordering of outcomes than anything.
Differing utilities for loss vs. gain introduce an apparently absurd degree of path dependence, in which, say, gaining $10 is perceived differently from gaining $20 and immediately thereafter losing $10. Loss vs. gain asymmetry isn’t in conflict with expected utility maximization (though nonlinear probability weighing is), but it is inconsistent with stronger intuitions about what we should be doing.
It would really be good if I knew a bit more about the different descision theories at this point.
“Different decision theories” is usually used to mean, e.g., causal decision theory vs. evidential decision theory vs. whatever it is Eliezer has developed. Which of these you use is (AFAIK) orthogonal to what preferences you have, so I assume that doesn’t answer your real question. Any reference on different types of utilitarianism might be a little more like what you’re looking for, but I can’t think of anyone who’s catalogued different proposed selfish utility functions.
Differing utilities for loss vs. gain introduce an apparently absurd degree of path dependence, in which, say, gaining $10 is perceived differently from gaining $20 and immediately thereafter losing $10.
Yes—the example I’ve seen is that a loss-averse agent may evaluate a sequence of say ten coinflips with -$15/+$20 payoffs positively at the same time as evaluating each individual such coinflip negatively.
One thing that came to mind just this morning: Why is expected utility maximization the most rational thing to do? As I understand it (and Im a CS, not Econ. major), prospect theory and the utility function weighing used in it are usually accepted as how most “irrational” people make their descisions. But this might not be because they are irrational but rather because our utility functions do actually behave that way in which case we should abandon EU and just try to maximize well being with all the quirks PT introduces (such as loss being more costly than gain and so on)...
Or is this how most people here already do things? Any and all feedback on this idea would be really apreciated (especially links to relevant discussion of this idea as I am sure Im not the first to come up with it).
Sorry. I thought about things a little and realized that a few things about prospect theory definately need to be scrapped as bad ideas.. The probability weighing for instance. But other quirks (such as loss aversion or having different utilities for loss vs gain) might be useful to retain…
It would really be good if I knew a bit more about the different descision theories at this point. Does anyone have any good references from where one would get an overview and good references?
The standard argument against anything other than EU maximization (note that consistent loss-aversion may arise from diminishing marginal utility of money; loss-aversion only is interesting when directionally inconsistent) in economics involves Dutch-booking: the ability to set people up as money pumps and extract money from them by repeatedly offering subjectively preferred choices that violate transitivity. Essentially, EU maximization might be something we want to have because it induces consistency in decision-making.
For instance, imagine a preference ordering like the one in Nick_Tarleton’s adjacent comment, where +10 is different from +20-10. Let us say that +9=+20-10 (without loss of generality; just pick a number on the left side).
Then I can offer you +9 in exchange for +20-10 repeatedly, and you’ll prefer it every time, but you ultimately lose money.
The reason that rational risk aversion (which is to say, diminishing marginal utility of money) is not a money pump is that you have to reduce risk every time you extract some expected cash, and that cannot happen forever.
Ultimately, then, prospect theory and related work are useful in understanding human decision-making but not in improving it.
Question—is there a uniqueness proof of VNM optimality in this regard?
VNM utility is a necessary consequence of its axioms but doesn’t entail a unique utility function; as such, the ability to prevent Dutch Books is derived more from VNM’s assumption of a fixed total ordering of outcomes than anything.
Differing utilities for loss vs. gain introduce an apparently absurd degree of path dependence, in which, say, gaining $10 is perceived differently from gaining $20 and immediately thereafter losing $10. Loss vs. gain asymmetry isn’t in conflict with expected utility maximization (though nonlinear probability weighing is), but it is inconsistent with stronger intuitions about what we should be doing.
“Different decision theories” is usually used to mean, e.g., causal decision theory vs. evidential decision theory vs. whatever it is Eliezer has developed. Which of these you use is (AFAIK) orthogonal to what preferences you have, so I assume that doesn’t answer your real question. Any reference on different types of utilitarianism might be a little more like what you’re looking for, but I can’t think of anyone who’s catalogued different proposed selfish utility functions.
Yes—the example I’ve seen is that a loss-averse agent may evaluate a sequence of say ten coinflips with -$15/+$20 payoffs positively at the same time as evaluating each individual such coinflip negatively.
Hmm:
I didn’t know that. Cool.