The Bias in the flip of a coin!

The Judicial Council of California Civil Jury Instructions- Instruction 5009 on Pre-deliberations-? admonishes? jurors who are about to retire to decide the verdict that while the judge knows that the jurors will not do so, he/she? is “required to advise you that you must not base your decisions on chance, such as a flip of a coin.”?? And indeed, sometimes in mediation, I have mentioned to one party or the other, that the decision to be made should NOT be made by flipping a coin.

The accepted reason for not deciding something by flipping a coin is that a decision is being made purely by chance rather than by considering the facts and evidence or the strong /weak points of a case.

But it turns out that bias is actually involved. And, as we all know, we should not make decisions based on our biases – whether implicit or explicit. ( Id. at? Instructions 113 and 5003)

An October 15, 2023 article in The Economist entitled “How to Predict the Outcome of a Coin Toss” discusses a study by a trio of American mathematicians that found that bias was involved in tossing a coin.?? In 2007, Persi Diaconis, Susan Holmes, and Richard Montgomery analyzed the flipping of a coin and

noticed something intriguing. Besides sending it somersaulting end-over-end, most people impart a slight rotation to a coin. That causes the axis about which the coin is flipping to drift while it is in the air, a phenomenon called precession.

After crunching the numbers, the physicists concluded that a coin thrown by a human should exhibit a subtle but persistent bias. There was about a 51% chance that a coin would land the same way up as it had been prior to being thrown. If it was heads-up in the thrower’s hand, in other words, it would be slightly more likely to land heads-up too. Or at least, that was the prediction. (Id.)

A subsequent study by Mr. Bartos confirmed this finding. He convinced 48 volunteers to perform 350,707 coin tosses using various coins from different countries and his data confirmed the same bias: they landed the same side up 50.8 of the time. (Id.)

So, while the coins themselves do not display any particular bias, like everything else, it is the human element that adds the bias.? Apparently, humans are not able to toss a coin straight up but unwittingly/ implicitly impart a slight rotation or bias to the toss.

So, the next time someone suggests to you that a matter be decided by a toss of the coin, be wary. Not only are you leaving the decision to chance but also to the built-in bias of the coin tosser to add a slight rotation so that the coin lands on the same side up. (Alternatively, armed with this knowledge, simply choose the side facing up before the toss knowing that you have a 50.8% chance of it landing on this same side!)

… Just something to think about.

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