I think the point wasn’t having a unit norm, it was that impact wasn’t defined as directional, so we’d need to remove the dimensionality from a multidimensionally defined direction.
So to continue the nitpicking, I’d argue impact = || Magnitude * Direction ||, or better, ||Impact|| = Magnitude * Direction, so that we can talk about size of impact. And that makes my point in a different comment even clearer—because almost by assumption, the vast majority of those with large impact are pointed in net-negative directions, unless you think either a significant proportion of directions are positive, or that people are selecting for it very strongly, which seems not to be the case.
I think the point wasn’t having a unit norm, it was that impact wasn’t defined as directional, so we’d need to remove the dimensionality from a multidimensionally defined direction.
So to continue the nitpicking, I’d argue impact = || Magnitude * Direction ||, or better, ||Impact|| = Magnitude * Direction, so that we can talk about size of impact. And that makes my point in a different comment even clearer—because almost by assumption, the vast majority of those with large impact are pointed in net-negative directions, unless you think either a significant proportion of directions are positive, or that people are selecting for it very strongly, which seems not to be the case.