A model of population ethics: we represent all possible lives as points in a bounded metric space with a probability measure, call this space L. First we define the "capacity" C of a set of lives E by the integral on L of x -> 1-inf{d(x,y) | y in E}/diam(L). What this means is that to maximize the capacity of a set we need to minimize the average distance from a random point in L to its closest point in the set. Sometimes greater capacity is given to a set with fewer points if it is more diverse. This is intuitive : for example it really seems like a larger part of that space is captured by the ~8.2 billion humans currently alive than by even infinitely many wireheads. Then let f be a bounded function associating to each person a real number representing how good their life is. To give value to a set of lives E we take the integral from 0 to +inf of x -> C({y in E | f(y) > x}) - C({y in E | | f(y) < -x}). Some properties this model has : Adding a good (bad) life that does not already have arbitrarily close approximations adds (removes) value. Adding lives of value zero does not add or remove any value. A set of lives of value <=epsilon has value <=epsilon, so there is no repugnant conclusion. All of this is true even if the set of lives is infinite.
A model of population ethics: we represent all possible lives as points in a bounded metric space with a probability measure, call this space L. First we define the "capacity" C of a set of lives E by the integral on L of x -> 1-inf{d(x,y) | y in E}/diam(L). What this means is that to maximize the capacity of a set we need to minimize the average distance from a random point in L to its closest point in the set. Sometimes greater capacity is given to a set with fewer points if it is more diverse. This is intuitive : for example it really seems like a larger part of that space is captured by the ~8.2 billion humans currently alive than by even infinitely many wireheads.
Then let f be a bounded function associating to each person a real number representing how good their life is. To give value to a set of lives E we take the integral from 0 to +inf of x -> C({y in E | f(y) > x}) - C({y in E | | f(y) < -x}).
Some properties this model has : Adding a good (bad) life that does not already have arbitrarily close approximations adds (removes) value. Adding lives of value zero does not add or remove any value. A set of lives of value <=epsilon has value <=epsilon, so there is no repugnant conclusion. All of this is true even if the set of lives is infinite.