Fair Division: The Moving Knife Method


– WELCOME TO A LESSON
ON THE MOVING KNIFE METHOD OF FAIR DIVISION. A SOMEWHAT DIFFERENT APPROACH
TO CONTINUOUS FAIR DIVISION IS CALLED
THE MOVING KNIFE METHOD. STEP ONE, A REFEREE STARTS
MOVING A KNIFE OR VERTICAL LINE FROM LEFT TO RIGHT
ACROSS AN OBJECT. TWO, AS SOON AS ANY PLAYER
FEELS THE PIECE TO THE LEFT OF THE KNIFE
OR VERTICAL LINE IS WORTH A FAIR SHARE,
THEY SHOUT, “STOP.” THE REFEREE THEN CUTS THE OBJECT AT THE CURRENT KNIFE
OR LINE POSITION. THE PLAYER WHO CALLED, “STOP,” GETS THE PIECE TO THE LEFT
OF THE KNIFE OR LINE. STEP THREE, THIS PROCEDURE
CONTINUES UNTIL THERE IS ONLY ONE PLAYER
LEFT. THE PLAYER LEFT GETS
THE REMAINING PIECE. SO AS AN EXAMPLE, LET’S USE
THE MOVING KNIFE METHOD TO DIVIDE UP AN ISLAND
AMONG FOUR PLAYERS, P SUB 1 THROUGH P SUB 4. SO THE REFEREE WOULD START
WITH THIS VERTICAL LINE, AND START MOVING THE VERTICAL
LINE TO THE RIGHT. LET’S SAY, FOR EXAMPLE, AS THE
LINE REACHES THIS POSITION HERE, PLAYER TWO SHOUTS, “STOP,” AND THEREFORE PLAYER
TWO RECEIVES THE PIECE TO THE LEFT. THE REFEREE THEN BEGINS TO MOVE
THE VERTICAL LINE TO THE RIGHT. AS IT REACHES THIS POSITION
HERE, LET’S SAY PLAYER FOUR SHOUTS,
“STOP.” THEN PLAYER FOUR RECEIVES
THIS PIECE HERE. ONCE AGAIN THE REFEREE BEGINS
MOVING THE LINE TO THE RIGHT. AS IT REACHES
THIS POSITION HERE, LET’S SAY PLAYER THREE SHOUTS,
“STOP,” AND THEREFORE PLAYER THREE RECEIVES
THIS PIECE OF THE ISLAND. AND THEN FINALLY PLAYER ONE, THE REMAINING PLAYER,
RECEIVES THE REMAINING PIECE. THIS IS THE MOVING KNIFE METHOD
OF FAIR DIVISION. I HOPE YOU FOUND THIS HELPFUL.  

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