This can be extended to arbitrarily many agents. Moreso, the valuable insight here is that cooperation is achieved when the evidence that the group cooperates exceeds each and every member’s individual threshold for cooperation.A formalism of the intuitive strategy ‘I will only cooperate if there are no defectors’ (or perhaps ‘we will only cooperate if there are no defectors’).
You should include the highlighted insight in your summary. Also, why does your setup not lead to inconsistencies when Abram Demski isn’t sure his setup does? Is it just that you don’t have ”⊢a→b, then ⊢p(┌a┐)≤p(┌b┐) ”?
We know that the self-referential probabilistic logic proposed in Christiano 2012 is consistent. So, if we can get probabilistic Payor in this logic, then as we are already operating within a consistent system this should be a legitimate result.
Yudhister’s treatment here does not satisfy me: the assumption he calls syntactic-probabilistic correspondence is false. For example, in Paul’s probability distributions, the self-referential sentence L: P(L)<1 must be assigned probability 1, but is not true and not provable.
You should include the highlighted insight in your summary. Also, why does your setup not lead to inconsistencies when Abram Demski isn’t sure his setup does? Is it just that you don’t have ”⊢a→b, then ⊢p(┌a┐)≤p(┌b┐) ”?
We know that the self-referential probabilistic logic proposed in Christiano 2012 is consistent. So, if we can get probabilistic Payor in this logic, then as we are already operating within a consistent system this should be a legitimate result.
Will respond more in depth later!
Yudhister’s treatment here does not satisfy me: the assumption he calls syntactic-probabilistic correspondence is false. For example, in Paul’s probability distributions, the self-referential sentence L: P(L)<1 must be assigned probability 1, but is not true and not provable.