The problem with this is that the setup suddenly becomes a whole lot handwavy. Equality is mathematically “hard”, correlation is not, it’s a statistical “soft”. Which correlation (Pearson’s? why this one?), how much is enough (is 5% sufficient? 50%? does it depend on the amount of noise present?), etc.
For example you say:
Everyone can expect everyone else in the group to follow the same logic, and get the same conclusion. It’s not possible to game the system
but if equality is replaced with correlation, this doesn’t hold.
“agents with enough decision-theoretic sophistication will converge on this outcome”
Regardless of their values?
“there should be more of our kind” is wishful thinking
I disagree. Human history is full of “there should be more of our kind and we will make it happen”. The typical route is killing competitors and taking their resources. There are also cultural factors (e.g. the “protect the women” virtue), religious/ideological influences (see the population growth in Roman Catholic countries until recently), etc.
The problem with this is that the setup suddenly becomes a whole lot handwavy. Equality is mathematically “hard”, correlation is not, it’s a statistical “soft”. Which correlation (Pearson’s? why this one?), how much is enough (is 5% sufficient? 50%? does it depend on the amount of noise present?), etc.
For example you say:
but if equality is replaced with correlation, this doesn’t hold.
Regardless of their values?
I disagree. Human history is full of “there should be more of our kind and we will make it happen”. The typical route is killing competitors and taking their resources. There are also cultural factors (e.g. the “protect the women” virtue), religious/ideological influences (see the population growth in Roman Catholic countries until recently), etc.
And I still cannot follow your train of logic.