If all we are doing is binary comparisons between a set of items, it seems to me that it would be sufficient to represent relative values as a binary—i.e., is item1 better, or item2? Or perhaps you want a ternary function—you could also say they’re equal.
Using a ratio instead of a binary indicator for relative values suggests that you want to use the function to extrapolate. I’m not sure that this approach helps much with that, though. For example,
costOfp001DeathChance = ss(10 to 10k) // Cost of a 0.001% chance of death, in dollars chanceOfDeath001 = ss(-1 * costOfp001DeathChance * dollar1) // Cost of a 0.001% chance of death
does not tell me how many $ a 0.01% chance of death is worth; rather, it tells me how many times better it is than $1. Without a function f(outcome in $)->value, this doesn’t enable a comparison to any other amount of dollars. We can, of course, add such a function to our estimation, but if we do then I think the function is doing much more than the value ratios to enable us to extrapolate our value judgements. Unless we have f(outcome2)=f(outcome1)*outcome2/outcome1, I don’t see how we can use ratios at all, but if we do have it then we’re back to single values.
The alternative approach seems to me to be to treat it as a machine learning problem—given binary value judgements, build a binary classifier that tells you whether item1 or item2 is better. I expect that if we had value ratios instead of binary comparisons we might do a bit better here, but they might also be harder to elicit.
If all we are doing is binary comparisons between a set of items, it seems to me that it would be sufficient to represent relative values as a binary—i.e., is item1 better, or item2?
Why do you think this is all we’re doing? We often want to know how much better some items are than others—relative values estimate this information.
You can think of relative values a lot like “advanced and scalable expected value calculations”. There are many reasons to actually know the expected value of something. If you want to do extrapolation (“The EV of one person going blind is ~0.3 QALYs/year, so the EV of 20 people going blind is probably...”), it’s often not too hard to ballpark it.
Related, businesses often use dollar approximations of the costs of very different things. This is basically a set of estimates of the value of the cost.
If all we are doing is binary comparisons between a set of items, it seems to me that it would be sufficient to represent relative values as a binary—i.e., is item1 better, or item2? Or perhaps you want a ternary function—you could also say they’re equal.
Using a ratio instead of a binary indicator for relative values suggests that you want to use the function to extrapolate. I’m not sure that this approach helps much with that, though. For example,
does not tell me how many $ a 0.01% chance of death is worth; rather, it tells me how many times better it is than $1. Without a function f(outcome in $)->value, this doesn’t enable a comparison to any other amount of dollars. We can, of course, add such a function to our estimation, but if we do then I think the function is doing much more than the value ratios to enable us to extrapolate our value judgements. Unless we have f(outcome2)=f(outcome1)*outcome2/outcome1, I don’t see how we can use ratios at all, but if we do have it then we’re back to single values.
The alternative approach seems to me to be to treat it as a machine learning problem—given binary value judgements, build a binary classifier that tells you whether item1 or item2 is better. I expect that if we had value ratios instead of binary comparisons we might do a bit better here, but they might also be harder to elicit.
Why do you think this is all we’re doing? We often want to know how much better some items are than others—relative values estimate this information.
You can think of relative values a lot like “advanced and scalable expected value calculations”. There are many reasons to actually know the expected value of something. If you want to do extrapolation (“The EV of one person going blind is ~0.3 QALYs/year, so the EV of 20 people going blind is probably...”), it’s often not too hard to ballpark it.
Related, businesses often use dollar approximations of the costs of very different things. This is basically a set of estimates of the value of the cost.
I don’t think it’s all you are doing, that’s why I wrote the rest of my comment (sorry to be flippant).
The point of bringing up binary comparisons is that a table of binary comparisons is a more general representation than a single utility function.