jryan

I'm not thrashing any more than you are, DH. You are simply arguing that we have no way of knowing which way it would go so therefor your choice is teh right one. But further note that this version of the game doesn't ask you to maximize the payout to the proposer. Instead it states explicitly that the execs would prefer few execs... so the predisposition of other voters is to vote no. We can also assume that the proposer wants to keep their job, so I still don't see where your pirate solution is valid.

I'm attributing a value to the job, which makes far more sense then assuming it's valueless. It also doesn't play out the same as pirate because the rewards and punishments are different. There is a lot assumed in the pirate puzzle that, if assumed in the sales exec puzzle, would make a rather peculiar situation. In other words, the fact that they are pirates is important to how the pirate puzzle plays out. In the case of the sales exec, however, the $1 doesn't work because the intrinsic valuation is different. Lacking any further information it is safe to assume that the pirates could and would concede to the toughest pirate and accept 1 gold. In the case of a sales exec it is safer to assume a solution based on compromise. As such, my solution balances fairness, need and security since all would play a part in that determination. Absent other information you can also only divide the known bonus and balance that against the job.

We all are until the obvious solution arises. As you mentioned, the fairness aspect plays into this decision, which is why #5 is a problem. 7 can't happen, and 6 is easy, but #5 places "Job" directly at odds with "Bonus", and without job specifics (salary, turnover, etc.) we are left guessing. If #5 made $350,000 a year salary, and #7 made $150,000 then the fair split would be $400,000 to #5 and $600,000 to #7.... but we don't know that so we can't answer that. If we assume that #5s compentation is $1 million or greater then we can assume that the fair split is to give all the money to #7 and #7 really has all of the leverage in that case. I think that even absent the information there is enough here to answer the question, however, and there is a way to deduce a fair distribution in round 1 that would garner support from the 3 necessary voters due to the variability of possibilities after the initial offer is rejected. A bird in the hand is worth two in the bush. In this case, assuming $1 million+ salaries, neither 6 or 3 are guaranteed any money in any permutation and would accept the offer made by #1 because it is the only given that have while #2 would accept it because they are guaranteed money and job which the wouldn't be in round #2.

Here is a quick matrix, based on the assumption that the proposer is most interested in keeping their job, and therefor has no real leverage: Round 1 - 7, total votes needed=3, pool=5, share=$333,333.33 Round 2 - 6, total votes needed=2, pool=4), share=$500,000.00 Round 3 - 5, total votes needed=2, pool=3), Share=$500,000.00 Round 4 - 4, total votes needed=1, pool=2), share=$500,000.00 Round 5 - 3, total votes needed=1, pool=1), Share=$???????????? Round 6 - 2, total votes needed=0, pool=0), Share=$1,000,000.00 By round 5 Exec#5 really has no real control, and may need to hand all $1,000,000 to Exec#7 just to keep their job. So I see no reason to treat #7 any differently than #6. As a matter of fact, #6 now seems completely out of the running for any money as round 5 would almost certainly resolve the issue in #7s favor as #5 would be looking to keep their job. #5 would definitely have leverage over 7 in a "take it or leave it" fashion, but then #7 would have leverage over #5 in a "make me happy or you're fired" fashion. Merged post follows: Consecutive posts mergedAfter some consideration I think that #7 should be left out of the equation rather than #6. If #6 is a rational person then they have to realize that, while they can't lose their job, they have no chance of ever getting to make their "$1 million to me" proposal. #5 would split the bonus with #7 before that (though the nature of that split would be interesting!). So I would change my group to 2,3 and 6 getting $333,333.33 as 2 and 6 have nothing to lose by voting yes, and 3 won't get a better deal either way. Merged post follows: Consecutive posts mergedAlso, I figured you all might be interested in this article: http://euclid.trentu.ca/math/bz/pirates_gold.pdf It's a discussion of a similar application of game theory.. but I think the restrictions and demands are sufficiently different that we can cast out their conclusion.

True, as such #7 is also always a yes vote when you give them money. But they can never make more than $500,000. But I stand by the decision that the plan creator must accept $0 or $0.01 of the total payout simply to maximize their chance to keep their job. As such, by the second in line viting "No" to any plan they are essentially voting themselves into seniority, but with $0 compensation. With the exception of #6 who will always vote against any plan other than their own because they are the only one with the potential to get everything. Leaving #2, 3, 4 and 5 at play, obviously. Also, I would say that we have to decide based on the info given since it's not a given that various sales executives would even know each others total compensation, so that knowledge should not be required. Actually, given that compensation is not known, we will have to ignore the seniority aspect, I think, and realize that the decision maker will always have their job on the line and therefor try to maximize the votes by taking $0 on $0.01 in compensation.... except that bastard #6. Merged post follows: Consecutive posts mergedSo, if we assume that #1 is gone, and the vote choice falls to #2, his choice would be: #2 - 0 #4 - $500,000 #? - $500,000 In this case #7 is not necessary to win, so it is really a toss up for #5 and 7... as so I think it is in #2, 3 and 7s bets interest to take option 1 rather than risk losing everything (though it is impossible for #7 to lose their job, so their vote is always dependent on bonus money).

Well, I think that #2s strategy might have to include #5 as #6 can hold out for a $1 million pay day, #3 will be eyeing the senior spot leaving 4 and 7 I suppose... which would then need to bet a $0-$500,000-$500,000 split to make it worth #4 and #7's consideration as they are already looking at a $500,000 payday if it makes it to #4s choice. So in #2s best interest, answering the question with the data provided, the proposal I stated still seems to be the best option for all 4 yes voters as #1 skips the pay out in favor of their job and #2 and #3 get a pay out that they would have had to skip otherwise, and #7 plays the pivotal vote as they were never going to get more than $500,000 anyway, but the cascading cancer of seniority + Bonus would likely mean that #6 would wind up with all the money and seniority anyway.

Well shoot. That puts some unknowns into the original question (salary differences, etc.) that would need to be considered. But in your #3,5 and 7 scenario it is not in #5's best interest to vote for #1's solution as you spelled it out as he is better off voting against #1 and holding out for a $500,000 pay day that he would likely get in later votes.

If the order of voting was known before hand, the first exec would split the money evenly between #2, 3 and 4, forgoing his own compensation (or grant himself one penny) but keeping him his job and giving #2, #3 and #4 a split they would not otherwise be entitled to due to their place in line. Merged post follows: Consecutive posts mergedOops, hang on a minute... scratch that. #4 would be entitled to $500,000. So yeah, it is in #6s best interest to always vote no, so #6 will never be floated any money. So the money would be divided like this: #1 - $0.01 #2 - $333,333.33 #3 - $333,333.33 #4 - $0 #5 - $0 #6 - $0 #7 - $333,333.33 This way #2 and #3 get a split greater than or equal to what they would expect anyway, and #7 Would certainly vote for it as they would be eligible for no money otherwise. For #1, passing on the money is the only way to keep their job.

I created this to explain to a friend the difference between liberals, Liberals and Libertarians: