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Method of Markers

Method of Markers. 3 players, Ali, Bob, and Carol, agree to divide the colorful toys above by the method of markers. Method of Markers. Ali. Ali. Ali doesn’t really care what colors or shapes she gets, so she uses her markers to divide the objects into 3 piles of 5. Method of Markers. Bob.

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Method of Markers

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  1. Method of Markers 3 players, Ali, Bob, and Carol, agree to divide the colorful toys above by the method of markers.

  2. Method of Markers Ali Ali Ali doesn’t really care what colors or shapes she gets, so she uses her markers to divide the objects into 3 piles of 5.

  3. Method of Markers Bob Bob Bob really likes the blue objects. So a fair division to him is one which can have fewer objects as long as some are blue, or more objects if none are blue, as shown.

  4. Method of Markers Carol Carol Carol’s preference is for squares, so she places her markers as shown:

  5. Method of Markers Carol, Bob Ali Ali Bob Carol Looking at everyone’s markers together:

  6. Method of Markers Carol, Bob Ali Ali Bob Carol We look from left to right to find the first marker anybody placed. Since that is Bob’s, he gets his first segment.

  7. Method of Markers Carol, Bob Ali Ali Bob Carol We look from left to right to find the first marker anybody placed. Since that is Bob’s, he gets his first segment.

  8. Method of Markers Carol, Bob Ali Ali Bob Carol We give Bob his segment, and erase his other markers, since he’s already received his share.

  9. Method of Markers Carol Ali Ali Carol We give Bob his segment, and erase his other markers, since he’s already received his share.

  10. Method of Markers Carol Ali Ali Carol We now ignore (for the moment) the other players’ first markers, and look for the first second marker.

  11. Method of Markers Carol Ali Ali Carol The first second marker belongs to Ali, so she gets her 2nd segment.

  12. Method of Markers Carol Ali Ali Carol The first second marker belongs to Ali, so she gets her 2nd segment.

  13. Method of Markers Carol The first second marker belongs to Ali, so she gets her 2nd segment.

  14. Method of Markers Carol Notice that the red circle was not part of either of the piles given out so far, so it is just left behind (for now).

  15. Method of Markers Carol We can continue in the same way as long as needed. In this case, all that remains is to give Carol her 3rd segment

  16. Method of Markers Carol We can continue in the same way as long as needed. In this case, all that remains is to give Carol her 3rd segment

  17. Method of Markers At this point, everyone has received a share that they consider fair, and some pieces are leftover. The leftovers can be given in any random way - after all, everyone is already happy with their share, so they can’t really complain if they don’t get anything more. (Remember – our goal is fair not greedy.)

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