Re: Twenty Bank Robbers -- Solution?

[jim bell <jimbell@pacifier.com>]

At 01:13 PM 7/25/96 -0500, Igor Chudov wrote:
 
>> Twenty cypherpunks robbed a bank. They took 20 million bucks. Here's
>> how they plan to split the money: they stay in line, and the first guy
>> suggests how to split the money. Then they vote on his suggestion. If
>> 50% or more vote for his proposal, his suggestion is adopted.
>> 
>> Otherwise they kill the  first robber and now it is the turn of guy #2
>> to make another splitting proposal. Same voting rules apply.
>> 
>> The question is, what will be the outcome? How will they split the
>> money, how many robbers will be dead, and so on?
>
>I forgot to say what the GOALS are. The goals of every individual
>cypherpunk are (in from highest to lowest priority): 
>
>1. Stay alive
>2. Get as much money as possible
>3. Keep as many cypherpunks alive as possible, all other things being equal.

Getting closer:

#1 says to the rest:  "We're going to have a sequential vote, #1 to #20.  
The first 10 who vote "yes" to this proposal get to share in the loot, 
equally."

#1 must vote in favor, obviously.  The second can "guarantee" himself a part 
of the pot, if it's given out in this first round, by voting "yes."  The 
#2 is only motivated to vote "no" if he thinks he can get a better deal 
on subsequent iterations, and it's conceivable there won't BE more 
iterations if at least 9 people after him vote "yes" and he's voted no.  
Also, if this first proposal is rejected, the #2 wouldn't be in an 
appreciably better position than #1 was.  So #2 will vote yes, as well.

This procedure will repeat.  As more people vote "yes," the danger in 
defecting (voting "no") will increase, because it will be effectively 
certain that  someone else will collect that reward.  As long as there are 
more people left to vote than would be necessary to increase the vote total 
to 10, nobody can afford to vote "no."

So the proposal will pass, and the first 10 intelligent people will win. 



Jim Bell
jimbell@pacifier.com