Fair Division:  The Sealed Bid Method

Fair Division: The Sealed Bid Method

November 9, 2019 8 By Luis Garrison


– WELCOME TO A LESSON
ON THE SEALED BIDS METHOD OF FAIR DIVISION. THE SEALED BIDS METHOD PROVIDES
A METHOD FOR DISCREET FAIR DIVISION, ALLOWING FOR THE DIVISION
OF ITEMS THAT CANNOT BE SPLIT
INTO SMALLER PIECES, LIKE A HOUSE OR A CAR. THE METHOD DOES
REQUIRE ALL PARTIES TO HAVE A LARGE AMOUNT OF CASH
AT THEIR DISPOSAL TO BALANCE OUT THE DIFFERENCE IN ITEM VALUES. THIS METHOD CAN BE USED FOR SUCH
THINGS AS A DIVORCE SETTLEMENT OR DISSOLVING BUSINESS ASSETS. THE METHOD BEGINS BY COMPILING
A LIST OF ITEMS TO BE DIVIDED, AND THEN STEP ONE, EACH PARTY INVOLVED LISTS
IN SECRET A DOLLAR AMOUNT THEY VALUE EACH ITEM
TO BE WORTH. THIS IS THEIR SEALED BID. TWO, THE BIDS ARE COLLECTED
FOR EACH PARTY. THE VALUE OF ALL THE ITEMS
IS TOTALED, AND DIVIDED BY THE NUMBER
OF PARTIES OR PLAYERS. THIS DEFINES THEIR FAIR SHARE. THREE, EACH ITEM IS AWARDED
TO THE HIGHEST BIDDER. FOUR, FOR EACH PARTY THE VALUE
OF ALL ITEMS RECEIVED IS TOTALED. IF THE VALUE IS MORE THAN THAT
PARTY’S FAIR SHARE, THEY PAY THE DIFFERENCE
INTO A HOLDING PILE. IF THE VALUE IS LESS THAN THAT
PARTY’S FAIR SHARE, THEY RECEIVE THE DIFFERENCE FROM
THE HOLDING PILE IN CASH. THIS ENDS THE INITIAL
ALLOCATION. AND THEN FIVE, IN MOST CASES
THERE WILL BE A SURPLUS, OR LEFTOVER MONEY IN THE HOLDING
PILE. THE SURPLUS IS DIVIDED EVENLY
BETWEEN ALL PLAYERS. THIS PRODUCES
THE FINAL ALLOCATION. SO LET’S LOOK AT AN EXAMPLE. A GRANDMOTHER LEAVES ALL OF HER
ASSETS TO CHARITY EXCEPT THREE ITEMS. SHE LEAVES HER HOUSE, CAR, AND DIAMOND RING TO HER THREE
GRANDCHILDREN. WE WANT TO DIVIDE UP THE ASSETS
USING THE SEALED BIDS METHOD. SO EACH GRANDCHILD HONESTLY
AND INDEPENDENTLY PLACED THE FOLLOWING BIDS IN THOUSANDS
OF DOLLARS FOR THE THREE ITEMS. REMEMBER, THE HIGHEST BIDDER
RECEIVES THE ITEM. SO LOOKING AT THE HOUSE,
HERE’S THE HIGHEST BID, SO PLAYER TWO
RECEIVES THE HOUSE. FOR THE CAR HERE’S THE HIGHEST
BID. PLAYER THREE RECEIVES THE CAR. AND FOR THE RING HERE
IS THE HIGHEST BID. NOTICE PLAYER TWO ALSO RECEIVES
THE RING. SO PLAYER ONE RECEIVES NOTHING, PLAYER TWO RECEIVES THE HOUSE
AND THE RING, AND PLAYER THREE
RECEIVES THE CAR. NOW LET’S DETERMINE EACH
PLAYER’S FAIR SHARE FOR THE FIRST SETTLEMENT. REMEMBER, TO FIND THE FAIR SHARE
FOR EACH PLAYER, WE SUM THEIR BIDS AND DIVIDE BY
THE NUMBER OF PLAYERS. SO FOR PLAYER ONE THE SUM OF THE
BIDS IS 159 DIVIDED BY 3=53, AND THEREFORE PLAYER ONE’S FAIR
SHARE IS $53,000. NOTICE PLAYER TWO’S FAIR SHARE
WOULD BE $61,000, AND PLAYER THREE’S FAIR SHARE
WOULD BE $46,000. NOW WE LOOK AT THE VALUE OF THE
ITEMS RECEIVED AND THE FAIR DOLLAR SHARE. IF THE TOTAL OF THE ITEMS
RECEIVED IS MORE THAN HIS OR HER
FAIR SHARE, THEN THE PLAYER PAYS THE ESTATE
THE DIFFERENCE. IF THE TOTAL OF THE ITEMS
RECEIVED IS LESS THAN HIS OR HER FAIR
SHARE, THEN THE PLAYER GETS
THE DIFFERENCE IN CASH. WELL, AGAIN,
PLAYER ONE RECEIVED NOTHING, AND THEREFORE THEY RECEIVE
THEIR FAIR SHARE IN CASH, OR $53,000 IN CASH
FROM THE ESTATE. BUT PLAYER TWO RECEIVED
THE HOUSE AND THE RING, WHICH THEY VALUED AT $175,000. AND THEIR FAIR SHARE
WAS ONLY $61,000, SO THEY PAY THE DIFFERENCE
TO THE ESTATE. AND THEREFORE THEY PAY $114,000, BUT THEY DO RECEIVE THE HOUSE
