Comments on: Incompleteness and the precautionary principle

By: Club Troppo » Green all the way through

Club Troppo » Green all the way through — Sat, 21 Jan 2006 08:15:38 +0000

[...] Environmentalism has changed the way leftists think about government led social change. Like the natural environment, the social environment is complex and poorly understood. With their oversimplified models, reformers accept serious risk because they don’t see it. Lack of understanding makes them overconfident. [...]

By: Deb Frisch

Deb Frisch — Tue, 14 Dec 2004 16:50:42 +0000

ogmb: Shorter JQ: If I assume away all obstacles to Pareto optimality, Pareto optimal outcomes are inevitable. DF: Nice – but it’s actually worse than that. If I assume away all obstacles to Pareto optimality, Pareto optimal outcomes are probable. JQ1: Theorem: Two omniscient agents will never fight a war. Proof: A rational agent will never choose a Pareto-dominated option. War is dominated by the would-be warriors divvying up resources (e.g., land, water, horses, women) in a way that corresponds to the final outcome of the war. DF: How do you know the outcome of the war unless you fight the war? JQ’s proof implicitly assumes omniscience. No one, including the most delusional game theorists, assumes that humans are omniscient. JQ2: ”There are some standard game theoretic conditions under which the proposition “No two rational players will choose a Pareto-dominated outcome” is true. For example, these include full Bayesian rationality (not omniscience – the argument copes fine with uncertainty as long as the players are EU maximisers) unbounded reasoning capacity, and free communication between players.” Theorem: Two agents who: a. are SEU maximizers (DMs that maximize SEU automatically will be Bayesians) b. have “unbounded reasoning capacity” and c. have free communication with each other will never choose war. Proof: Not provided. Again, there’s a blatantly false assumption. We’ve dropped “omniscient” but added “unbounded reasoning capacity.” But even if we grant JQ2’s premise b, it’s possible to construct a scenario where these two DMs would choose war. That is, in JQ1, a blatantly false assumption (omniscient) was sufficient to prove the theorem. In JQ2, the bfa (unbounded reasoning capacity) is not sufficient to prove the theorem. A Bayesian with unbounded reasoning capacity would have the capacity to assign coherent probabilities to states of the world in a way that reflects all of the evidence available. Let’s imagine the two adversaries occupy contiguous pieces of land. Group A wants more land. They are too crowded, have to ration water and food, etc. Although the A people have ethical system that prohibits one A from killing another A, the system does not apply to B’s. The Bs are perceived to be subhuman because the B-folks worship the sun and A-folks worship an alleged guy in the sky. So the A folks decide they will attack the B folks, kill them all and take their land. Since there are 10 times as many A folks as B folks, they think the chance of success is high. So A folks say p(A win a war against B)=.8 They rate the utility of the status quo as 0. Let’s say U(win)=10, U(loss)=10. [If they win, everyone’s better off. If they lose, some people are worse off (the dead soldiers) and everyone else is the same.] So EUwar= 8-2=6 EUnowar=0 A prefers war. It’s tempting to say that if A and B are both Bayesians, with unbounded reasoning capacity and the ability to communicate with each other, the B folks would also say p(A win a war against B)=.8. And it’s tempting to say if EUwar>EUnowar for A, then EUnowar>EUwar for B so B would surrender once A showed it was serious about burning some gunpowder. I think both assumptions are false. There is no reason that A and B need to assign the same probabilities to p(A will win the war). Any “facts” that A tells B are not 100% trustworthy. Ditto for any “facts” that B tells A. So even if A and B “freely communicate,” they will not converge on a single probability that A would win a war. Also, the utilities are different for B. If the status quo =0, u(losing) approaches negative infinity. U(win)=0. No matter how low the probability of winning, a tiny chance of 0 is preferable to a huge chance of negative infinity. [This has the same flavor as Pascal’s wager.] So EUwar>EUnowar for A. And though B preferred no war, once A aggresses, EUwar>EUnowar for B too. I think JQ wants it to be true that rationality is sufficient to avoid war. I wish it were true also. But I don’t think that it is.

