How Coin Flipping Can Make Polls More Accurate

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How Coin Flipping Can Make Polls More Accurate
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With midterms upon us, can we find out what voters are really thinking?

After the noisy 2020 election season in the United States, journalists wrote extensively about the inaccuracy of preelection polls. They weren’t the only ones. According to a report by the American Association for Public Opinion Research entitled 2020 Pre-Election Polling: An Evaluation of the 2020 General Election Polls, 2020 polls were off by the largest magnitude in decades at both the federal and state levels.

With the 2022 election year underway, one way to counteract the “shyness” problem is for pollsters to give the people they survey plausible deniability. That is, a person should be able to respond to a question honestly, while preventing the pollster from knowing whether the answer is that person’s actual opinion. This could be especially useful in countries having autocratic leaders who might wreak vengeance on dissenters.

Let’s say, two hundred people answer the poll: 140 pick Scarecrow and 60 pick Tin Man. Given what the pollsters have told the pollees, roughly 100 people will respond “Scarecrow” regardless of their preference just because of the 50-50 probability of a coin toss; they flipped tails. Of the remaining 100 who flipped heads, 40 prefer Scarecrow and 60 prefer Tin Man, so Tin Man is the favorite.

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