05 Dec 05
I've got two kids 8 & 6, one of each, everytime I pour them a glass of coke or cut them a piece of cake. Regardless of how accurate I pour or cut, they're always squabbling over who got the bigger measure. I was telling this to my friend, and he gave me an interesting solution to the problem. Get one of them to do the pouring or cutting on the understanding that the other gets to choose first. I haven't had the opportunity to try it yet but think its got a good chance of working. Anybody who's got kids or had kids knows exactly how annoying they are when they're squabbling, so if you've got any good ideas please post them up 🙂
05 Dec 05
Originally posted by Jay PeateaYour friends suggestion is a good one.
I've got two kids 8 & 6, one of each, everytime I pour them a glass of coke or cut them a piece of cake. Regardless of how accurate I pour or cut, they're always squabbling over who got the bigger measure. I was telling this to my friend, and he gave me an interesting solution to the problem. Get one of them to do the pouring or cutting on the understan ...[text shortened]... oying they are when they're squabbling, so if you've got any good ideas please post them up 🙂
I' feel that coke and cake are ingredients for moody children, healthier food and drink may lead to calmer kids.
Try sushi!
05 Dec 05
Originally posted by invigorateSpot on that man! Make sure it's well prepared though, you can get some pretty nasty diseases from poorly preped fissshhhhh, precious.
Your friends suggestion is a good one.
I' feel that coke and cake are ingredients for moody children, healthier food and drink may lead to calmer kids.
Try sushi!
Oh, and a good sound thrashing before breakfast every morning is good too! :-P
05 Dec 05
Originally posted by invigorateI agree, there is definately something in that & its worth cutting down giving them these sugary stuff. Still its not just coke & cake. They are the same with just about everything!
Your friends suggestion is a good one.
I' feel that coke and cake are ingredients for moody children, healthier food and drink may lead to calmer kids.
Try sushi!
06 Dec 05
Originally posted by Jay PeateaThis is a well-known Nash equilibrium for dividing a cake (or other convex set) among two individuals. Can anyone think of the extension to N individuals (without cheating online)?
I've got two kids 8 & 6, one of each, everytime I pour them a glass of coke or cut them a piece of cake. Regardless of how accurate I pour or cut, they're always squabbling over who got the bigger measure. I was telling this to my friend, and he gave me an interesting solution to the problem. Get one of them to do the pouring or cutting on the understan ...[text shortened]... oying they are when they're squabbling, so if you've got any good ideas please post them up 🙂
06 Dec 05
Originally posted by telerionOne person cuts what they believe to be an nth (1/n) size piece. Everyone is then given the chance to make the piece smaller by removing some and adding it to the remainer (n-1/n). The last person to remove some of the piece gets that piece. The remaining people continue the process until the cake is divided. This will leave each person with a piece they believe to be 1/n or larger.
This is a well-known Nash equilibrium for dividing a cake (or other convex set) among two individuals. Can anyone think of the extension to N individuals (without cheating online)?
The solution is relatively simple (if not entirely practical for large groups), where it gets tricky is why you need to divide a resource so that every person believes they have the largest piece (envy-free).
06 Dec 05
Originally posted by XanthosNZwhile the mainstream media is breathing down your neck:
One person cuts what they believe to be an nth (1/n) size piece. Everyone is then given the chance to make the piece smaller by removing some and adding it to the remainer (n-1/n). The last person to remove some of the piece gets that piece. The remaining people continue the process until the cake is divided. This will leave each person with a piece they b ...[text shortened]... need to divide a resource so that every person believes they have the largest piece (envy-free).
"look!!! he got a bigger piece!!!"
06 Dec 05
Originally posted by Jay PeateaI got 8 younger brothers and sisters, and thats how we do it all the time, not only on food, but on games, seats, beds, etc For example, my two younger brothers are playing pingpong, they both think that the other has more space, so one moves the table, the other picks the side. it works great
I've got two kids 8 & 6, one of each, everytime I pour them a glass of coke or cut them a piece of cake. Regardless of how accurate I pour or cut, they're always squabbling over who got the bigger measure. I was telling this to my friend, and he gave me an interesting solution to the problem. Get one of them to do the pouring or cutting on the understan ...[text shortened]... oying they are when they're squabbling, so if you've got any good ideas please post them up 🙂
07 Dec 05
Originally posted by XanthosNZI don't know how you'd divide it so that everyone believing that they have the largest piece is a Nash equilibrium. I think your plan works though. I had a button style auction in mind.
One person cuts what they believe to be an nth (1/n) size piece. Everyone is then given the chance to make the piece smaller by removing some and adding it to the remainer (n-1/n). The last person to remove some of the piece gets that piece. The remaining people continue the process until the cake is divided. This will leave each person with a piece they b ...[text shortened]... need to divide a resource so that every person believes they have the largest piece (envy-free).
Place the point of the knife into the center of the cake and cut down. This makes a first cut line. Now keeping the tip of the knife at the center, begin slowly rotating the knife blade clockwise away from the first cut line. When some one says, "Stop!" push down to make another cut. This completes on piece. The person who called out takes the piece and the remaining people continue the process, calling stop when they want to take a piece.
In equilibrium, every one should call stop at the same time. Thus a tie-breaking rule is needed. So each person has a 1/N chance of getting a piece when they call stop.
In this equilibrium, everyone believes that they have equal pieces and could not get any larger piece.
07 Dec 05
Originally posted by telerionThe envy-free solution was found by Brahms and Taylor. It involves cutting 1+2^(n-2) pieces and has rather a lot of rules about order of choice and other things. I don't fully understand it myself.
I don't know how you'd divide it so that everyone believing that they have the largest piece is a Nash equilibrium. I think your plan works though. I had a button style auction in mind.
Place the point of the knife into the center of the cake and cut down. This makes a first cut line. Now keeping the tip of the knife at the center, begin slowly ro ...[text shortened]... s equilibrium, everyone believes that they have equal pieces and could not get any larger piece.