Is prospect theory still a thing? I distinctly remember reading that the main empirical result it's based on it's based on - loss aversion, didn't replicate except for large sums of money.
And for large sums of money, you don't need prospect theory to explain loss aversion. Plain old marginal utility will do.
Great question! One of the core results of this paper was to explain this discrepancy. Basically, we found a 'mixture of theories' - a hybrid of prospect theory and expected utility theory, where people essentially arbitrate between one of the two decision-making mechanisms depending on the complexity of the gamble.
> Curious that you can "mix" PT & EU functionals (with perceptron) but not the corresponding "decision-making mechanisms"..?
Great push. We actually can't make any mechanistic claims from the data/math in this paper. From an ML prediction standpoint, we're mixing a PT and EU theory together. But to what extent that is the actual cognitive process we have to remain agnostic about. That being said, a reason this arbitration between EU and PT is intriguing is because there's a lot of work about arbitration between dual process models in psychology (System 1 and 2; model-free and model-based; labor versus leisure; etc.)
Prospect theory is an analysis of how people make decisions in certain contexts that don't line up with utility maximization. That is, it studies a psychological phenomoneon. Think of a $1.99 price tag vs a $2.00 price tag. The difference looks much larger than it is. That's psychology.
It's unsurprising that the effects are seen most when the amounts are small. With large amounts, people think harder and are more likely to follow rational choice theory.
You can generalize theories of decision-making into broad functional forms and then apply gradient descent to find the best parameters for that functional form. For example, prospect theory is multiply a utility weighting function U(x) with a probability weighting function p(x). Kahneman and Tversky proposed one specific set of U(x) and p(x), but we can use autodiff to generate all.
Can you explain what a “differentiable” decision theory is? I understand, for instance, maximizing expected value (and taking a derivative to get a maximum), but I don’t understand how the concept of maximizing expected value could itself be made into a derivative.
Edit: Seems like a “differentiable theory” is just one that can be framed in terms of an optimization problem that can be solved by gradient descent. Is that right?
Is prospect theory still a thing? I distinctly remember reading that the main empirical result it's based on it's based on - loss aversion, didn't replicate except for large sums of money.
And for large sums of money, you don't need prospect theory to explain loss aversion. Plain old marginal utility will do.
Great question! One of the core results of this paper was to explain this discrepancy. Basically, we found a 'mixture of theories' - a hybrid of prospect theory and expected utility theory, where people essentially arbitrate between one of the two decision-making mechanisms depending on the complexity of the gamble.
Curious that you can "mix" PT & EU functionals (with perceptron) but not the corresponding "decision-making mechanisms"..?
(I might have missed an explicit description of these "decision-making mechanisms" in the paper)
>we find that the ... most complex class ... lies outside the simple classes
Another curious statenent
> Curious that you can "mix" PT & EU functionals (with perceptron) but not the corresponding "decision-making mechanisms"..?
Great push. We actually can't make any mechanistic claims from the data/math in this paper. From an ML prediction standpoint, we're mixing a PT and EU theory together. But to what extent that is the actual cognitive process we have to remain agnostic about. That being said, a reason this arbitration between EU and PT is intriguing is because there's a lot of work about arbitration between dual process models in psychology (System 1 and 2; model-free and model-based; labor versus leisure; etc.)
Prospect theory is an analysis of how people make decisions in certain contexts that don't line up with utility maximization. That is, it studies a psychological phenomoneon. Think of a $1.99 price tag vs a $2.00 price tag. The difference looks much larger than it is. That's psychology.
It's unsurprising that the effects are seen most when the amounts are small. With large amounts, people think harder and are more likely to follow rational choice theory.
I'm one of the co-authors of this article.
The TLDR of this paper:
You can generalize theories of decision-making into broad functional forms and then apply gradient descent to find the best parameters for that functional form. For example, prospect theory is multiply a utility weighting function U(x) with a probability weighting function p(x). Kahneman and Tversky proposed one specific set of U(x) and p(x), but we can use autodiff to generate all.
We can apply this method to any functional form.
Happy to answer any questions!
Can you explain what a “differentiable” decision theory is? I understand, for instance, maximizing expected value (and taking a derivative to get a maximum), but I don’t understand how the concept of maximizing expected value could itself be made into a derivative.
Edit: Seems like a “differentiable theory” is just one that can be framed in terms of an optimization problem that can be solved by gradient descent. Is that right?
(2021)