By: Katz

Katz — Mon, 13 Dec 2004 22:07:29 +0000

[This post refers to a discussion on JQ’s blogsite. Sorry about the discontinuity and my sympathies regarding JQ’s problems with the lunacies and criminalities of cyberspace.] JQ wrote: “If the expected benefits of investment are large enough, they outweigh the gain from waiting.” According to the model proposed, if the expected benefits are large enough, I would have thought that the aggressor will decide for war at period (n). I’m trying to think of conditions that might improve the expected rewards of war within realistic time constraints. Some possibilities: 1. Discovery of new resources. 2. Development of new technologies that cause a revaluation of already known resources. (Mesopotamia, for example, was just a bunch of sand in the eyes of Westerners until the discovery of uses for oil.) 3. The lure of a tied market for domestic industries. (There was a huge literature on this aspect of imperialism spearheaded by Lenin and Hobson.) 4. Domestic political benefits arising from acting on demonisation of the enemy regime or the politico/cultural arrangements promoted and/or imposed by the enemy regime. (The Cold War and its episodic hot spots, such as the Vietnam War, conforms to this pattern.) But with the exception of the lure of tied markets, it seems to me that these benefits develop too slowly to be encompassed in a coherent decision-making sequence. (This question of the persistence of memory and the framing of a coherent purpose may need to be added to any robust model for decision-making of the type that leads countries to form foreign policies, including starting wars.)

By: ogmb

ogmb — Mon, 13 Dec 2004 19:34:41 +0000

Shorter JQ: If I assume away all obstacles to Pareto optimality, Pareto optimal outcomes are inevitable.

By: Deb Frisch

Deb Frisch — Sun, 12 Dec 2004 22:26:28 +0000

JQ: There are some standard game theoretic conditions under which the proposition “No two rational players will choose a Pareto-dominated outcome” is true. For example, these include full Bayesian rationality (not omniscience – the argument copes fine with uncertainty as long as the players are EU maximisers) unbounded reasoning capacity, and free communication between players. DF: Great. Now we’re getting somewhere. I’m 98.235% sure that we agree that two omniscient rational agents would never fight a war, because they’d just make a contract for the end state and skip the blood and gore. You can fancy it up and call it a Pareto optimal Nash equilibrium, but that would be kind of silly, since it’s an utterly trivial “result in game theory,” given the impossible, implausible assumption. Glad to see you’ve abandoned this line of reasoning. Now you’ve redefined the claim “At least one irrational agent is necessary for war” to mean “Two rational Bayesian expected utility maximizing decision makers will never engage in war.” This is a more interesting hypothesis than the one about omniscient agents, but it still seems to me it’s blatantly false. My USA/Canada war example assumed rational Bayesian expected utility maximizers. I think it is easy to construct scenarios where two subjective expected utility maximizers (as you know, this implies they are Bayesians) choose to engage in war. The hypothesis on the table is: Will SEU maximizers ever choose to engage in war with each other? I said yes and I provided an example. JQ says no, and provides more handwaving. He says “the argument copes fine with uncertainty as long as the players are EU maximisers.” This is a tad sketchy – what exactly is the argument for why Bayesians won’t engage in war? I am 97.59% sure that if you asked mutually acknowledged experts in Bayesianism whether the new version of Quiggin’s conjecture is true (e.g., Shafer, Edwards, von Winterfeldt, Clemen, Hacking (is he still alive?), etc.), 100% would say two Bayesians might choose to duke it out, even if we allow the false assumption of “unbounded reasoning capacity.”

