A theory of rationality

After some thought, and much discussion, I am finally ready to publish my first draft of the theory of rationality.

Proposition 1: All people make rational decisions.

We first define rational as follows: a rational decision is the decision made by an individual in a given situation that maximizes his benefit. The key point here is the term "a given situation". By a given situation, we take it to mean that "given the current circumstances, current information known by the person, and current frame of mind". As such, it can be argued that a person making a decision would always take the decision that most benefits him at that time. It would be irrational to argue otherwise.

How then, do we account for sacrifices made by people to benefit others? Surely, a person would only take an action that benefits himself, by Proposition 1.

Proposition 2 (also called the Love Theory): Between any two people A and B, if A's happiness is increased by x, B's happiness will be increased by px, where p, which I will call the love factor, can be any real number.

To put the above statement more clearly, whenever one perceives another's happiness to increase by x amount, his/her own happiness will increase by px. This is an important distinction, as the gain in one's happiness is proportional to the amount of happiness one perceives another to gain, not necessarily the actual amount.

The existence of correlation in happiness cannot be denied. Seeing a loved one being happy will make one happy as well, with this level of happiness dependent on the relationship between the two people concerned. It is this contribution to one's happiness from the love factor that can cause one to make sacrifices (ie. reduce his own happiness) to benefit another (ie. increase his/her happiness). The benefit from the love factor accrues to the person making the sacrifice and thus makes his decision rational.

Example: If for example, a boyfriend's love factor for his girlfriend is 0.5 (which I will not comment as being high or low, as this is subjective), he will be willing to take sacrifices as long as he perceives his girlfriend to gain at least double the value of his sacrifice. In other words, he would be willing to put in 100 units of disutility if he expects his girlfriend to gain at least 200 units of utility from it. If he had to do something more (like give up his life, or his kidney), he probably would not unless his love factor was higher.

The love factor does not have to be positive. For strangers, it would generally be 0, or a very small number. Like for example, you would hold a door open for a stranger, even if you do not expect any thanks for it (this is to eliminate the benefit from getting thanked), if your love factor for all strangers was some positive number, valuing the disutility of holding open the door as so minimal compared to the happiness one would gain from having the door held open for him/her. Good-natured people have a higher likelihood of having positive love factors for strangers. If one was foul-natured, he probably would never hold the door open for strangers if he did not expect to get thanked for it (and even so).

The love factor can also be negative, in which case it would be prudent to rename to the hate factor. When the love factor is negative, one would gain happiness when one perceives another to lose happiness. This would generally apply to enemies. A good example would be a crime of passion: Seeing his wife in bed with another man, a husband's love factor with that man suddenly drops to an extreme negative number. He could gain maybe 10 to 20 times the satisfaction per unit pain inflicted on the man. Thus this incredibly high benefit to him would outweigh possible costs (like being arrested and put to trial). If it did, it would be rational to blow the man's brains out with a Pancor Jackhammer (but don't use burst mode, or you might damage your house).

As can be seen from the examples, the existence of the love factor is undeniable.

Proposition 3: In order for one to be rational, one must assume everyone else (more specifically, the people he is dealing with) is rational.

(This took me a long time to prove, but I finally got it.)

I will attempt to prove this by contradiction.

Assume that the proposition is false, ie. One cannot always assume the other person is rational.

That is to say, it is rational to expect the other person to be irrational some of the time.

Lets say that it is rational to expect another person to be rational, say, only 90% of the time.

So, when one is dealing with another person, one can expect that:

1) 90% of the time, the person is rational. Ie. 90% of the time, the other person (whom I will call he, for simplicity's sake) expects you to act rationally 90% of the time.

2) 10% of the time, the person is irrational. Ie. 10% of the time, he does not expect you to act rationally 90% of the time.

Thus, in the case that he is rational (which is 90% of the time), you are expected to be rational 90% of those times, which means that in all, you are expected to be rational 81% of the time from just case 1).

From case 2), if the person is irrational, he would be expecting you to act rationally x% of the time, where x cannot be 90 (or he would be rational). Which means that in all, you are expected to be rational NOT 9% of the time, from case 2).

Thus, on the whole, you are not actually expected to act rationally 90% of the time. But by our initial definition, that would make him always an irrational person. If you thus assume that he is irrational all the time, you would not be rational yourself, because rationality states that you must assume he is rational 90% of the time.

Therefore, it can be seen that the definition for rationality cannot hold. As long as rationality involves expecting a certain percentage (above 0) of irrationality in others, this definition will not hold.

The only rational solution is to define rational as assuming that everyone else is rational. In which case, the definition proves itself. It would be irrational to assume otherwise.