In 1962
Brams and Taylor developed what is now known as the “Adjusted Winner” where two parties need to distribite assets that can not be divided. The authors suggest it produces solutions that are envy-free, efficient and equitable. It has far reaching implications on Joint Ventures, Asset liquidation and even sensitive geopolitical processes such as peace in the Middle East. I will walk you through the process via a (albeit hypothetical) real-world example.
Adjusted WinnerUnder adjusted winner the parties start with 100 points and divide these points among the asset(s) being challenged. As our hypothetical example we will look at the circuit city liquidation and examine how adjusted winner could be used for a fair distribution of its assets.
For simplicity purposes we will focus on the following liquidatable assets: the real estate portfolio, brand name, credit card portfolio, circuitcity.com and the corporate jet.
Now lets look at two imaginary debtors for these assets: Debtor1 and Debtor2. Under adjusted winner they would have to allocate 100 points across the 5 assets.
Supposed they distribute their points as follows:
| Asset | Debtor1 | Debtor2 |
| Real Estate | 40 | 15 |
| Brand Name | 25 | 30 |
| Credit Cards | 10 | 10 |
| CircuitCity.com | 10 | 40 |
| Corporate Jet | 15 | 5 |
| Total Points | 100 | 100 |
Here is how the process works: Each debtor is assigned as a "winner" for an item in which they allocated the highest points. In our case (marking in red indicates winner)
| Asset | Debtor1 | Debtor2 |
| Real Estate | 40 | 15 |
| Brand Name | 25 | 30 |
| Credit Cards | 10 | 10 |
| CircuitCity.com | 10 | 40 |
| Corporate Jet | 15 | 5 |
| Total Points | 100 | 100 |
So in the first round Debtor2 would get the Brand Name & CircuitCity.com and Debtor1 would get the RealEstate portfolio and Corporate Jet. The Credit Cards remain undivided (because the points are a tie).
Because Debtor2 has more total points (30+40=70) than Debtor1 (40+15=55), we now award the Credit Cards to Debtor1.
| Asset | Debtor1 | Debtor2 |
| Real Estate | 40 | 15 |
| Brand Name | 25 | 30 |
| Credit Cards | 10 | 10 |
| CircuitCity.com | 10 | 40 |
| Corporate Jet | 15 | 5 |
| Total Points | 100 | 100 |
That Brings Debtor1's points up to 65 (55 + 10 for the Credit Cards) still five points less than Debtor2. This is where the adjusting phase begins in which items (or fractions of them) are transferred between the parties until they reach an equillibrium of points.
We now need to shfit assets (one or more or fractions thereof) to Debtor1. For each item Debtor2 won we look at the following ratio: # debtor2 points/# debtor1 points. For
Brand Name that ratio is 30/25=1.2, and for
CircuitCity.com is 40/10=4. Adjusted winner establishes the ORDER in which the items are transferred: from low (ratio) to high.
So the
Brand Namewill be the first to be transfered (with a 1.2 ratio) but we can not transfer the entire
Brand Name asset to Debtor1 because then Debtor2's points will go down to 70-30=40 and Debtor1 will go up to 40+10+15+25=90. So we need to distribute the Brand Name between the Debtors.
We need to transfer a portion (p) of Brand Name from Debtor 2 so that the Debtor2 points and Debtor1 points are equal. In other words:
Debtor1 Points (65) + Debtor1 value of Brand Name portion (25*p) =
Debtor2 Points without the Brand Name being transferred (40) + Debtor2 value of whats left of Brand Name ( 30*(1-p))
65+25p=40+30(1-p)
65+25p=70-30p
55p=5
p=1/11
So Debtor1 will get 1/11th share of the Brand Name, driving Debtor1's points up to: 65+25/11=67.27 and Debtor2's points end up being 40+30*10/11=67.27.
Knaster "Inheritance procedure"When there are more than two parties involved, the Knaster Inheritance procedure can be used. Here is an example: In April 2008 Nielsen acquired IAG Research for $225m. The prior owners consisted of a group of six PE firms (AlpInvest, Blackstone, Hellman & Friedman, Kohlberg Kravis Robert, Carlyle and Thomas H. Lee Partners).
Assuming each partner had the first right of refusal, what would be the most fair way to open IAG for an internal bid amongst the six PE firms to buy the rest of the group members out before opening the bid up for outside contenders?
Commonly it works this way: the investment is valuated (by the partners or by an outside audit). Each partner decides how much they will “bid” for the buyout and the highest bidder wins and pays the others out.
The problem with simple bidding is that we all perceive an investment differently. An iPhone is a status symbol to one person and a necessary communication and productivity device to another. I might not be willing to spend $200 for the same product you are quite comfortable shelling twice that amount.
Similarly the value of IAG is different to each of the PE firms invested in it. Blackstone, for instance, is an investor in other media holdings that may find IAG worth much more than its book value because of its audience research capabilities. Other PE firms might look at IAG solely from a debt leverage perspective and be content with unloading it off their books.
Adjusted Winner &
Knaster Inheritance are two methods that help solve the dilemma how interested parties can compensate each other for their perceived value. Here is how the Knaster Inheritance procedure works:
Suppose the partners write down their bid offer in a sealed envelope with the following bids:
| AlpInvest | $180m |
| Blackstone | $210m |
| Hellman & Friedman | $198m |
| Kohlberg Kravis Robert | $114m |
| Carlyle | $144m |
| Thomas H. Lee Partners | $126m |
Assuming they all have equal shares (i.e. 1/6th of IAG):
The winning bid seems to be that of Blackstone at $210m. They have a claim to 1/6th of the company which they value to be (1/6) of ($210m) or $35m.
Because Blackstone has a fair claim to 1/6 of IAG they will compensate the other partners with the remaining 5/6th of their perceived value of IAG (5/6) of ($210m) or $175m and deposits it into a “kitty” account.
Now each of the other 5 partners withdraw 1/6th of what they estimated as the value of the company from the “kitty”:
| AlpInvest | Withdraws 1/6 of $180m = $30m |
| Hellman & Friedman | 1/6 of $198m = $33m |
| Kohlberg Kravis Robert | 1/6 of $114m = $19m |
| Carlyle | 1/6 of $144m = $24m |
| Thomas H. Lee Partners | 1/6 of $126m = $21m |
The total withdrawal from “kitty” account is 30+33+19+24+21 = $127m
The difference between $175m and the “withdrawals” is a surplus of $48m. That surplus is equally divided among the 6 partners (including Blackstone) so each partner gets $8m.
So (if this example were not as hypothetical as it really is):
Blackstone Gets IAG and pays $175m less the $8m back = $167m
AlpInvest Gets $30 + $8m = $38m
Hellman & Friedman Gets $33 + $8m = $41m
Kohlberg Kravis Robert Gets $19 + $8 = $27m
Carlyle Gets $24 + $8 = $32m
Thomas H. Lee Partners Gets $21 + $8 = $29m
Adjusted Winner and the Middle East Peace ProcessMoshe Hirsch, Vice Dean Faculty of Law at the Hebrew University of Jerusalem
published an article in which he suggests applying the same logic to the equitable division of East Jerusalem as part of a middle east peace settlement.
Jostein Tellne (of the University of Oslo)
offers Adjusted Winner as a way to help wealth sharing negotiations in Sudan.
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