The scientific method is wonderfully simple, intuitive, and above all effective. Based on the available evidence, you formulate several hypotheses and assign prior probabilities to each one. Then, you devise an experiment which will produce new evidence to distinguish between the hypotheses. Finally, you perform the experiment, and adjust your probabilities accordingly. 

So far, so good. But what do you do when you cannot perform any new experiments?

This may seem like a strange question, one that leans dangerously close to unprovable philosophical statements that don't have any real-world consequences. But it is in fact a serious problem facing the field of cosmology. We must learn that when there is no new evidence that will cause you to change your beliefs (or even when there is), the best thing to do is to rationally re-examine the evidence you already have.

I would strongly advise you to look at the short review on Thomas Schelling's Strategy of Conflict posted on Less Wrong some time back. The idea that deliberately constraining one's own choices can actually leave a person better off in a negotiation is a very interesting one. The most classic game theoretic example of this is the game of Chicken. In the game of Chicken, two people drive toward each other on a wide freeway. If neither of them swerve, they both stand to lose by way of substantial financial damage and possible loss of lives. If not, the first one to swerve is the proverbial "chicken" and stands to lose face against the other person who was brave enough to not swerve. If one person were to throw away their steering wheel and blindfold themselves before driving on the freeway, that would force the other person to swerve given that the first person has completely given up control of the situation. 

     There is a slightly more generalizable example of a similar principle at work. Suppose you wanted to buy a used car from a car dealer and were prepared to pay up to $5000 for the car and the car dealer in turn was willing to sell it for any price above $4000. In such a situation, any price between $4000 and $5000 is an admissible solution. However you ideally want to pay as close to $4000 as possible, while the car dealer would like you to pay close to $5000. In a such a situation, each party would pretend that their "last price" (the price that represents the worst possible outcome for them, which they would nonetheless be willing to accept) was different from the true last price, since if one party realizes the other party's true last price, that party can put it to effective use in the negotiation. Let us now assume a situation wherein you and the car dealer know perfectly well about the each other's financial details, the degree of urgency in having the transaction done etc., and have a very reliable idea of the last price of the other person. Now, you can break the symmetry and get the best possible deal out of the situation by deliberately handicapping yourself in the following fashion. You sign a contract with a third party individual which states that if you happen to do this transaction and pay more than $4000, you will have to pay the third party $1500. Now, all you need to do is show this contract to your used card dealer which would make it clear to him that your last price has now shrunk to $4000 since paying anything above that effectively means paying in excess of $5500 which is well past your original last price.

    For countries that face the menace of airline hijacking, it can likewise be an effective deterrent to future hijackers if release of terrorists or other kinds of negotiations with hijackers were explicitly prohibited by the country's laws, and these laws would be impossible to overturn during a hijacking incident. 

     This brings to mind the following question. Why don't there exist companies that explicitly sign contracts with individuals or other entities for a fee, which would handicap the entities in some way that cannot be easily overturned and consequently give them negotiating leverage as a result. 

      One example I can think of is pertaining to wealthy individuals in California and other US States with Community Property laws. Given the high divorce rates in the US, it would be prudent for such individuals to have as tight prenuptial agreements as possible prior to getting married, to minimize financial loss in the event of a divorce and also to avoid financially incentivizing one's spouse to initiate a divorce with a promise of a financial windfall. However there are some practical difficulties which might make many such individuals shy away from doing this. A couple of the practical issues are:

A. It is clearly rather unromantic to have to haggle with one's fiancée and their lawyers regarding a prenuptial agreement. The implied "lack of belief" in the potential durability of the marriage might be a turn off for one's partner and other close people involved.

B. The individuals themselves might get carried away by emotion and believe that they have found "the one" and assign a much lower probability of divorce or forcible concessions that they would need to make in future when faced with the threat of divorce. In such a situation, they would fail to realize that probably 50% of Americans who felt they found "the one" just like them, went on to eventually get divorced.

   Now imagine the beneficial role a company signing such contracts could provide. The individual in question could sign a contract with this company stating that if they were to get married without a bullet proof pre-specified prenuptial agreement, the company could lay claim to half their net worth immediately after the wedding were registered. Ideally, the individual in question could sign such a contract when they were single or not seriously seeing anyone with the intention of getting married. The advantage of such a contract is the following:

1. Community property and other modern divorce laws essentially change the defaults with regard to what happens in the aftermath of a divorce, compared to how marriages worked prior to the existence of such laws. Such a contract would reset the default state to one where neither party would financially profit in the aftermath of a divorce. Most of the awkwardness comes when trying to override the default state with a bunch of legal riders at the time of a wedding. 

