In the statement:
If P then Q,
P is known as the antecedent and Q is known as the consequent. So, in logic, the statement "If P then Q" has truth value as follows:
I've added a column to illustrate the example, let's say the subject is sex.
| P | Q | If P then Q |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
So, logic is actually pretty easy. Let's plug in some expressions, let P = "I want it", and Q="recommend to give (on) to others", then the golden rule says:
| I Want it | Give (on) to Others | Commanded by the Golden Rule | Sex |
|---|---|---|---|
| Y | Y | Y | I want sex, so do sex to others. |
| Y | N | N | not recommended. |
| N | Y | Y | I don't want sex, so do sex to others. |
| N | N | Y | I don't want sex, so don't do sex to others. |
Similarly the silver rule:
| I don't Want it | Don't Give (on) to Others | Commanded by the Silver Rule | Sex |
|---|---|---|---|
| Y | Y | Y | I don't want sex, so don't do sex to others. |
| Y | N | N | not recommended. |
| N | Y | Y | I want sex, so don't do sex to others. |
| N | N | Y | I want sex, so do sex to others. |
Let's see, so, under goldern rule, if I want sex, I must do sex to others. But under the silver rule, even if I like sex, I don't have to do to others. I have the choice of doing it or not doing it to others.
Under the golden rule if I don't like sex, I have the choice of doing it to others or not, but under the silver rule, when I don't want sex, I must not do it to others.
Initially, we must recurse in analysis:
Under the golden rule, if I believe it is the right ethical thing to do, then I do onto others, that they follow the golden rule as well. And if I don't believe it, then fine, I can do whatever I want--including forcing it onto another person.
Under the silver rule, if I believe it's right, I can do whatever I want, I don't have to enforce the rule. But if I don't believe it, then I must not only not follow the silver rule, I must also ensure others do not follow it.
Knowing this, let's look into a situation of two person, one following golden rule, and one following the silver rule. The golden rule person will force the silver rule person to follow his system. The person believing in the silver rule does not try to force it onto the golden rule person. However, the silver rule person will not believe the golden rule, so he will try to persuade the golden rule person from following the golden rule. The golden rule person has one goal, which is to make silver into gold. The silver rule person has a more diverse goal, which is to make the golden rule follower deviate from the golden rule. One insists on absolute perfection, the other one does his best to prevent the worst from happening.
The state of the silver person believing the silver rule causes golden person no anxiety, only his own believe in the golden rule forces him to try to convert the silver. The state of the golden person believing in golden rule causes the silver person his anxiety. His own believe in the silver rule doesn't compel him into action. It is out of his concern for golden person that he tries to persuade him.
So, from the perspective of the reason for action, golden person is in some sense more selfish then the silver. The silver tries to help golden person out of altruistic goals where as the golden person tries to help the silver person, intentionally, or not, to expend the coverage of the golden rule.
Of course, both suffers from the perspective of not considering if others want it or not. But I think both tries to use the heuristic that my wants correlates with others' wants.
| I Want | Others Want | Golden Rule Win | Silver Rule Win |
|---|---|---|---|
| Y | Y | 1 | 1 |
| Y | N | -1 | 1 |
| N | Y | 1 | -1 |
| N | N | 1 | 1 |
If the desires are completely correlated, both scores 2, if the desires are completely anti-correlated(your stupid spouse decides to only dislike things you like and like things you don't like), then both scores 0. If the desires are uncorrelated (say that the probability in this contingency table is 0.25 for each outcome), then the score is 0.5 for each rule.
We can construct pathological case for each. Say all the things in the world are like this:
| I Want | Others Want | Probability in Reality | Golden Rule Win | Silver Rule Win |
|---|---|---|---|---|
| Y | Y | 0 | 1 | 1 |
| Y | N | 1 | -1 | 1 |
| N | Y | 0 | 1 | -1 |
| N | N | 0 | 1 | 1 |
If the world was like this, where you like everything and everybody else hates everything, then the silver rule wins 100% and golden rule loses 100%. And similarly, if you dislike everything and everybody loves the whole world, then golden rule wins 100% and silver rule loses 100%.
How the world is distributed in the case of Y/Y and N/N is unimportant. It only matters which of the following two cases happens more:
A.) I like something and others don't like it
B.) I don't like something and others like it.
Simple example I.) I like English because I speak it. A.) is probably the case. and Golden rule loses near 100%.
Simple example II.) I don't like grain alcohol (hypothetically speaking), B.) is the case, because a lot of people in Asia like grain alcohol... so person following silver rule loses 100% and golden rule wins 100%.
The research question for the future is this. What is the distribution of A versus B in reality over all people. One-Versus-Rest:
A~\sum_{p \in all people}\sum_{q \in all people}\sum_{t \in things both p and q have feelings for} {p likes t and q doesn't like t}
B~\sum_{p \in all people}\sum_{q \in all people}\sum_{t \in things both p and q have feelings for} {p doesn't likes t and q likes t}
Seeing it this way, leads us to believe, that over the whole population of humans, and over all things they have in common, the golden rule and silver rule are equivalent in utility if applied uniformly.
Because A=B by expansion of summations.
An exercise for the future is to take p out of a population with x% golden rule follower and the rest silver rule follower, and seeing how thing work out. (The flipping point is obviously when x reaches 50%)
Second exercise is to think of two large populations, say US and China, and suppose US follow golden rule 95% of the time, and China follow silver rule 95% of the time. Taking notice of the population and cultural difference, what is the utility of this application of both rules?
Thirdly, extend the second into analysis of several major continents simultaneously.
Lastly, perform cost-sensitive analysis of the system from 3rd exercise and analyse the utility considering the cost of applying golden rule and silver rule.
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