How do philosophers actually become the human rulers in the sense of Plato? Well, here is my version based on an extremely simple equation/formula. It involves PI Game Theory.
First of all, anybody who has ever looked into Game Theory is likely to abandon all hope. It tends to be a mess. Even translating it into simple English may be impossible. It talks about minimums of maximums of minimums of maximums of....and so on.
Welcome to the Probable Causation/Influence (PI) Game Theory Simple Equation/Formula. Recall that:
1) P(A-->B) = 1 + P(AB) - P(A)
2) P ' (A-->B) = 1 + P(B) - P(A), where P(B) < = P(A).
We will restrict ourselves to (2) here.
How do you make P ' (A-->B) maximum? Well, probability is always on a scale from 0 to 1 inclusive. So to make P ' (A-->B) maximum, it has to be 1. So we get:
3) P ' (A-->B) = 1 + P(B) - P(A) = 1
The equation 1 + P(B) - P(A) = 1 is the same as P(A) = P(B):
4) P(A) = P(B)
This says: the Probability of the Cause is (equal to) the Probability of the Effect. Formally:
5) The Probability of the Cause is (equal to) the Probability of the Effect for the "winning Strategy" in PI Game Theory, no matter what A and B are as long as they are respectively Cause and Effect.
There is a simple translation of (5) into simple English:
6) The Winner of any PI Game is the "Perfect Tracker" - the person or group (or whaever) who "tracks" his opponent perfectly, in the sense of matching his probability to the probability of the opponent.
Here are some examples.
7) The "Perfect Spy": someone whose behavior and attitudes and thinking and so on are almost totally indistinguishable from the "Enemy's".
8) The "Perfect Teacher": a teacher who looks like, talks like, thinks like, and so on, the student(s). This is obviously impossible unless the students resemble each other or one another enormously, and it is rather useless if they are all Dunces, although a teacher who is also a Dunce of the same type will at least be the winner among Dunces.
9) The "Perfect Philosopher": someone like John Le Carre's Oxford Don/Professor, at least in philosophy, except that in this case he almost totally matches the leading political party's best M.P. (although under some conditions he might condescend to match an alternative party's best M.P.). Since it might take millions of years to get a philosophical M.P., various ruses or gambits may be required to transform the M.P. in the sense of "One-Upmanship" perhaps. He might be persuaded to visit Oxford often for example for a romantic interest :>) who absolutely will not tolerate romance without philosophy.
10) The "Perfect Missile": for the more Violence-Oriented philosophers (I jest, I think), it is a fact that present mathematical Kalmer Filter-Predictor programs do guide missiles to perfectly or almost perfectly track targets. They are also usable for moon flights, for those slightly more restrained in their enthusiasm :>) Look up Kalmer Filter, for example, on the internet.
Osher Doctorow
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I meant "Kalman Filter," not "Kalmer Filter," in my last sentence. Being tongue-tied may have led me subconsciously to another example: "The perfect calmer (person who calms others or himself/herself)."
ReplyDeleteOsher Doctorow
I enjoyed the game. Especially the bit about Plato, and of course LeCarre.
ReplyDeleteYes, I don't know what Plato was thinking with the philosopher king. I have had MANY teachers who were philosophers in my life, but NONE of them ever took THAT theory seriously! I suppose the students (I included) would have laughed at him!
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LeCarre's Oxford philosophy don is a good one, too. We should explore him at some length. P. D. James, another good writer, I once asked: "Why haven't you set a novel in Oxford?". "Why, Dorothy Sayers did it for me." And right she was.
Perfect Spy and Perfect Teachers are good, too.
My introduction to game-theory vis a vis Grice came via Hintikka of course. Hintikka contributed to the Grandy/Warner book on Grice with a chapter, pretty Finnish in parts (I love Hintikka) on how game theory is ok and solves all the problems Grice never thought could be solved (I talk in jest, I think). Then I read another book on that, by Lauri Carlson, called "Dialogue Games" and imagine my surprise when I read his affiliation and it's Finland. Kant they do anything else but Play, these Finns? (I love them).
Interesting, but many Game Theory types tend to overlook that most games involve uncertainty, and thus relate to likelihood which cannot easily be calculated. So, games that involve uncertainty don't really solve much (this might relate to Rawls' Theory of Justice, and "rational choice"--Rawls grants that the original position involves an element of chance...). --in the case of gambling, usually you will lose playing just house odds (one reason for card counting)--what's more, the longer you play--say blackjack-- the more likely you are to lose. And the exact probabilities of card games are unknown, certainly by ordinary citizens (ie you don't know what's left in the deck).
ReplyDeleteSkilled games are different, but I don't think probability even enters the usual calculation. Even great chess players cannot easily compute all possible positions beyond 4-5 moves in advance. While I think game theory might apply to some political situations (or perhaps philosophical), it's not very workable. And for that matter, not everyone--people, or nations-- agrees to the same rules (that might apply to Rawls' AToJ as well--there are things to admire about AToJ, but ...the element of chance or uncertainty--or applicability for that matter--was not really hammered out)
J -
ReplyDeleteI find it useful to look through the other end of the game theory telescope, to analogize from it rather than abstract to it. Hobbes's Leviathan coordinates a massively multiplayer iterated Prisoners' Dilemma. Indeed, civilization and all of its coercions, moral, social, and legal, are about coordinating plus sum games where defection would be the best uncoordinated strategy. There's plenty of uncertainty in any given policy prescription, but one ought at least to ask how a policy would be most likely to affect the "state of play" of the polity's ongoing games.
OK, in the sense of Hobbes' model of a social contract, I agree somewhat (and Rawls slightly in that traditional I suppose, tho' reaches different conclusions)--humans would presumably choose certain policies, even peace--tho' not all would. I don't see how that relates to the post that much. And keeping in mind economic, and shall we say Malthusian factors, I'm not sure even Hobbes' practical advice holds (oil reserves running out, or famine, drought, religious zealots etc tend to ruin the game). The game at some point might be more like ..Road Warrior than Clue (or whatever card games Oxbridge dons play..Whist? Pea-knuckle? )
ReplyDeleteLawrence J. Kramer and J, thank you for your interesting replies. Of course, I prefer Kramer's reply because it is pro-game-theory, although of course, there is room for many different opinions in game theory - for example, I much prefer Probable Causation/Influence Game Theory to the standard Mainstream type now in use commonly by most researchers.
ReplyDeletePerhaps I can win J over by figuring out how to study Philosophy's various branches with Game Theory. However, I must run now to post on another topic - BOUNDARIES. I must not run out of time, like the hare in Alice in Wonderland. I am only 71 years old, but my long-lived ancestors did not quite live through a world continually on the verge of nuclear and financial and mental/social destruction.
Osher Doctorow
Well, I am not "anti-game theory" per se, Mr Doctorow, but questioning how you apply it to, dare we say, real world scenarios (say economics). The Prisoner's Dilemma merely suggests sometimes it may be in someone's interest to cooperate. But one might..."meta" the issue--and ask whether the analogy holds in any real sense. I don't think it does. Perps (and..disclosure--I know a few) making a deal with a DA probably rarely are offered a deal like that. Unless it was like old-school mafia types (where ratting might ...result in their death), they would probably rat their crony out to save themselves (and get witness protection, etc). I don't see the probability issue too much (and rather difficult to calculate). There's rarely the proverbial "Win-Win" (well, maybe for very wealthy investors there might be)...
ReplyDeleteAs I said, probability (stats as a whole, really) applies when you have a lot of data to work with---one reason insurance people use it, as do sociologists, or econo-types. It's about large samples--not just a few flips of the coin, or rolls of the dice.
(Now, yr example #10--that looks like applied statistical mechanics. Businessmen want to knows what's "the bang for the buck" of some stats.app., whether for the DoD, or finance, or vegas odds, etc. Like hiring a stockbroker. A reasonable person wants to see a broker's score card)
Good. Good to see J wants to play the game. I enjoyed his reference to decision theory (which I like to connect with Suppes and Davidson -- (1957) and the other book by Suppes that Doctorow was citing. And then of course there's Hobbes.
ReplyDeleteOn the other hand, to use another example with J, you cannot "play" with Katrina, can you?
---- The point of the rational choice, decision theory, probability-based game theory is Skyrms's (and sometimes Grice's): it's the new dimension of homo oeconomicus.
And Grice played auction bridge. Actually championed it for Oxfordshire!