Condom Logic #1

26 Nov 2004

In Swingerland, there lives a band of condom collectors who live according to the logical application of three simple rules in priority order:
Priority 1. Protect your position as a member of the condom collectors
Priority 2. Collect as many condoms as possible without risking your membership
Priority 3. Get rid of as many other condom collectors as possible without risking your own condoms
The condom collectors govern themselves by a simple democratic process: The senior condom collector makes all the policy proposals then puts them to the vote. If the majority reject his proposal they expel him from the group, and the leadership passes to the next most senior member.
One day, the senior condom collector and four others successfully infiltrated an SH Munch, gathering one hundred condoms between them. Naturally, it fell upon the senior to decide how the condoms should be divided and, by tradition, only the five who actually took part in the theft were allowed to vote on his proposal. If he were to lose the vote, he would be thrown out and the next most senior condom collector would propose how to split the loot, and so on.
Given that all the condom collectors are supremely logical, and their proposals/votes are based purely on the priorities of survival within the group, personal profit, and removal of the competition, as defined above, how many condom collectors were ejected from the group, and how many condoms did each survivor end up with?

26 Nov 2004

So the head condom collector has to divide the condoms without getting chucked out for being unfair?

26 Nov 2004

Are the Condoms Used or Un-used ??
Fred(medic1)

26 Nov 2004

By lose the vote does a majority have to be reached or is it a unaimous deciosn required?
If the latter - one collector remained (4 ejected) and the final one had 100 condoms.
(Sorry my spelling is crap but i can't be arsed to change it!)

26 Nov 2004

Quote by MISSCHIEF
So the head condom collector has to divide the condoms without getting chucked out for being unfair?

Fairness has nothing to do with it. These people are ruthless and base all their decisions on the priorities listed above. But, yes, the leader has to try and maintain his position with the minimum amount of bribes. The questions you need to ask yourself are how many votes does he need, and how does he secure those votes, bearing in mind that the other collectors will also be considering the consequences of throwing him out.

26 Nov 2004

Quote by Ice Pie
the next most senior condom collector would propose how to split the loot, and so on.

Not sure I like the idea of splitting condoms confused

26 Nov 2004

Quote by AndyS-NE
By lose the vote does a majority have to be reached or is it a unaimous deciosn required?

Majority decision.

If the latter - one collector remained (4 ejected) and the final one had 100 condoms.

No. If the senior proposed to keep them all for himself, he would be voted out on the grounds that three of the other collectors know that they would get some condoms in the next round of voting. The scenario of 4 in succession voted out can't happen because when you get down to 2 there is no majority.

26 Nov 2004

So he can just deal them out equally until there are none left?

26 Nov 2004

Quote by Ice Pie
By lose the vote does a majority have to be reached or is it a unaimous deciosn required?

Majority decision.

If the latter - one collector remained (4 ejected) and the final one had 100 condoms.

No. If he proposed to keep them all for himself, he would be voted out on the grounds that three of the other collectors know that they would get some condoms in the next round of voting.
Yeah - ii didn't think it would be that easy for a total agreement as the lowest ranked memeber would keep saying no unitil the whole stash came to him.
Time to get me thinking cap on!

26 Nov 2004

Quote by MISSCHIEF
So he can just deal them out equally until there are none left?

He would survive if he did that and get 20 condoms for himself, but his second priority is personal profit. He can take more than 20 condoms and still stay in.
Remeber, it's a majority vote, so he only needs the support of two colleagues.

26 Nov 2004

Which Munch did they infiltrate? :shock: :shock: :shock:

26 Nov 2004

The best i can come up with
Two are ejected.
The head honcho gets 34 condoms, there other two get 33 each.
Based on the the leader and the other two will vote yes as it will protect their positions, they have an equalish share without jeopardising their postion, and will get rid of the maximum amout of collectors without jeopardising their postion.
I'll keep thinking about it but the best i can do at the moment!

26 Nov 2004

this is bugging me i am starting to doubt myself!!what happens when if there were two collectors left / a 50/50 split in the votes would the top one have the casting vote?

26 Nov 2004

Quote by AndyS-NE
The best i can come up with
Two are ejected.

Only the leader can be ejected if the majority vote against him. If the first leader gets ejected, his successor can easily survive by bribing the two who can't possibly get thrown out.

