From: David Sternlight <david@sternlight.com>
Date: Fri, 26 Jul 1996 19:58:14 +0800
To: Jeremey Barrett <ichudov@algebra.com>
Subject: Re: Twenty Bank Robbers -- CLARIFICATION
In-Reply-To: <199607251813.NAA02650@galaxy.galstar.com>
Message-ID: <v03007803ae1e1fb13219@[192.187.162.15]>
MIME-Version: 1.0
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At 4:33 PM -0700 7/25/96, 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):
>
>1 must propose that 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19 all split
>the money evenly. All of these will vote for it, assuming they're all
>perfectly smart and deduce the inevitable outcome.
>
>I arrived at this working backward from the case where two robbers are left.
>
>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. Since 19 knows this, 19
>will vote for whatever 17 says, which must include 19 in the deal, and so
>forth. Eventually you arrive at the conclusion that 1,3,5...,19 must
>all agree to split the money at the beginning.

Your solution fails if the proposer is determined by lot, stage by stage.
Any other approach will be felt unfair by some, but that approach will be
thought fair by all.

David