# Math Helps Us Decide

How can we understand the Kavanaugh hearing and people’s reaction to it? The well-established logic of probabilities can help.

The testimony before the Senate Judiciary Committee left a lot of uncertainty and a lot of room for interpretation. Was Christine Blasey Ford really assaulted? Did Brett Kavanaugh do it? Is her testimony a sincere public service or a con job? Is his reaction authentic indignation or the rage of an entitled bully?

We can call on Bayes’ Rule to help us understand how we and others can come to different conclusions. Bayes’ Rule is a venerated tool in science for analyzing uncertainty, and sometimes, belief states of mind. With appropriate problem formulation, we can disentangle the evidence and hypotheses before us. Not surprisingly, what you conclude depends on your prior assumptions, which largely depend on political persuasion. Bayes’ Rule lets us isolate and examine those assumptions.

• What do Kavanaugh and Ford believe today about what happened? (Sincere belief vs. lying?)
• In what manner did they testify in the Senate hearing? (Testify or not, Calm vs. Angry?)
• KI = Kavanagh is Innocent.
• FBG = Ford sincerely Believes that Kavanaugh is Guilty of assaulting her.
• FBI = Ford actually Believes Kavanaugh is Innocent.
• KBG = Kavanaugh secretly Believes that he assaulted Ford (Guilty).
• KBI = Kavanaugh sincerely Believes that he did not assault Ford (Innocent), either because he actually did not do it, or else he blacked out, forgot, or put it out of his memory.
• FTC = Dr. Ford Testifies, emotional yet Calm.
• FNT = Dr. Ford does Not Testify, either because she does not come forward, or because the political mechanations do not allow her to testify. Even though this is historically not the case, it is a counterfactual we must consider. It could have turned out this way.
• KTA = Judge Kavanaugh Testifies in an emotional Angry manner.
• KTC = Judge Kavanaugh Testifies in a Calm and collected manner. Even though this is historically not the case, it is another counterfactual we should consider. He could have testified differently.

# Discussion

Why are the conclusions so different? There are three main reasons.

First, Red gives significant credence to a conspiratorial view of Ford and the Democrats. If it is 50% possible that Ford is lying and the Democrats conspired to get her into the hearing, then that discounts the value of her testimony. Conversely, Blue believes that the only way she could have gone through with this is that she is really deeply sincere. Moreover, she is an intelligent, got-it-together person who is unlikely to have just made up this episode in her head.

The second reason for the difference is Kavanaugh’s own reaction. To the Red viewpoint, it is perfectly natural for a falsely accused person to blow up, even if he is a federal judge. To the Blue viewpoint, this smells like a caged animal reacting to getting caught, and if he really believed in his own innocence, he would be cooperative in persuading the Democrats that they are simply wrong. If Kavanaugh had reacted calmly, then under the other assumptions, the Blue conclusion would have been only 47% that he is actually guilty.

A third important difference between Red and Blue are their differing prior probability that Kavanaugh could have committed the assault he is accused of. Red thinks it extremely unlikely, Blue thinks it’s unlikely but not out of the question.

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## More from Eric Saund

Eric Saund is a researcher in Cognitive Science and a consultant in AI and Machine Learning.

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Eric Saund is a researcher in Cognitive Science and a consultant in AI and Machine Learning.