Hello Internet!
This one's not book related at all, just based on something that's got my mind in a twist, so I felt compelled to write it out here.
In the run up to a twenty-four hour ethics and values exam, I had a crack at reading the fourth section of Derek Parfit's "Reasons and Persons." (I also read through Section 3 about identity for my Knowledge and Reality Exam, but that's a discussion for another day).
Needless to say I was utterly engrossed, and my mind was totally in a twist about what we can consider to be a better world when thinking about total quality of life versus average quality of life. If you want the following stuff to make sense, go read that and come back - in fact I'd thoroughly recommend reading the book anyway, it's fascinating and very well written.
Anyway, while writing the essay about Parfit in the exam, I had an idea for a potential mathematical expression that I personally would be comfortable using when referring to what makes one potential world better than another (incidentally I had a mathematics exam this morning so that might have played a part). I'd be curious to hear any philosophers' thoughts on the matter:
As you can see, this is similar to Parfit's idea of a "valueless level," which suggests that below a certain quality of life the total quantity of quality of life would have no effect (avoiding some of the repugnant conclusion), but this would be a more gradual approach. It occurred to me as I was writing this that you might want to adjust the effects that Q and Q/n each have on G, and so I added constants A and B. These constants don't necessarily mean or represent anything on their own, but would depend on how much you want Q and Q/n to affect G overall.
I realise there is contention (including from Parfit) over the idea of levels below which Q would have less effect as these would be tricky to place, but I'd suggest it's just as arbitrary of measuring quality of life. And yes, this would still entail a reduced form of the Repugnant Conclusion and the Absurd Conclusion, but for me they're so reduced that they don't feel quite so Repugnant or Absurd that they turn my stomach or keep me up at night. Perhaps the Repugnant or Absurd Conclusions would still look about the same higher values of Q, but you could set the constants A and B so that this value of Q would have to be unthinkably, unfeasibly high. Gotta compromise somewhere!
I also realise people might question my choice of using e here, as opposed to some other way of using the average quality of life per person to enhance or diminish the goodness caused by the total quantity of life. I'm sure other variations of this equation might exist based on that general idea, and I encourage them. Using an exponential just felt right for me, especially given it would help significantly reduce the overall goodness for huge values of Q and low values of Q/n.
If people can decide on how to measure quality of life and what the baseline x would be, then perhaps they could use this equation or a variation of it as a reference for deciding between policies that affect future generations
If you do philosophy or maths, let me know what you think of this. I'm sure a variation of this already exists somewhere out there in the world so let me know about that if you find it too :)