Dividing money brain teaser

[jryan]

No, there isn't. You are making up information about salaries and such precisely because the problem lacks specificity. The only solution that makes any sense given the (limited and incomplete) information at hand is a 999997,0,1,0,1,0,1 split. The even numbered execs get nothing, execs numbers 3, 5, and 7 get a pittance, and exec #1 gets almost everything.

 

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.

[D H]

jryan, you're still thrashing. Suppose the jobs have an immense amount of value. Execs #2, #3, and #4 may well go along with anything that exec #1 proposes because they foresee that should they vote against his proposal they will suffer the same fate as will exec #1. In other words, exec #1 can propose a split in which all of the money goes to exec #1; nobody else gets a dime. On the plus side, everyone gets to keep their fantastic jobs.

 

We don't know what the value of the jobs are. All we can say is that the problem is underspecified -- or we can ignore the salary aspect and treat this as a mathematical rather than humanistic problem. (In which case you get to the Nash equilibrium solution.)

[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.

[Zolar V]

I think you could just throw all of your maths and hard thinking away and just base the motivation of greed and the demotivator of fear on how the money will be split, and with that being said, the best split would be 1/4

[D_G]

Even though this is late, I think the answer would go like this. 1 offers 2,6,7 1/3. This is the only viably solution for everyone to keep their jobs. 2 will vote, because if it comes to him, he will have to offer the same deal to 3,6,7. and of course 6,7 would vote because if it drops to number 3 the only way then to keep their job would be to offer 4,5 half. Since they all wish to keep their jobs first, and they all hold the same position, this is the only viable way for everyone to keep their jobs. (Seniority does not imply a higher position, and in most cases does not mean the next person in line would inherit their salary should it be more.)

[D_G]

And now that I've given it more thought, my previous statement is wrong. 1 takes 700k, offers 100k to 5,6,7. If 2 makes it to vote, they would only need 2 other votes, however 5/6 votes stock drops, because they stand to gain nothing when it reaches 4. likewise 7s vote would only be vitally important in 1s vote, while 5/6 would be targets until 4, but 4 stands to make the most money by always voting no. If it reaches 4, he could literally offer anything to 7 and get a yes, since the same would also apply for 5s vote. and 2 and 3s vote would most likely be the same, offering themselves the lion's share while offering a pittance to 5 and 6. to ensure the vote goes through, 1 would offer 1/10, since it would be far more than 5,6,7 stand to gain by voting no.