The power of information?

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.

Right, I understand why you want to make it a function. But as I see it your practical options are, 1) make a gross generalization from insufficient data that might have no relation to the function of information to power in the future and hope that you get close enough to reality that your model has at least some accuracy in its predictions OR 2) come up with 4-5 plausible but as-different-as-possible functions relating information to power and model with each of them. The result 4-5 times more predictions to sort through and instead of conclusions like "Starting conditions x,y,z, lead to a singleton" you'll get conclusions like "Starting conditions x,y,z, given assumptions a,b,c about the relation of information to power, lead to a singleton." The second option is harder and less conclusive. But it is also less wrong.

One more thing about the offense/defense distinction. One implication of the theory is that technological advancement can actually undermine an agents position in a multi-polar system. If Agent A develops an offensive weapon that guarantees victory if Agent A strikes first then other agents are basically forced to attack preemptively and likely gang up on Agent A. Given this particular input of more information, the function of information to power seems to output less power.

So, you have a simulator in which you implement its control system? This sounds elaborate. I'd like to hear more about it.

A (thermal, say) random number generator is easy to build and a good source of both Shannon and algorithmic (Kolmogorov) information. Having lots of information in these senses is not helpful for winning battles.

probably a much-less-than-linear increase in the number of types of genes known

I should clarify: We still have an exponential increase in the number of protein families known; but a less-than-linear increase in the number of protein domains known. Proteins are composed of modules called "domains"; a protein contains from 1 to dozens of domains. Most "new" genes code for proteins that recombine previously-known domains in different orders.

A digression: Almost all of the information content of an organism resides in the amino-acid sequence of these domains; and a lower bound of about 64% of domains (and 84% of those found in eukaryotes) evolved before eukaryotes (which include all multicellular organisms) split from prokaryotes about 2 billion years ago. (One source: Michael Levitt, PNAS July 7 2009, "Nature of the protein universe".) So it's accurate to say that most of evolution occurred in the first billion years; the development of more-complex organisms seems to have nearly frozen evolution of the basic components. We would likely be more complex today if those ancient prokaryotes had been able to hold off evolving into eukaryotes for another billion years, so that they could develop more protein domains first. There's a lesson for aspiring singularians in there somewhere.

(Similarly, most evolution within eukaryotes seems to have occurred during a period of about 50 million years, just before the Cambrian explosion, half a billion years ago. Evolution has been slowing down in information-theoretic terms, while speeding up in terms of intelligence produced.)

I guess this depends on your view of the world. I would say that if you simply write a power function then that would indicate an arbitrary assumption to begin with, that has had to simplify a number of significant factors. Writing a power function might be simple, but I am not sure that it would be significant.

For example one view of the world would be at the surface layer, where you see the end result of a combination of small events. This is what I think you are doing with your power function, although I may be misunderstanding. Another view says that you will not worry about the surface layer, and will instead come up with a number of simple rules (some based on probabilities) for the various actions & interactions that can take place. The execution of the rules by the Agents over multiple turns gives the emergent behavior, or what I called the surface layer. If the surface layer emerges that you would expect (guns are better than knives in a war for example), then this indicates the model is hopefully not grossly off. So instead of getting one big function right, you instead have a number of small rules that determine actions and probable outcomes.

You could even play some games with determining probable power functions after running a number of these, by representing them as genetic strings and then doing standard genetic algorithms to see what gives the closest match over all the outcomes for the different scenarios/times. I think this is more powerful than starting with the power function because your assumptions are at a lower level that is easier to get right, not to mention simpler. This is also why I mentioned Epsteins book, its a great example of using simple rules to get emergent behavior.