I think this would be easier to explain with a two-sector model: ie, just H and F. Also, would it be easier to just work with algebra? Ie, H=[−a,b]×[−c,d].
Assuming a budget of 6 units
How does this fit with H+4F+5W? That’s 10 units, no?
I will assume, for simplicity, constant marginal cost-effectiveness across each domain/effect/worldview
It’s worth emphasizing that this assumption rules out the diminishing returns case for diversifying; this is a feature, since we want to isolate the uncertainty-case for diversifying.
I think this would be easier to explain with a two-sector model
I think it would get part of it across slightly more easily, although I don’t think the burden is large. I think a 2-sector model might give the false impression that you should try to pair interventions so that each makes up for the negatives of the other, whereas with a good enough example for 3, people might more intuitively grasp that you have far more flexibility.
Also, would it be easier to just work with algebra? Ie, H=[−a,b]×[−c,d].
I’d have to write down a bunch of inequalities to get a portfolio that’s better than N and ensure that one even exists, which I think would be much harder to follow (and do, for me). I expect people would get that the general problem is a system of linear inequalities, although it’s not central to the point I’m making.
How does this fit with H+4F+5W? That’s 10 units, no?
Ha. Thanks for pointing this out! I’ll fix this.
It’s worth emphasizing that this assumption rules out the diminishing returns case for diversifying; this is a feature, since we want to isolate the uncertainty-case for diversifying.
Ya, this is a good point. I’ll mention this in the text.
I think the general case (with the independence and constant marginal cost-effectiveness assumptions) will be harder to follow for some readers (and not easier to follow for anyone), much more work for me (I’m not sure how I would approach it yet), and not general enough to be very useful. Even more generally, it’s a multi-objective linear program, which we would solve algorithmically, not symbolically for a closed form solution.
I think this would be easier to explain with a two-sector model: ie, just H and F. Also, would it be easier to just work with algebra? Ie, H=[−a,b]×[−c,d].
How does this fit with H+4F+5W? That’s 10 units, no?
It’s worth emphasizing that this assumption rules out the diminishing returns case for diversifying; this is a feature, since we want to isolate the uncertainty-case for diversifying.
I think it would get part of it across slightly more easily, although I don’t think the burden is large. I think a 2-sector model might give the false impression that you should try to pair interventions so that each makes up for the negatives of the other, whereas with a good enough example for 3, people might more intuitively grasp that you have far more flexibility.
I’d have to write down a bunch of inequalities to get a portfolio that’s better than N and ensure that one even exists, which I think would be much harder to follow (and do, for me). I expect people would get that the general problem is a system of linear inequalities, although it’s not central to the point I’m making.
Ha. Thanks for pointing this out! I’ll fix this.
Ya, this is a good point. I’ll mention this in the text.
Re algebra, are you defending the numbers you gave as reasonable? Otherwise, if we’re just making up numbers, might as well do the general case.
I think the general case (with the independence and constant marginal cost-effectiveness assumptions) will be harder to follow for some readers (and not easier to follow for anyone), much more work for me (I’m not sure how I would approach it yet), and not general enough to be very useful. Even more generally, it’s a multi-objective linear program, which we would solve algorithmically, not symbolically for a closed form solution.