You Don’t Have to Settle for Less Than the Biggest Piece of the Pie

You are a lawyer or a mediator and a client comes to you about a disputed piece of property. He thinks he is entitled to half of it. If you had a risk free way to guarantee that he gets at least half of it, would you use it?

It isn’t always used. Take the high profile case of Barry Bonds’ 73rd home run ball. On October 6, 2001, Barry Bonds hit home run numbers 71 and 72 in Pac-Bell park in San Francisco, breaking Mark McGwire’s two year old season record of 70. McGwire’s 70th home run ball was sold for 3.2 million dollars. Bonds’ 72nd ball bounced back onto the playing field so no fan obtained it. If Bonds hit another (and last of the season) home run on the last day of the season (October 7), the ball was estimated to be worth at least a million dollars.

Alex Popov had a seat behind home plate for that last game. He wasn’t going to catch the home run ball there so he traded for a ticket that allowed him to choose a place on the walkway beyond the outfield fence. Incredibly, Bonds did hit his 73rd and last home run of the season into the glove of Popov. Unfortunately for him, it didn’t stay there. In the ensuing scramble, the ball fell or was jostled out of his glove and ended up in the hands of Patrick Hayashi. Several bystanders told Popov that they would testify that he had caught the ball. In addition, someone had recorded the scramble on a video camera. Encouraged by this, Popov decided to sue for the possession of the ball.

After pre-trial meetings did not resolve the issue, the case went before Superior Court Judge Kevin McCarthy, who heard the case without a jury. He determined that it was not clear that Popov had caught the ball and declared that Popov and Hayashi had joint and equal ownership of the ball. When they could not agree on a resolution, Judge McCarthy ruled that a third party would determine the worth of the ball. Judge McCarthy would have been the wisest judge since Solomon had he not made the mistake of having a third party decide the worth of the ball.

Why is it a mistake to introduce the third party? Here is why. There are now three numbers on the table, what each interested party thinks the ball is worth (evidently different) and the third party’s determination. Ranking these by magnitude from largest to smallest, there are six scenarios.

If the third party estimate is lower than yours, you are unhappy. So in four of the six scenarios , at least one party is unsatisfied (here those indicated by a *). In the last two, they are satisfied but those scenarios seem to be the most unlikely. Furthermore, each party is dissatisfied half of the time. This is the prognosis in the Bonds case. It could be worse. If one of the parties is to be the buyer and the price is determined by a third party then the scenarios are:

Only the last scenario is satisfactory to both the buyer and non-buyer. In each of the above, one can see that each party is satisfied in only half of the scenarios. The odds are not good. Why be satisfied with this?

Especially since it can be arranged that both parties can be guaranteed that they will be satisfied. In fact, if the parties disagree then the judge can guarantee that each party gets more than half of the ball (it is fair), and each party will get more than the other party (envy free).
This claim sounds outrageous but all you have to do is follow The Rule.

The Rule Each party submits a sealed (and secret) bid for the full value of the disputed object. The highest bidder gets physical possession of the object and pays the other on the basis of the average bid. A tie is broken by an agreed upon random device.

To see how this might work suppose the ball has been valued at $400,000 by Party A and $600,000 by Party B. By The Rule, B gets the ball and pays on the basis of the average bid, $500.000 , ie. pays A $250,000.

Party B wanted a rise in equity of $300,000 but actually got a $600,000 ball less the $250,000 payment which is $350,000. This is $50,000 more than half and $100,000 more than Party A got. Meanwhile Party A who wanted $200,000 got $50,000 more than that and calculates what he thinks Party B got. He thinks that Party B got a $400,000 ball and paid out $250,000 so his rise in equity is $150,000. That is $100,000 less than what Party A got. The outrageous claim is verified.

What is the guarantee? As soon as Party B claims a value of $600,000, then he is guaranteed to get a value of $300,000 regardless of what the other bid will be. If the other bid is less, then he gets the object and pays out on the basis of an average that is less than $600,000 so will be less than $300,000 and he gets a bonus. If the other bid is more than $600,000, then he will be the recipient of a cash payment based upon an average that is more than $600,000. The payment is thus larger than $300,000. A similar guarantee is made to Party A. Note the paradox. If the parties disagree on the value then each party gets more than half. If they agree they get exactly one half. So disagreement is better than agreement.

If Party B is guaranteed half of his announced value, why does he not lie and bid say $800,000? In that case, the average is $600,000 so he pays $300,000 which is clearly worse than when he was honest. His guarantee of at least $400,000 is reached through the possession of a ball whose value was artificially inflated by him. So honesty is the best policy. Secrecy is also important. If Party B knows that Party A will bid $400,000 then he might reduce his own bid to $400,001 get the ball and only pay $200,00.50, but he cannot deprive Party A of his $200,000. Similarly, Party A could take advantage of knowledge of Party B’s bid to up his to $599,999.50 to increase his take but he cannot deprive Party B of his $300,000. If both simultaneously do the above it is a disaster for both. Secrecy is the best policy also.

Note that neither party is asked to justify the value given to the object, nor are they asked to compromise their stated value. Although the presentation of The Rule is in an adversarial context, it might be used in situations where continued amiability is a goal.

Had Judge McCarthy mandated use of The Rule and done a calculation of the result as we have done above, he would have created quite a stir. Of course, he was not the only one to not invoke The Rule. Either party in the dispute or their lawyers could have asked to use the rule. You have to convince the other party to do this. But it should be a strong selling point that you can guarantee the opponent more than half of the ball. Apparently, no one connected with the case knew about The Rule. Journalists predicted that the value of the ball would go down as time passed. In the actual case, settled more than a year after the homer was hit, the ball was declared to have a value of only $450,000.

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A. M. Fink

 A. M. Fink is a retired research Mathematician.  His interest in game theory led to devising and lecturing on fair and envy free distribution of assets.  He presents seminars on practical ways to divide property or responsibilities to judges, mediators, and lawyers interested in collaborative law.  He is a Quaker… MORE >