7 Sales executives have 1 million dollars to divide amongst themselves. The most senior sales executive propses a particular split and then everyone votes (each person's vote is equal). If at least 50% of the people accept, then the money is divided the way that was suggested. Otherwise the sales executive who propsed it gets fired...and then we move on to the next senior sales exec and the whole process repeats. The executives are rational (want to keep their jobs first and also get as much money as possible), and they also would prefer fewer executives in the group if given a choice (all else equal). How should the cash be split ?
The 1 million is split between the senior exec and three others, ie each gets 250k, the remaining 3 get nothing. The 4 execs "in the money" will outvote the 3 who get nothing.
Interesting puzzle. Not sure I am happy with my answer, but here's what I have (so far): Assuming full "rationality" and the order is by seniority, the most senior guy keeps all but three bucks, offering a dollar each to the most junior guy, the guy two notches above him and the guy two more notches up. To solve it, work backwards. What happens when it's just one guy? He keeps it all. What happens when it's two guys? One guy votes for him to keep it all and the other guy's vote doesn't count. Etc. But it wouldn't work in real life. The most junior guy has zero chance of being fired, so unless somebody offered him a serious chunk of change, he'd say no. Even if it went all the way down to the second guy who voted to give himself the full bonus and the junior guy gets nothing, he'd at least have the satisfaction of telling the other chiselers to go @*&( themselves and laugh as they got fired. It'd only cost him a dollar. More interestingly, what happens next year if the survivors managed to clean out some of the team?
Exactly, the answer only works if the most junior executive values one dollar as being significantly better than getting nothing. She might be happy to sacrifice that dollar in exchange for being promoted (by virtue of the elimitation of competition) to no.2 executive. So therefore, the no.1 executive should buy their vote outright in the first place and propose the following: No.1 exec $250,000 No.3 exec $250,000 No.5 exec $250,000 No.7 exec $250,000 If 3, 5, and 7 don't vote for 1's proposal, they will all end up getting nothing and instead No.6 will walk away with all of the money and still have a job next year.
can YOU answer why does it work out like this? why not just toast first 2 slices both sides, then the third? brain teaser for you
I suspect you may have gone and made the puzzle unsolvable. If we accept the premise that the newbie assigns any value whatsoever to any other executive getting the axe, then who's to say what that value is? It might be 300k. It might be a million. That's why I went with a dollar. The weak spot to my answer (IMO) is what if keeping your job is significantly more important than getting any bonus? Think Zimbabwe for a moment. A million might be peanuts, and the senior guy might be very willing to not get anything other than his usual paycheck. I haven't walked this path yet, so I don't know.
Agree. There isn't enough information to make that kind of judgement so I probably shouldn't have mentioned it in the first place. If we stick with the original information where each executive wants to get as much money as possible and also wants to keep their job I believe the answer I gave is the most appropriate. No. 3, 5, and 7 know this is the maximum amount they can get for supporting No.1's proposal. If they don't support No.1's proposal they will end up getting nothing. If you offer only $1 to No. 3, 5 and 7 they know they have not received as much as they could and therefore will not vote for No.1's proposal. I guess it would be nice to hear what the answer should be.
Ultimately the new guys have more incentive to be naysayers and let their elders get kicked off the islan. . .errr. . . removed from the bonus pool, especially the two most junior guys. Their chance of getting fired is zero. Answer please.