The head honcho gets 34 condoms, there other two get 33 each.

A 3 way split would ensure his survial, but he can still make more profit.
You need to think of the problem from the point of view of each collector individually. What would be the consequences to each of them if they eject the leader and let the next in line take over, and so on?

26 Nov 2004

Quote by AndyS-NE
this is bugging me i am starting to doubt myself!!what happens when if there were two collectors left / a 50/50 split in the votes would the top one have the casting vote?

Yes, a majority is needed to get him out. In the event of a tie, the leader therefore wins.

26 Nov 2004

I get you now - cheers

26 Nov 2004

I bet it was the Notts Munch!!
I told Clare their security wasn't up to much. confused

:? :? :?

26 Nov 2004

Quote by Sgt Bilko
I bet it was the Notts Munch!!
I told Clare their security wasn't up to much. :? :? :?

I take it you heard about those two gate crashers and how fast they ran when they found out who we were?

:rotflmao: :rotflmao: :rotflmao:

26 Nov 2004

Had someone changed the lightbulb (sorry - lamp) confused

:

26 Nov 2004

I think i have an answer but before i post it can i check one thing out, does a memeber of the club have to have at least one condom or can they remain in the club with none to fight another day?

26 Nov 2004

Quote by AndyS-NE
I think i have an answer but before i post it can i check one thing out, does a memeber of the club have to have at least one condom or can they remain in the club with none to fight another day?

Their first priority is survival within the group, so if they needed to accept being skint as a condition of staying in, they would put up with that.

26 Nov 2004

OOooooh soooooooo if the head collector kept divided the condoms up equally between four of them, left one person with none??
He would still win the casting vote?

26 Nov 2004

None are evicted all 100 go to the top man because,Hard to explain but here i go.
The first priority is to stay in - no matter what the first guy offers only he can be evicted but men 2 and 3 are aware of this themselves when it comes to thier voting round so they would agree as to not jepardise thier place in the club, as only the first three men can be evicted (the fourth round of voting would always go the fourth mans way (two voters - joint vote goes to the higher person) the first three wouldn't put them selves in teh postion to get voted off.
Poor explaination i know but thats my final answer and will wait for the full explaination to put me out of my misery!

26 Nov 2004

Quote by MISSCHIEF
OOooooh soooooooo if the head collector kept divided the condoms up equally between four of them, left one person with none??
He would still win the casting vote?

Yes but he doesn't need that much support - he only needs two people to support him.
Clue: Start from the point of view of the most junior member of the group - how does the fate of successive leaders affect him personally?

26 Nov 2004

So am i wrong?

26 Nov 2004

Quote by AndyS-NE
None are evicted all 100 go to the top man because,Hard to explain but here i go.
The first priority is to stay in - no matter what the first guy offers only he can be evicted but men 2 and 3 are aware of this themselves when it comes to thier voting round so they would agree as to not jepardise thier place in the club, as only the first three men can be evicted (the fourth round of voting would always go the fourth mans way (two voters - joint vote goes to the higher person) the first three wouldn't put them selves in teh postion to get voted off.
Poor explaination i know but thats my final answer and will wait for the full explaination to put me out of my misery!

Based on the 3 priorities, If the leader proposes to take all the condoms for himself, he will be voted out by all of the others for various reasons - They can all survive without him, and some of them can make a profit.

26 Nov 2004

when you going to give out the answer cause i am beat now- going for a cigarette to think about it!!

26 Nov 2004

do they only apply the logic to that round of voting - or the consequeces of the vote?

26 Nov 2004

OK the two most junior get none. The next two get two each (they get the zero juniors share of 1) - the leader keeps the other 96.
They will go with this vote, cos they don't want to be cast as juniors, which they will if they disagree, and one of the juniors would take his place and gets the 2 (2 more than he would have had).
Yayyyyy did I win? do I get a prize? :bounce:

26 Nov 2004

Quote by MISSCHIEF
OOooooh soooooooo if the head collector kept divided the condoms up equally between four of them, left one person with none??
He would still win the casting vote?

Or head collector could offer to only split with the next two senior collectors (the two who would also be at risk of being voted off if they become successors) and give the least two senior none. Still having a majority and getting a larger share.