Golden V. Silver Round II

I want to revisit the Golden Rule and Silver Rule of ethics comparison.

 Recall that Golden Rule, is most commonly stated as “Do unto others as you would have them do unto you“, where the silver rule is the negated form that most frequently appears as:”己所不欲,勿施于人

In my previous posts(here, and again here), it would appear that we have written about a result concerning two person one following the golden rule and one following the silver rule benefitting differently based on his or her likes and dislikes.

I should think a second analysis is in order on this Thanksgiving eve of 2012. We begin with the observation that both the golden rule and silver rule appear to be stated for sentences who’s verb is transitive.
A Verb B
Golden rule says if you want to be B of a sentence, then you should always be A of that sentence.
Silver rule says if you do not want to be B of that sentence, then you should never be A of that sentence.
These imperatives are translated into logical conditionals as follows:
Golden: if “I want to be B” then “(Jesus says) always be A” of the action “A verb B”.
Silver: if “I do not want to be B” then “(Confucius says) never be A” of the action “A verb B”.
I want, ->O, Gold, Silver
Y, Y, T, T
Y, N, F, T
N, Y, T, F
N ,N, T,T
So this means under golden rule, the following can take place :
I want, do to O (*)
I don’t want to be done onto, do to O
I don’t want to be done onto, don’t do to O.
under silver rule, the following can take place:
I want, do to O
I want, don’t do to O
I don’t want to be done onto, don’t do to O. (*)
In reality, when there are two outcomes to the same antecedent, we usually cannot both do and do not do Verb onto O. So, a easy simplification, without biasing towards either rule is to take a maximum entropy approach. For the strategic ethicists, here are the strategies for this game of ethics:
Golden rule:
I want, do to O 100%
I don’t want, 50% do to O 50% don’t do to O.
Silver rule:
I don’t want, do not do to O 100%
I do want, 50% do to O, 50% don’t do to O.
With these relaxation in mind we shall commence analysis in a world where there are only two people, one strictly following the golden rule and one strictly following the silver rule. Given any want/don’t want combinations there are several possibilities in the utility a person may take from a situation. 
A verb Me and I want to be verbed:  1
A verb Me and I don’t want to be verbed:  0
A does not verb Me and I want to be verbed:  0
A does not verb Me and I don’t want to be verbed: 0
To person G or S, the utility of A Verb B taking place under these circumstances are
S1: G wants B, S wants B
S2: G wants B, S doesn’t wants B
S3: G doesn’t wants B, S wants B
S4: G doesn’t wants B, S doesn’t wants B
S1: G 0.5, S 1
S2: G 0, S 0
S3: G: 0, S 0.5
S4: G:  0, S 0
Summing everything up, G gets 0.5, s gets 1.5
Here, we will also consider the concept of a winner if in this world, under these rules and these strategies applied according to the rules that the rule’s follower gains higher utility. In this case Silver rule follower wins, by 200%. This is quite interesting, because the golden rule is setup as if one is only rewarded by action when the same is desired, therefore, when Silver rule follower enters, the Golden rule follower suffers. This inspires us to reverse this and create a world where Silver rule follower is disadvantaged:
A verb Me and I want to be verbed:  0
A verb Me and I don’t want to be verbed:  0
A does not verb Me and I want to be verbed:  0
A does not verb Me and I don’t want to be verbed: 1
That is, if the world really is such a way that would cause one to create the silver rule, then what are each party’s utility?
S1: G 0, S 0
S2: G 0, S 0
S3: G: 0.5, S 0
S4: G:  1, S 0.5
Totals G:1.5, S: 0.5
Aha, when the world is such that one would want to create the silver rule, silver rule follower benefits less when interacting with a golden rule follower, again by 200%. These two worlds seem to have produced very intuitive results: in the prior case, our world is one where one is only rewarded when actions on taken onto him only when he himself desires it; in this case silver rule following wins when in presence of gold rule follower, even tho he himself does not act with certainty when he desires it. In the latter case, our world is one where one is only rewarded when he is not done onto when he does not desire it. But in this case Golden rule wins. The conclusion one is tempted to draw from this is that rules are made in a world/society under its reward system to gain the most utility, but when interacting with members following rules from different world with different reward structure, then members of the foreign rule tend to benefit more from world/society than the natives.
Suppose our world is where inaction never create any disutility. And suppose also that doing the opposite thing is only half the damage as reward of doing the right thing:
A verb Me and I want to be verbed:  1
A verb Me and I don’t want to be verbed:  -.5
A does not verb Me and I want to be verbed:  0
A does not verb Me and I don’t want to be verbed: 0
Totals G: 0.25, S: 0.75
So, in this world where inaction does no damage and wrong action is somewhat forgivable then Silver rule follower is 200% better off than Golden rule follower. 
Another interesting case is the inaction world is where one is rewarded for wanting. Even when one doesn’t get what one wants, he is still rewarded, though not as much as getting what he wants.
A verb Me and I want to be verbed:  1
A verb Me and I don’t want to be verbed:  0
A does not verb Me and I want to be verbed:  0.5
A does not verb Me and I don’t want to be verbed: 0
Totals: G: 1.25, S:1.75
In this case, Golden rule follower actually loses by 20% to silver rule.  Similarly if we are slightly rewarded for not wanting even if we get something, the winner is reversed and Silver rule follower loses by 20%. As in the first two cases, the losing rule in a situation tend to be the rule inspired by that world, and that rule will lose when interacting a rule that would have been inspired by the opposite world. It seem to suggest that the society/world that inspired the silver rule would have rewarded members for not wanting where as the opposite is true of the society that inspired the golden rule.
These two widely known rules of moral and ethics known as Golden rule and ethics and Silver rule of ethics arise from different places in the world of different language and culture. Upon closer inspection, we discover that the logical interpretation of their meaning yields an extremely interesting problem regarding what to do in the situation when the rule gives no prescription for what to do. In this analysis we have taken a maximum entropy approach and created a mixed strategy profile for two persons one using golden rule and one using silver rule. In both cases when no prescription is given the follower will do one of two possible actions with 50% probability.
Under this relaxation of both rule, we put two people, one following each rule, together in an artificial world where utilities are assigned for four combination of one wanting to be B of “A verb B” and whether “A verb B” happens. It is found that the world with utility seeming to inspire a rule tend to favor the other rule’s follower, follower of rules inspired by the world seem to suffer and gain less utility in the process of interacting with the other rule’s follower. This would make sense in two ways: when the world rewards for some kind of action, the follower of the rule suffers when he does positive things to others but does not receive the same action in return. And secondly when the world punishes some action, the person coming from a world where there is no such punishment and does not know (from his rules) that he should not avoid it, and is therefore does bad things the native and hurts him.
With this in mind, the winners in two groups of worlds suggest that golden rule comes from a world/society where inaction never creates disutility where as silver rule come from a world where lack of desire (not wanting) is always rewarded.

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