This is great. Your PUSA formula bears comparison with some of the other formulas for rational decision-making that have been proposed. And “pú sà” is how you say “buddha sattva” in Mandarin Chinese (pú for buddha, sà for sattva). Easy-to-remember equation, a good brand name—you already have everything you need to be a successful management consultant, at least. :-)
Regarding the actual formula… One of the basic checks is whether changing the inputs to the formula, causes the output (the “rationality score”) to also change in an appropriate way. For example, if variable “a” (evidence for the concept) goes up, you want the rationality score to go up. But if variable “d” (evidence against the concept) goes up, you want the rationality score to go down. As far as I can see, the PUSA rationality score changes appropriately, for all of your input variables.
As Yair implies in his comment, you could have achieved this outcome with a different way of combining your inputs. For example, summarizing the current formula as “Numerator divided by the Denominator”, if it had instead been “Numerator minus the Denominator”, it still would have passed the basic checks in the previous paragraph. The rationality score would still change in the right direction, when the inputs change. But the rate of change, the sensitivity of the rationality score to the various inputs, would be very different.
The technical literature on decision theory must contain arguments about which formulas are better, and why, and maybe one of Less Wrong’s professional decision theorists will comment on your formula. They may provide a mathematical argument for why it should be different in some way. That would be interesting to hear.
But I will say in advance, that another consideration is whether it’s practical in real life. In this regard, I think the formula works very well. The procedure for the calculation is simple, and yet takes into account a lot of relevant factors. (Maybe we need a formula for rating the quality of decision formulas...) The ultimate test will be if people use it, and actually find it useful.
I think (or rather: I hope) that no one takes the mathematical equations literally. But for the mathematically inclined, the intuition is the following:
“a+b” means substitutes; if you do more of one, it is okay to do less of the other; which implies that you should focus on the one that happens to be cheaper (e.g. in time and energy) at the moment
“a*b” means that both are necessary; if you do one without the other, you are just wasting time; which implies that you should probably focus on the smaller one, because there you can probably achieve a greater improvement measured in percents (diminishing returns; beginners learn quickly)
From the perspective of physics, “a+b” means that they are the same unit, for example a resource obtained one way, and the same resource obtained a different way; while “a*b” usually means different units, often something like “X” and “Y per unit of X”, for example how many resources you have, and how efficiently you can convert those resources to the result you want.
One aspect that I think is directionally correct is that a is (up to the other things) divided by d. Where a is the number of pieces of evidence that this is a good idea and d evidence that it is bad. This (when all else is neglected) feels right. 10 points for and 5 points against seems like it would be close to 100 points for and 50 points against, rather than 10 times less relevant.
This is great. Your PUSA formula bears comparison with some of the other formulas for rational decision-making that have been proposed. And “pú sà” is how you say “buddha sattva” in Mandarin Chinese (pú for buddha, sà for sattva). Easy-to-remember equation, a good brand name—you already have everything you need to be a successful management consultant, at least. :-)
Regarding the actual formula… One of the basic checks is whether changing the inputs to the formula, causes the output (the “rationality score”) to also change in an appropriate way. For example, if variable “a” (evidence for the concept) goes up, you want the rationality score to go up. But if variable “d” (evidence against the concept) goes up, you want the rationality score to go down. As far as I can see, the PUSA rationality score changes appropriately, for all of your input variables.
As Yair implies in his comment, you could have achieved this outcome with a different way of combining your inputs. For example, summarizing the current formula as “Numerator divided by the Denominator”, if it had instead been “Numerator minus the Denominator”, it still would have passed the basic checks in the previous paragraph. The rationality score would still change in the right direction, when the inputs change. But the rate of change, the sensitivity of the rationality score to the various inputs, would be very different.
The technical literature on decision theory must contain arguments about which formulas are better, and why, and maybe one of Less Wrong’s professional decision theorists will comment on your formula. They may provide a mathematical argument for why it should be different in some way. That would be interesting to hear.
But I will say in advance, that another consideration is whether it’s practical in real life. In this regard, I think the formula works very well. The procedure for the calculation is simple, and yet takes into account a lot of relevant factors. (Maybe we need a formula for rating the quality of decision formulas...) The ultimate test will be if people use it, and actually find it useful.
I think (or rather: I hope) that no one takes the mathematical equations literally. But for the mathematically inclined, the intuition is the following:
“a+b” means substitutes; if you do more of one, it is okay to do less of the other; which implies that you should focus on the one that happens to be cheaper (e.g. in time and energy) at the moment
“a*b” means that both are necessary; if you do one without the other, you are just wasting time; which implies that you should probably focus on the smaller one, because there you can probably achieve a greater improvement measured in percents (diminishing returns; beginners learn quickly)
From the perspective of physics, “a+b” means that they are the same unit, for example a resource obtained one way, and the same resource obtained a different way; while “a*b” usually means different units, often something like “X” and “Y per unit of X”, for example how many resources you have, and how efficiently you can convert those resources to the result you want.
One aspect that I think is directionally correct is that a is (up to the other things) divided by d. Where a is the number of pieces of evidence that this is a good idea and d evidence that it is bad. This (when all else is neglected) feels right. 10 points for and 5 points against seems like it would be close to 100 points for and 50 points against, rather than 10 times less relevant.