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landmark Inner circle within a triangle 5194 Posts |
Here's a dandy little logic puzzle.
Five pirates, Aronson, Berglas, Curry, Diaconis, and Elmsley, (let's call them A, B, C, D, E) have found a treasure of $100. They decide to split it amongst themselves according to the following rules: 1) Pirate A will make a proposal as to how to split the money. 2) In order for the proposal to be accepted, the proposal must receive a majority of the votes, not just 50%. 3) If the proposal is accepted, no other proposals occur, and the money is distributed according to the proposal. 4) If the proposal is rejected, the pirate is killed, and then the next pirate gets to make a proposal with the same rules. The question is: If the pirates are all perfect logicians, what proposal should A make in order to maximize his profit? Assumptions: 1) The pirates as stated before have perfect logic and assume perfect logic from the others. 2) Each pirate's first priority is survival. 3) Each pirate's second priority is to make money. 4) Each pirate's third priority is to to see the death of the other pirates. Example: suppose A proposes an even distribution of the money. You might think that that would satisfy everyone. But on the other hand, B, C, D, and E might vote against such a proposal because by killing A they would have fewer people to divide up the $100 when B makes his proposal. On the other hand, if A proposes to keep all the money for himself, that too would be a non-starter because the others would vote to kill him.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
Simon Aronson 1943 - 2019 74 Posts |
Hey, just a minute! While I appreciate the august company I’m among, I’m not too keen on the “ordering” of the pirates (since I’m personally the “first” to walk the plank). With only a hundred bucks at stake, I’d rather pay to stay alive.
But, in the interest of keeping your puzzle (as well as myself) alive, I will graciously quit the list, and in my stead I am appointing F (=Funsky) who, to maintain the required alphabetical order, will naturally go to the end of the list. So, with the list now restructured at B, C, D, E, F, let the logicians go forth. Simon Aronson
"There's a world of difference between a spectator's not knowing how something is done versus his knowing that it can't be done."
Shuffle-bored (1980) http://www.simonaronson.com |
Mergel Funsky New user 14 Posts |
Yeah, I like that idea.
Just send me the $100 by PayPal. Mergel Funsky
“Just because something’s imaginary doesn’t mean it isn’t real.”
-- Mergel Funsky Frontispiece, Who Is Mergel Funsky? (unpublished and likely to remain so) |
landmark Inner circle within a triangle 5194 Posts |
But Simon, A stands to win some money if he behaves as all good logicians should.
And Mergel, that proposal will definitely get you voted off the island. In a very permanent-type way.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
WilburrUK Veteran user 389 Posts |
Does the pirate making the proposal get a vote, or just the others?
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WilburrUK Veteran user 389 Posts |
If so, I reckon I'll change my name to Annemann and step into the breach, reckon there's an easy $97 in it for me.
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landmark Inner circle within a triangle 5194 Posts |
Quote:
On May 21, 2015, WilburrUK wrote: Excellent! Yes, the pirate gets a vote. Perhaps, WilburrUK, you'd like to explain to readers how Annemann got his $97...
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
WilburrUK Veteran user 389 Posts |
I'll do my best.....if we ever get the the 2-pirate scenario, the results are obvious, so we'll start there and work backwards...
With 2 pirates left (D and E) D Will accept his own proposal, because not doing so is suicide E Will reject any proposal, because doing so guarantees him the best possible outcome (survival, all the loot and all the others dead) So any proposal will be tied, and D will be killed A DEAD B DEAD C DEAD D DEAD E $100 All the pirates know this from the start. When 3 pirates left remain (C,D,E): C will accept, or he's swimming with the fishes. D Holds the casting vote, and will accept any offer as rejecting it moves us onto the 2-pirate situation, in which D is a dead man E will do anything to see it rejected, as this guarantees him the best outcome, but he's outnumbered Therefore C can propose keeping all the money himself and is guaranteed an ally in D A DEAD B DEAD C $100 D $0 (but survives) E $0 (but survives) All the pirates know this from the start. With 4 pirates (B,C,D,E) B Will accept his own proposal, because otherwise, he's walking the plank C Will reject any offer as getting to the 3 pirate situation is better than any offer B can make D Will accept anything better than penniless survival (priority 3 is other pirates killed, so he will reject $0 but accept $1) E Will accept anything better than penniless survival (priority 3 is other pirates killed, so he will reject $0 but accept $1) So B will offer both D and E $1 (as he needs both their votes) but C nothing as there's no persuading him A DEAD B $98 C %0 D $1 E $1 All the pirates know this from the start. With 5 pirates (A,B,C,D,E) A Will accept his own proposal, or else he's got an imminent appointment with Davy Jones B Will accept any offer that gets him more than the $98 that he gets from the 4 pirate scenario C Will Accept any offer that gets him more than $0 D will accept any offer that gets him more than $1 E Will accept any offer that gets him more than $1 A Needs 2 allies, one of whom will be C (because C is the cheapest) the other will be either D or E (doesn't matter which) So A Proposes A $97 B $0 - Which B will reject, but he's outnumbered C $1 - which C accepts, because it's better than the $0 he will get if the proposal fails D $2 - which D Accepts, as it's better than the $1 he will get if the proposal fails (Aronson favours Diaconis for reasons too complex to explain here) E $0 - Which E will reject, but he's outnumbered and the proposal is accepted by 3 votes to 2 |
landmark Inner circle within a triangle 5194 Posts |
And there you have it...
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
landmark Inner circle within a triangle 5194 Posts |
Quote:
(Aronson favours Diaconis for reasons too complex to explain here) Best I can tell, unless I've missed something, A can give the $2 to E instead of D as well.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
WilburrUK Veteran user 389 Posts |
Quote:
On May 22, 2015, landmark wrote: You're right, I just threw that line in there, because I like to imagine people scratching their heads about the reason |
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