By: John Quiggin

John Quiggin — Sun, 12 Dec 2004 02:47:55 +0000

Sorry for getting frustrated. I’ll try one more time. There are some standard game theoretic conditions under which the proposition “No two rational players will choose a Pareto-dominated outcome” is true. For example, these include full Bayesian rationality (not omniscience – the argument copes fine with uncertainty as long as the players are EU maximisers) unbounded reasoning capacity, and free communication between players. I claim that all of these conditions are either required to be satisfied for Posner’s example to work at all (for example, full Bayesian rationality is needed to work out the numbers in his toy example) implied by symmetry when we take account of the existence of another player (common knowledge of rationality) or crucial for the normative relevance of Posner’s claims (for example, it’s true that communications problems like those in the Prisoners Dilemma can lead to a Pareto-dominated Nash equilibrium, but the obvious, and standard, conclusion is to improve communications, not to fight wars). If you accept all the above, then the occurrence of wars is evidence that the premises necessary for Posner’s argument to work properly are not satisfied, something we know anyway from experimental evidence and introspection. So, I reach the conclusion that it is unwise to apply Posner-style reasoning to wars.

By: John Quiggin

John Quiggin — Sun, 12 Dec 2004 00:53:09 +0000

I’m obviously doing something wrong here, so I’ll just restate that I’m disagreeing with Posner, not agreeing with him and leave it at that.

By: ogmb

ogmb — Sun, 12 Dec 2004 00:11:47 +0000

This is part of the assumption of rationality standard in game theory. I (…) conclude that using game theory to justify preventive war is a silly idea. But Posner doesn’t even use game theory. He sets up a simple decision making under uncertainty example in which the adversary acts as force of nature. He then offers a sensitivity analysis over the variable “imminence (= probability) of attack” and concludes that under carefully chosen parameters the choice alternative “preventive attack” becomes expected payoff maximizing at an imminence level lower than one. This is crude stuff, but his use of the word rationality is justified here, because in this context it doesn’t mean more than choosing the action with the best expected payoff given ones expectations. Btw, Posner posted an update on their blog where he responds to some of the criticism. Nothing relevant to this discussion though.

By: Deb Frisch

Deb Frisch — Sat, 11 Dec 2004 23:58:41 +0000

John, I am really not sure why this is so difficult. You made a very specific claim: “According to game theory, two rational agents will never choose war.” I disagreed. I provided a counterexample – a plausible scenario in which Nation A (e.g., USA) would threaten to wage war against Nation B (e.g., Canada) unless Nation B did x, y and z and Nation B said “Bring it on” and Nation A said “You got it.” Instead of responding to my counterexample to your conjecture, you said: “I think we are arguing at cross-purposes.” Sometimes you wave your hands in the direction of “what everyone knows is true about game theory.” Other times you wave your hands in the direction of “Posner’s definition of rationality.” When that fails, you resort to deflection and suggest our disagreement is illusory. You seem to think that Posner and game theorists in general believe that people are omniscient. You seem to think that game theorists think that the payoffs in the cooperation/defect matrix can be specified with certainty. In a prisoner’s dilemma, this might be true. The warden says “If you say X and he says Y, you go to prison for 4 years and he goes to prison for 8; if you say Y and he says Y, you both go to prison for 2 years, etc.” In the real world, the consequences/payoffs are not known with certainty. Even though I think game theory is kooky, I don’t think it’s as kooky as you do. I think that game theory would say that the consequences associated with waging war are uncertain. The consequences are very different depending on whether you “win” or “lose” and this is up for grabs unless and until you actually wage war. I provided a blurb about von Neumann showing that like me, he thought that a rational agent might choose to go to war. I agree with you that in general, nations that choose to attack others are almost always irrational. I think Sam’s nuts, Saddam’s kooky and Osama’s certifiable. It’s an empirical fact that most people who wage war are irrational. But the British citizens who lived in North American in the mid-1700s who chose to wage war against their government were not irrational. The fact that most warmongering nations are ruled by lunatics is an empirical fact, not an analytic truth.

