Hi, and welcome to Less Wrong!
It's great to see you trying to improve your decision making process, and being prepared to put your work in front of the public!
Here's a few thoughts on how to improve what you wrote:
Firstly, a terminology note. A theorem usually refers to a statement about the world that is either true or false, like "1+1=2" or "humans have 4 legs". What you have is not a theorem but a technique to improve decision making.
Secondly, you present a framework with some seemingly arbitrary calculations. Why is it (a*b+c)/(d+e), and not (a+b*c/d*e), or most simply of all a+b+c-d-e? To make your post convincing, try to explain what you're aiming to achieve, and why you made the decisions you did.
Thirdly, you give an example where it sounds like buying a Porsche 911 is a great idea, but for most people it really isn't - they're expensive and not all that practical. Is that a failure in the framework, or are you making some implicit assumptions about the status of the person whose making the decision? Maybe give some examples where intuitively someone might make the wrong decision, but this framework stops them, or the framework is useful for comparing two different options.
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.
Hello all!
I'm Jaivardhan Nawani, a 12-year-old enthusiast on rationality and how using it can improve our day-to-day lives.
Recently, I discovered this forum from a few friends who introduced me to many useful principles, and I thought to come up with an idea to make rationality easier to implement for first-timers.
So here's a basic theorem that I made upon this concept. I've come to LessWrong looking for feedback on it. And that's mostly it.
Here's the link to my theorem: https://docs.google.com/document/d/1Y2jvSR6RNFp_l-D-wX-KjHDrNUyhfdcM/edit?usp=sharing&ouid=100577114717816710937&rtpof=true&sd=true
Have a good day and with regards;
Jaivardhan Nawani.