The Mathematics Of Uncertainty About Allegations Against Kavanaugh

The Mathematics Of Uncertainty About Allegations Against Kavanaugh
By U.S. Court of Appeals for the District of Columbia Circuit [Public domain], via Wikimedia Commons

Game Theory and Stock Investment Practice Can Provide Valuable Guidance 

WASHINGTON, DC, October 1, 2018 – There’s a great deal of uncertainty and confusion about how senators should vote, once all the evidence is finally in, despite uncertainty about the sexual misconduct allegations against Kavanaugh, but both game theory and stock investment practice should help provide some guidance to any senator whose vote will depend primarily on this one key issue, says public interest law professor John Banzhaf.

Banzhaf invented the mathematical tool now known as the Banzhaf Index, which he used to prove the unconstitutionality of weighted voting, and to analyze voting power under the Electoral College and in many other real-world voting situations.

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As a result, he has been called one of the world’s top game theorists by Wikipedia, and was featured in Newsweek and in several political science books for his contributions to this field – one defined as the study of mathematical models of strategic interaction between rational decision-makers.

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Before looking at the mathematics of the decisions senators must make, it is important to note that Kavanaugh does not enjoy any presumption of innocence, since that concept applies only in criminal proceedings where the burden of proof is "beyond a reasonable doubt."

For example, in a civil proceeding, as well as in many agency proceedings, Kavanaugh or any other person accused of something would not be entitled to a presumption of innocence.

Thus, if Kavanaugh sued Ford in an ordinary civil suit - e.g., claiming that she negligently injured him, and that he was free from negligence - he would have no such presumption of innocence.

Instead, he would have the burden of proof, and would have to prove his freedom from negligence by a preponderance of evidence.

Even worse, were he to sue Ford for allegedly making a false claim that he sexually assaulted her, he would not only lack any presumption of innocence, but would have to prove his case by clear and convincing evidence, an even higher and more difficult to meet evidentiary standard.

Similarly, in most states, applicants for the bar, such as Kavanaugh, enjoy no presumption of innocence.  Instead, he has the burden of proving his good moral character (e.g, no prior wrongdoings), and he likewise must do so by the higher evidentiary standard of clear and convincing evidence.

A central tenant of game theory is that a rational decision maker would not consider only the odds that something has or will happen, but also the consequences of each alternative.

So, in this case a senator would logically have to weigh the adverse consequences to the country of having a person on the Court if the allegations against him were correct, against the adverse consequences to the country (and perhaps in part to the applicant) if he is truly innocent but nevertheless is denied the position for which he was nominated because he was falsely charged.

For example, and as an extreme example to help prove the point, if there were any credible evidence that a Supreme Court nominee in the past had planned a terrorist act which killed many Americans, having him on the Court would be so unthinkable that he would probably have to rebut the evidence against him, and prove his innocence - possibly beyond any reasonable doubt, or perhaps by some even higher standard.

On the other hand, if the only credible evidence against the nominee suggested no more than that he occasionally drank to excess as a teen, the harm (if any at all) to the Court and to the country would be much smaller, so a rational decision maker might ignore such an allegation unless the evidence supporting that charge was at least clear and convincing, or even beyond a reasonable doubt.

In other words, the level of proof which a rational decision maker would require varies with the seriousness of the allegation of wrongdoing - the more serious the change, the lower the standard of proof.

The same type of very basic game theory analysis occurs when most people try to decide whether or not to purchase a stock.

Suppose the prospective buyer has some evidence that a disastrous event will occur which will cause the stock's value to hit zero, and the investor would lose his entire investment.

A logical investor would not take the risk of purchasing the stock expected to experience even a slightly better than average increase in value if, as he weighs the evidence, the chance of the disastrous event occurring appear to him to be small but not something he can afford to ignore - say only 5%.

The risk is simply too large to accept even if the evidence is quite weak and not very persuasive, since the magnitude of the adverse consequence is so serious as to be unacceptable  - especially if there are other stocks which he could purchase which are likely to be almost as good but without this small probability.

That would appear to be directly comparable to putting a nominee on the Supreme Court even if the evidence that he was a traitor is very small and not very persuasive.

On the other hand, if the adverse event - should it occur - would cause only a small dip in the market value of the stock, a logical investor would be much more willing and likely to buy the stock even if there is a somewhat larger chance that the disastrous event will in fact occur.

So, since the major allegations against Kavanaugh now being investigated - e.g., that he committed sexual assault, flashing, and perhaps lied - are far less serious than being a traitor, but much more serious that occasional drunkenness as a teen, each senator should first decide just how serious the allegation  - if true - would be for a Supreme Court nominee.

Then, based upon that assessment, he or she should establish a standard of proof which is consistent with the seriousness of the charge, and use that standard to weigh all the evidence, including any new evidence uncovered by the F.B.I., by the media, or by reliable third parties.

Clearly the advantage of a successful appointment will be perceived as higher for most Republicans than for most Democrats, and both may differ as to how serious the charge is, assuming it is true.

Thus there logically is not - and should not be - only one standard or level of proof for each senator, as there is (or at least should be) when a jury decides a criminal case, or a civil one, says Banzhaf.

But the argument that Prof. Christine Ford's claim should be completely ignored if no additional corroborating evidence is produced, or that senators should always "believe the women" any more than that they should always believe the judges or members of the bar, has no basis in law or logic, maintains Banzhaf.

Instead, the process requires that each senator weigh all the evidence available at the time the vote is taken, and do so with the same deliberation and logic they use when deciding about purchasing a stock.


Professor of Public Interest Law

George Washington University Law School,

FAMRI Dr. William Cahan Distinguished Professor,

Fellow, World Technology Network,

Founder, Action on Smoking and Health (ASH),

2000 H Street, NW, Wash, DC 20052, USA

(202) 994-7229 // (703) 527-8418  @profbanzhaf

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