Separating fully and boundedly rational actors is very helpful.
Would a fully rational actor need to have a universal prior? Wouldn’t they need to have justified one choice of a universal prior over all others? It seems like there might be a hard first step here that could prevent them from committing to a single joint probability distribution. Maybe you’d want a prior over universal priors, but then where would that come from?
Maybe this is the only place where multiple distributions can creep in for a fully rational actor, and all other probabilities would be based on your universal prior and observations.
I think it’s a bad (but frequently made, at least implicitly) assumption that boundedly rational actors should mimic the behaviour of fully rational actors in cases where they can work out what that is
For a particularly vivid example of (something at least strongly analogous to) this assumption breaking, see the theorem in the optimal taxation literature that the top marginal tax rate should be zero
Do you mean that they will fail to approximate the fully rational behaviour and sometimes be more biased when they try to approximate it? My instinct in response to the optimal top marginal tax rate being zero is that their model is probably missing very important features (which might be hard to measure or quantify).
Do you mean that they will fail to approximate the fully rational behaviour and sometimes be more biased when they try to approximate it?
Roughly yes. They might even exactly match the fully rational behaviour on some dimension under consideration, but in so doing be a worse approximation overall to full rationality.
I think a proper study of full rationality and boundedly rational actors would look at limits of behaviour as you impose weaker and weaker computational constraints. I think that it could be really useful to understand which properties of the fully rational actor are converged upon in a reasonable time and basically hold for powerful-enough boundedly rational actors, and which e.g. only hold in the very limit when the actors comprehension ability is large compared to the world.
My instinct in response to the optimal top marginal tax rate being zero is that their model is probably missing very important features (which might be hard to measure or quantify).
Yes, I think it is missing imperfect information and bounded rationality. (TBC, I don’t think that anyone working in optimal tax theory thinks that top marginal rates should actually be zero.) I think the theorem is pretty clear that in the perfect information case with all actors rational the top rate should be zero (basically needs an additional assumption about smoothness of preferences, but that’s pretty reasonable). And although this sounds surprising, it is just correct!
To set up an example that’s about bounded rationality in particular, suppose:
The taxpayers are fully rational
You, the tax-setter, have a lot of giant spreadsheets which express all of the taxpayer preferences for different levels of work/​consumption, marginal value of public funds etc. (so theoretically full information)
You now get to set all the tax rates (which could be quite complicated)
If you were fully rational and could calculate everything out, you would be able to set optimal tax policy
But calculating everything out is too much of a mess, and you can’t do it
You know for certain that the optimal solution would have a marginal top rate of zero somewhere
But as you can’t work out where that is, and as having a marginal top rate of zero is not that important, you’ll probably decide on a set of tax rates without a marginal top rate of zero, even though you know that that is certainly wrong
Would a fully rational actor need to have a universal prior? Wouldn’t they need to have justified one choice of a universal prior over all others? It seems like there might be a hard first step here that could prevent them from committing to a single joint probability distribution. Maybe you’d want a prior over universal priors, but then where would that come from?
I’d usually think of being fully rational as giving constraints after your choice of prior; there are questions about whether some priors are better than others, but you can treat that separately.
Separating fully and boundedly rational actors is very helpful.
Would a fully rational actor need to have a universal prior? Wouldn’t they need to have justified one choice of a universal prior over all others? It seems like there might be a hard first step here that could prevent them from committing to a single joint probability distribution. Maybe you’d want a prior over universal priors, but then where would that come from?
Maybe this is the only place where multiple distributions can creep in for a fully rational actor, and all other probabilities would be based on your universal prior and observations.
Do you mean that they will fail to approximate the fully rational behaviour and sometimes be more biased when they try to approximate it? My instinct in response to the optimal top marginal tax rate being zero is that their model is probably missing very important features (which might be hard to measure or quantify).
Roughly yes. They might even exactly match the fully rational behaviour on some dimension under consideration, but in so doing be a worse approximation overall to full rationality.
I think a proper study of full rationality and boundedly rational actors would look at limits of behaviour as you impose weaker and weaker computational constraints. I think that it could be really useful to understand which properties of the fully rational actor are converged upon in a reasonable time and basically hold for powerful-enough boundedly rational actors, and which e.g. only hold in the very limit when the actors comprehension ability is large compared to the world.
Yes, I think it is missing imperfect information and bounded rationality. (TBC, I don’t think that anyone working in optimal tax theory thinks that top marginal rates should actually be zero.) I think the theorem is pretty clear that in the perfect information case with all actors rational the top rate should be zero (basically needs an additional assumption about smoothness of preferences, but that’s pretty reasonable). And although this sounds surprising, it is just correct!
To set up an example that’s about bounded rationality in particular, suppose:
The taxpayers are fully rational
You, the tax-setter, have a lot of giant spreadsheets which express all of the taxpayer preferences for different levels of work/​consumption, marginal value of public funds etc. (so theoretically full information)
You now get to set all the tax rates (which could be quite complicated)
If you were fully rational and could calculate everything out, you would be able to set optimal tax policy
But calculating everything out is too much of a mess, and you can’t do it
You know for certain that the optimal solution would have a marginal top rate of zero somewhere
But as you can’t work out where that is, and as having a marginal top rate of zero is not that important, you’ll probably decide on a set of tax rates without a marginal top rate of zero, even though you know that that is certainly wrong
I’d usually think of being fully rational as giving constraints after your choice of prior; there are questions about whether some priors are better than others, but you can treat that separately.