AND THE RING. AND THEN PLAYER THREE
RECEIVED THE CAR, WORTH $10,000, BUT THE FAIR SHARE WAS $46,000. AND THEREFORE PLAYER THREE
RECEIVES THE CAR, AND ALSO STILL RECEIVES
$36,000 IN CASH FROM THE ESTATE. NOTICE HOW BEFORE THE ESTATE
PAYS THESE CASH AMOUNTS, IT DOES RECEIVE $114,000 FROM
PLAYER TWO. SO TO DETERMINE THE FINAL
SETTLEMENT, AND AGAIN THE ESTATE IS PAID
$114,000 FROM PLAYER TWO, BUT IT PAYS OUT CASH
TO PLAYER ONE AND PLAYER THREE IN THE AMOUNT
OF $89,000, LEAVING EXCESS CASH OF $25,000
TO BE DIVIDED AMONG THE THREE PLAYERS. SO $25,000 IS NOW DIVIDED EVENLY
AMONG THE THREE PLAYERS, WHICH COMES OUT TO $8,333.33
FOR EACH GRANDCHILD. THEREFORE, FOR THE FINAL
SETTLEMENT PLAYER ONE RECEIVES A TOTAL OF $61,333.33 IN CASH. PLAYER TWO RECEIVES THE HOUSE
AND THE RING, BUT ENDS UP PAYING A TOTAL
OF $105,666.67. REMEMBER INITIALLY
THEY PAID $114,000, BUT PLAYER TWO DID RECEIVE THIS
AMOUNT OF CASH BACK. AND THEN FINALLY,
PLAYER THREE RECEIVED THE CAR AND $44,333.33 OF CASH, AGAIN,
$36,000 PLUS THE EXTRA CASH. NOW LET’S TAKE A LOOK
AT ANOTHER EXAMPLE. FOUR HEIRS, A, B, C, AND D
MUST FAIRLY DIVIDE AN ESTATE CONSISTING OF TWO ITEMS,
A DESK AND A VANITY, USING THE SEALED BIDS METHOD. THE PLAYERS’ BIDS IN DOLLARS
ARE GIVEN HERE IN THE TABLE. THE FIRST QUESTION, THE ORIGINAL
FAIR SHARE OF PLAYER A IS WORTH WHAT? REMEMBER, TO FIND THE FAIR SHARE
FOR ANY PLAYER WE SUM THEIR BIDS AND DIVIDE BY THE NUMBER
OF PLAYERS. SO FOR PLAYER A’S FAIR SHARE
WE’D HAVE 300 + 180 DIVIDED BY 4, OR $120. NEXT, WHAT HAPPENS WITH PLAYER A
IN THE INITIAL ALLOCATION? LET’S FIRST IDENTIFY THE HIGHEST
BIDS. NOTICE HOW FOR THE DESK,
PLAYER A HAS THE HIGHEST BID, AND FOR THE VANITY, PLAYER
A ALSO HAS THE HIGHEST BID. SO PLAYER A IS GOING TO RECEIVE
BOTH THE DESK AND THE VANITY, BUT NOTICE HOW THE VALUE
OF THE DESK AND VANITY WOULD BE 300 + 180, OR $480. BUT SINCE PLAYER A’S FAIR SHARE
IS ONLY $120, PLAYER A WILL HAVE TO PAY
THE DIFFERENCE IN CASH TO THE ESTATE. $480 – $120=$360. SO AFTER THE INITIAL ALLOCATION
PLAYER A GETS THE DESK AND VANITY, BUT PLAYER A ALSO PAYS
$360 TO THE ESTATE. AND NOW FOR THE LAST QUESTION, AFTER THE PROCESS IS COMPLETE, WHAT IS THE FINAL OUTCOME
FOR PLAYER A? BEFORE WE ANSWER THIS QUESTION
THOUGH, WE WILL HAVE TO DETERMINE
THE FAIR SHARE FOR PLAYERS B, C, AND D. TO SAVE SOME TIME,
I’VE ALREADY DONE THIS. PLAYER B’S FAIR SHARE
WOULD BE THE SUM OF THEIR BIDS DIVIDED BY 4, OR $100, AND THE
SAME THING FOR PLAYERS C AND D. PLAYER C’S FAIR SHARE IS $100. PLAYER D’S FAIR SHARE IS $75. AND BECAUSE THEY DID NOT RECEIVE
ANY ITEMS, THEY RECEIVE THIS AMOUNT IN CASH
FROM THE ESTATE. SO PLAYER A PAID $360
TO THE ESTATE. NOTICE THAT $275 FROM
THAT AMOUNT GOES TO PLAYERS B, C, AND D,
LEAVING EXCESS CASH OF $85. SO IF WE TAKE THE REMAINING CASH
OF $85, AND DIVIDE BY THE NUMBER OF
PLAYERS, OR DIVIDE BY 4, THIS GIVES US $21.75,
WHICH EVERY PLAYER RECEIVES. WHICH MEANS PLAYER A INITIALLY
PAID $360 TO THE ESTATE, WHICH I’M SHOWING HERE
AS A NEGATIVE VALUE, BUT THEN PLAYER A RECEIVES
$21.75 BACK, AND THEREFORE ENDS UP PAYING
$338.75. SO THE FINAL OUTCOME FOR PLAYER
A WOULD BE PLAYER A RECEIVED THE DESK AND THE VANITY,
AND PAID $338.75.   I HOPE YOU FOUND THIS HELPFUL.