By: Kevin Donoghue

Kevin Donoghue — Sat, 11 Dec 2004 22:12:29 +0000

“If you go back to Posner’s original post, you’ll see that it depends on the assumption that the outcome of any strategy can be predicted in advance. This is part of the assumption of rationality standard in game theory.” I know nothing about Posner. Since he gave no clue where his assumptions came from, I assumed he plucked them out of the air (to put it politely). Perhaps the difference between JQ and Deb is that the former gives Posner undue credit. (Maybe the SSRN paper justifies JQ’s faith in Posner but I don’t have access to that.)

By: John Quiggin

John Quiggin — Sat, 11 Dec 2004 19:31:15 +0000

Looking at this statement from Deb “How do you know what outcome the war will produce without fighting it?” I think we are arguing at cross purposes here. If you go back to Posner’s original post, you’ll see that it depends on the assumption that the outcome of any strategy can be predicted in advance. This is part of the assumption of rationality standard in game theory. I make the point that (i) people aren’t as fully informed as this or rational in the way assumed by Posner (ii) if they were, they wouldn’t fight wars and conclude that using game theory to justify preventive war is a silly idea. Deb seems to agree with the conclusion, but also wants to challenge (ii) on a variety of grounds that aren’t clear to me. So Deb, if you think (ii) is wrong in a way that validates Posner’s argument please say so. Otherwise, insert the necessary technical conditions (common knowledge of rationality, Bayesian common priors, unbounded computational capacity, ability to monitor commitments and so on) that make (ii) formally correct and observe that Posner is implicitly relying on all of these conditions.

By: Deb Frisch

Deb Frisch — Sat, 11 Dec 2004 18:45:32 +0000

Yup, Jason, it’s easy to find examples of game theorists who disagree with JQ’s assertion that rational agents do not engage in war. Here are a few more: Although Von Neumann appreciated Game Theory’s applications to economics, he was most interested in applying his methods to politics and warfare… He used his methods to model the Cold War interaction between the U.S. and the USSR, viewing them as two players in a zero-sum game. http://cse.stanford.edu/classes/sophomore-college/projects-98/game-theory/neumann.html There are two Nash equilibria in this final move, Mutual Doomsday and Mutual Backdown. http://www.rh.edu/~stodder/BE/IntroGameT.htm I would love to see a reference for JQ’s claim that the proposition is “at least one irrational party is needed” is “standard stuff.”

By: Jason

Jason — Sat, 11 Dec 2004 17:56:57 +0000

Thomas Schelling ‘Strategy of Conflict’ A great book, and at one point he describes what seem to me situations where rational people can commit to war. For instance, it is sometimes rational to bind yourself to your statements/threats, so that the other party will be forced to concede because, yes, you will destroy the entire planet if you don’t get the last piece of Thanksgiving pie. Problems can arise when two parties bind themselves in incompatible ways (for instance, due to communication channel errors/delays).

By: Deb Frisch

Deb Frisch — Sat, 11 Dec 2004 17:08:33 +0000

“Any war is Pareto dominated by a contract under which both parties agree to the outcome that the war would have produced without fighting.” How do you know what outcome the war will produce without fighting it? And why do economists have so much faith in a theory of interpersonal relationships developed by a paranoid schizophrenic (John Nash)?

By: ogmb

ogmb — Sat, 11 Dec 2004 11:29:42 +0000

Deb, it seems that JQ and DD are trying to invoke the Nash bargaining solution. I can’t really argue with that as it is in fact “standard stuff”, but it would have been easier if they’d just referred to it rather than the ongoing handwaving and poorly worded defenses. And no, the Nash bargaining solution doesn’t establish that rational actors don’t go to war. It only establishes that they don’t go to war if bargaining is an option. Also, JQ started out by criticizing Posner for not incorporating that the other side might be acting rationally. Now he claims that Posner’s “analysis makes no sense on his own assumptions”. But all we’ve seen from JQ and DD is that war doesn’t happen if both sides act rationally, which is something Posner doesn’t assume.