tronvillain

God Fearing Atheist:
I was under the impression that the definitions were:

• Let p be the probability of identifying a cooperator as a cooperator, given that they are a cooperator.
• Let q be the probability of identifying a defector as a defector, given that they are a defector.

Apparently you intend the definitions to be:

• Let p be the probability of identifying a partner as a cooperator.
• Let 1-p be the probability of identifying a partner as a defector.

I assume this is what you intend because the mechanism you propose only works with the second set of defintions.

Now, using these definitions:

CM [1-r][1-p]u' + rpu"

SM [1-r]pu' + r[1-p]

SM is rational when [1/r]/r<[1-p-u"]/u'[1-2p]. Again, the larger r is, the smaller [1-r]/r is, and the better it is to be an SM. Now since the right side is negative if 1/[u"+1]>p>1/2, SM will not be a viable strategy if that is the case. Under all other conditions, a population of CM will be capable of supporting some number of SM.

Presumably p is some function of the ability to recognize cooperators, the ability to recognize defectors, and the ability to determine r. The relationship would have to be specified to examine its effects on the model.

[ February 01, 2002: Message edited by: tronvillain ]</p>

tronvillain

Actually, I think I've made an error there. The utility functions would be:

CM [1-r][1-p]u' + rpu" + r[1-p]u'

SM [1-r][1-p]u' + rp + r[1-p]u'

Huh. Now, u"&lt;1 so pu"&lt;p and the utility of CM is always less than that of SM. I don't think that definition of p is going to work.

God Fearing Atheist

Heh....now im getting confused Tron.

Let me try one more time:

p = the probability that CMs will achieve mutual recognition.

q = the probability that CMs fail to recognize SMs and but are recognized themselves.

r = the probability that a randomly selected memeber of the population is a CM.

(1-r) = the probability that a randomly selected actor is an SM.

A CM expects u' (non-cooperative value) unless she:

1) recognizes another CM is cooperates, which is r (contacting a CM) and p (they recognize each other as CMs), or rp. In this case she gains (u''-u') over the non-cooperative value, bringing the total expectation to [rp(u''-u')].

2) is exploited by an SM, which is (1-r) (contacting and SM) and q (fails to recognize him but is recognized herself), or (1-r)q. If this happens, she loses u' and gets nothing, reducing her expectation by [(1-r)qu']

Both together yeild {u'+[rp(u''-u')]-(1-r)qu'}

An SM will expect u' (non-cooperative value) as well, unless:

1) he exploits a CM, which is r (probability of contacting a CM) and q (he recognizes her, but is not recognized himself), or rq. If this is the case, he gain (1-u') over the non-cooperative expectation. His utility goes up by [rq(1-u')], and overall, expects {u'+[rq(1-u']}

So CM is only rational if it results in a higher expectation, which is in turn dependent upon p/q.

[ February 01, 2002: Message edited by: God Fearing Atheist ]</p>

God Fearing Atheist

Fuck...did it again.

[ February 01, 2002: Message edited by: God Fearing Atheist ]</p>

God Fearing Atheist

Poly, have you actually been reading my posts?

Now this one is pretty funny. We should act in way x vis-a-vis those with properties A and B. Where is the room for this "slippery slope"?

You went to anesthetized adults, Poly. I dont know about you, but rarely do i happen upon one of those!

No one should "be protected". Rights are rights from, not rights to.

Untenable...how? Because of a distinctly few marginal cases in adult humans?

1) How many people throughout the world are quadrapalegic? How many are in a coma? The examples you gave of the "severely disabled" seemed to me like nothing of the sort. Im a burn victim...so what? I ride around in a wheelchair...so what? These people cant reciprocate?

You're trying much to hard to find marginal cases that are really just that...marginal!

2) How many people lack pre-contract,secondary morals? Are there really many people that would harm the sorts of indivudals above?

3) How many of the disabled lack post-contract protection? How many lack care from relatives? How many live outside of explicitly contractual care obligations of any sort?

These three taken make this "problem" of yours seem rather silly. Couple it with comment on universality and you have your answer.

Think with your head, Poly, not your emotions.

God Fearing Atheist

I would probably agree.

But in many cases, those who kill their children are probably playing a different game altogether.

[ February 01, 2002: Message edited by: God Fearing Atheist ]</p>

Freedom's Minion

Sorry to misinterpret you. It seems that I mistook your question for a bit of rhetoric meant to demonstrate that divisions between "physical" and "merely aesthetic" preferences are arbitrary at best.

My claim, which was contra to what GFA implied, was that there was no difference in principle between aesthetic preferences and "physical dependence", that there is no way to really draw a line between them.

God Fearing Atheist

I think there is. Is emotional "hurt" enough to justify physical action, and therefore, reciprocation on the part of the one you're harming?

If you look at it from this way as well (that is, not just from the point of view of the one beating the crap out of babies), it becomes far less appealing.

But I may be wrong.

-GFA

tronvillain

I think the way you were approaching the problem may have thrown me off. Let me check something:

The probability of encountering a CM is r, the probability of recognizing that CM and being recognized in return is p, and the utility of mutual cooperation is u"?

Then the utility of this encounter is pru".

The probability of encountering a CM is r, the probability of anything other than mutual recognition is 1-p, and the utility of any of those situations is u'?

Then the utility of this encounter is (1-p)ru'

The probability of encountering an SM is 1-r, the probability of not recognizing the SM but being recognized as a CM is q, and the utility of this happening is zero?

Then the utility of this encounter is zero.

The probability of encountering an SM is 1-r, the probability anything else else happening is 1-q, and the utility of this happening is u'?

Then the utility of this encounter is (1-r)(1-q)u'.

If we sum these, the total utility of being a CM is pru" + (1-p)ru' + (1-r)(1-q)u', which turns out to be equivalent to what you have.

The probability of encountering a CM is r, the probability of recognizing the CM but not being recognized is q, and the utility of this happening is 1?

Then the utility of this encounter is rq.

The probability of encountering a CM is r, the probability of anything else happening is 1-q, and the utility of this happening is u'?

Then the utility of the encounter is r(1-q)u'

The probability of encountering an SM is 1-r, apparently we're assuming SMs always recognize each other, and the utility of this happening is u'?

Then the utility of this encounter is (1-r)u'.

If we sum these, the total utility of being an SM is rq + r(1-q)u' + (1-r)u', which again turns out to be equivalent to what you have. Of course, the assumption that SMs always recognize each other seems odd.

Anyway, I finally got around to checking and you're right, it's only rational to adopt CM for
p/q&gt;{(1-u')/(u''-u')+[(1-r)u']/[r(u''-u')]}. My formulation would have been equivalent, except I wasn't applying my definitions of p and q correctly. Damn.

God Fearing Atheist

Heh...im glad we got this all cleared up!