If your “ecosystem of recursively self-improving computer programs” is intended to model real-world polities, then perhaps the type of empirical study you have in mind would be useful. However, if it is intended to more broadly model conflicting (and cooperating) entities, perhaps a more abstract model would be appropriate.
The problem of developing a general conflict success function has been rather extensively studied by political scientists; one good introduction can be found in The Journal of Conflict Resolution, Vol. 44, No. 6 (Dec., 2000), pp. 773-792, an article entitled “The Macrotechnology of Conflict,” by Jack Hirshleifer. I’ve found his framework useful in my own work.
I don’t think I can get any more abstract than the model is now. The model doesn’t talk about military conflicts. I want to use historical data to parameterize my model. I’m hoping that there is a broad pattern relating information to power that is fundamental.
The article suggests two major formats for conflict success functions that might be relevant. Notationally, let Ix be the information held by entity x, and assume that information is the only relevant determinant of power.
One possibility is to have P(x wins) = (Ix)^s / ((Ix)^s + (Iy)^s), the “ratio form,” where y is the opposing entity and s is a parameter. You could run your model for a variety of s-values, which may be easier than trying to determine the effect of information on real conflicts. Alternatively, you could estimate s from the total resource input into real conflicts, rather than restricting it to information, with all the questions about intelligence and strategy that are endogenous to that concept.
The other major conflict success function is P(x wins) = exp(s.Ix) / (exp(s.Ix)+exp(s.Iy)), the “difference” form (periods indicate multiplication). The mechanics are the same, with the estimation of s the primary challenge.
For what it’s worth, the US military has long operated on the belief that they need a 3:1 force advantage in the relevant theater to produce victory (prior, one imagines, to the advent of guerrilla warfare). Let us say that P(x wins | Ix = Iy * 3) = .9. Then s = 2.
Seems like a decent starting point to say that the probability of each side winning is equal to the ratio of the square of its power/resources/information/whatever to the sum of the squares.
That’s great—adding the ^s gives some flexibility to the function. I was worried because the form I specified (s=1) might not fit the data.
I’m dubious of the difference form. If you used it on “raw information”, it could predict the same relative advantage for a 2009 WE opponent over a 2005 WE opponent, as for (say) a 1600 WE opponent over a 1000 WE opponent, because the difference in information is a small percent of the information either side has in the first case, but a large percentage in the second case.
If your “ecosystem of recursively self-improving computer programs” is intended to model real-world polities, then perhaps the type of empirical study you have in mind would be useful. However, if it is intended to more broadly model conflicting (and cooperating) entities, perhaps a more abstract model would be appropriate.
The problem of developing a general conflict success function has been rather extensively studied by political scientists; one good introduction can be found in The Journal of Conflict Resolution, Vol. 44, No. 6 (Dec., 2000), pp. 773-792, an article entitled “The Macrotechnology of Conflict,” by Jack Hirshleifer. I’ve found his framework useful in my own work.
I don’t think I can get any more abstract than the model is now. The model doesn’t talk about military conflicts. I want to use historical data to parameterize my model. I’m hoping that there is a broad pattern relating information to power that is fundamental.
The article suggests two major formats for conflict success functions that might be relevant. Notationally, let Ix be the information held by entity x, and assume that information is the only relevant determinant of power.
One possibility is to have P(x wins) = (Ix)^s / ((Ix)^s + (Iy)^s), the “ratio form,” where y is the opposing entity and s is a parameter. You could run your model for a variety of s-values, which may be easier than trying to determine the effect of information on real conflicts. Alternatively, you could estimate s from the total resource input into real conflicts, rather than restricting it to information, with all the questions about intelligence and strategy that are endogenous to that concept.
The other major conflict success function is P(x wins) = exp(s.Ix) / (exp(s.Ix)+exp(s.Iy)), the “difference” form (periods indicate multiplication). The mechanics are the same, with the estimation of s the primary challenge.
For what it’s worth, the US military has long operated on the belief that they need a 3:1 force advantage in the relevant theater to produce victory (prior, one imagines, to the advent of guerrilla warfare). Let us say that P(x wins | Ix = Iy * 3) = .9. Then s = 2.
Seems like a decent starting point to say that the probability of each side winning is equal to the ratio of the square of its power/resources/information/whatever to the sum of the squares.
That’s great—adding the ^s gives some flexibility to the function. I was worried because the form I specified (s=1) might not fit the data.
I’m dubious of the difference form. If you used it on “raw information”, it could predict the same relative advantage for a 2009 WE opponent over a 2005 WE opponent, as for (say) a 1600 WE opponent over a 1000 WE opponent, because the difference in information is a small percent of the information either side has in the first case, but a large percentage in the second case.
Got the article; hope to read it soon.