2. The advantage of signing up for a contract well in advance is that the aforesaid individual is then not exposed to issues A and B above. Signing a tight pre-nuptial agreement in the background of such a contract, simply means that the individual in question has no desire to part with half their finances to this third party company. It makes no implicit statement about the individual's probability estimate for the durability of the marriage. There always exists the plausible explanation that the individual in question was opposed to non-prenup marriages in the past, but now saw no need for that given that they subsequently found "the one". However they are constrained by a certain contract they signed in the past that they are now powerless to change.

   Do you know if there are entities that play the role of the third party company with regard to signing contracts that enable people to handicap themselves and consequently come out stronger in future negotiations? Do you know of people who did this specifically with regard to prenuptial agreements? If such companies don't exist, is that a potential business opportunity? I would love to hear from you in the comments. 

Okay, maybe not me, but someone I know, and that's what the title would be if he wrote it.  Newcomb's problem and Kavka's toxin puzzle are more than just curiosities relevant to artificial intelligence theory.  Like a lot of thought experiments, they approximately happen.  They illustrate robust issues with causal decision theory that can deeply affect our everyday lives.

Yet somehow it isn't mainstream knowledge that these are more than merely abstract linguistic issues, as evidenced by this comment thread (please no Karma sniping of the comments, they are a valuable record).  Scenarios involving brain scanning, decision simulation, etc., can establish their validy and future relevance, but not that they are already commonplace.  For the record, I want to provide an already-happened, real-life account that captures the Newcomb essence and explicitly describes how.

So let's say my friend is named Joe.  In his account, Joe is very much in love with this girl named Omega… er… Kate, and he wants to get married.  Kate is somewhat traditional, and won't marry him unless he proposes, not only in the sense of explicitly asking her, but also expressing certainty that he will never try to leave her if they do marry. 

Now, I don't want to make up the ending here.  I want to convey the actual account, in which Joe's beliefs are roughly schematized as follows: 

1. if he proposes sincerely, she is effectively sure to believe it.
2. if he proposes insincerely, she will 50% likely believe it.
3. if she believes his proposal, she will 80% likely say yes.
4. if she doesn't believe his proposal, she will surely say no, but will not be significantly upset in comparison to the significance of marriage.
5. if they marry, Joe will 90% likely be happy, and will 10% likely be unhappy.

He roughly values the happy and unhappy outcomes oppositely:

1. being happily married to Kate:  125 megautilons
2. being unhapily married to Kate:  -125 megautilons.

So what should he do?  What should this real person have actually done?¹  Well, as in Newcomb, these beliefs and utilities present an interesting and quantifiable problem…

Contents:

1.  The beautiful symmetry of Bayesian updating
2.  Odds and log odds: a short comparison
3.  Further discussion of information

Rationality is all about handling this thing called "information".  Fortunately, we live in an era after the rigorous formulation of Information Theory by C.E. Shannon in 1948, a basic understanding of which can actually help you think about your beliefs, in a way similar but complementary to probability theory. Indeed, it has flourished as an area of research exactly because it helps people in many areas of science to describe the world.  We should take advantage of this!

The information theory of events, which I'm about to explain, is about as difficult as high school probability.  It is certainly easier than the information theory of multiple random variables (which right now is explained on Wikipedia), even though the equations look very similar.  If you already know it, this can be a linkable source of explanations to save you writing time :)

So!  To get started, what better way to motivate information theory than to answer a question about Bayesianism?

The beautiful symmetry of Bayesian updating

The factor by which observing A increases the probability of B is the same as the factor by which observing B increases the probability of A.  This factor is P(A and B)/(P(A)·P(B)), which I'll denote by pev(A,B) for reasons to come.  It can vary from 0 to +infinity, and allows us to write Bayes' Theorem succinctly in both directions:

     P(A|B)=P(A)·pev(A,B),   and   P(B|A)=P(B)·pev(A,B)

What does this symmetry mean, and how should it affect the way we think?

A great way to think of pev(A,B) is as a multiplicative measure of mutual evidence, which I'll call mutual probabilistic evidence to be specific.  If pev=1 if they're independent, if pev>1 they make each other more likely, and if pev<1 if they make each other less likely.

But two ways to think are better than one, so I will offer a second explanation, in terms of information, which I often find quite helpful in analyzing my own beliefs: