Coin Tosses Not Random?

Professor Bainbridge offers a possible explanation for Hillary winning so many coin tosses in Iowa.

By now you will have heard that tied results in multiple Iowa Democrat caucuses were decided by coin flips, with Hillary Clinton beating Bernie Sanders in 6. Assuming the coin was unbiased, the odds of her doing so were 1 in 64.

So was Hillary very lucky? Maybe not. Maybe she (or her reps) were skilled. Because it turns out that US coins are not unbiased. I came across a while back a paper by Persi Deacons on “Dynamical Bias in the Coin Toss.” Deacons and his coauthors “prove that vigorously-flipped coins are biased to come up the same way they started.” The effect is not large and there are lots of variables, but it would give a statistically significant advantage to the person calling the flip if (s)he can see the initial starting position. (By the way, even more bias can be introduced if the coin is spun on a table top instead of flipped in the air, because the minting process results in different shapes on the sides, which means that one side weighs more than the other, and the heavier side tends to end up facing down.)

This doesn’t suggest Hillary’s supporters did anything unethical. Taking advantage of this phenomenon would have been smart. I’ll keep it in mind.

Even so, surely a significant amount of luck was involved. It’s hard for me to believe this bias is so large that six consecutive wins were likely.



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