Re: Twenty Bank Robbers -- CLARIFICATION

["James A. Donald" <jamesd@echeque.com>]

At 04:33 PM 7/25/96 -0700, Jeremey Barrett wrote:
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> Assuming "perfect" intelligence on the part of the robbers (i.e. they will
> follow deterministic behavior and do the "right" thing), then here's what
> must happen IMO (1 being the first guy and 20 being the last):

[...]

> If 2 are left (19 & 20), 19 gets all the money. So 20 will vote for whatever
> 18 says, which MUST include 20 in the deal. 

But here we run into the paradox, that it is not in each persons self
interest to pursue is self interest.

Example;  Suppose only two are left:  Then No. 19 get everything, 
and No. 20 gets nothing.  So if only three are left, it will 
maximize 20's return to vote for a proposal by number 18, that 
number 18 gets 19,999,999 dollars, and number 20 gets one dollar

But suppose that number 20 announces in advance that he considers
an unequal division morally wrong, and will always vote against
any unequal division.  If this threat is credible, which it is,
number 18 will have no choice but to propose an equal split, so
number 20 now gets 6,666,666 dollars, instead of one dollar.

Now if number 20 had threatened to vote against any proposal that
did not split the money equally between himself, and number 18,
thus going for ten million instead of six million, this threat
would be less credible, and he would very likely have wound up
with one dollar.

This is a particular example of the various well known paradoxes
of utilitarianism, that utility is maximized by a firm and credible
promise to utterly disregard utility maximization.



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