Earlier today I asked you the next puzzleabout voters giving wrong answers to opinion polls because they were embarrassed to admit their preferences. Here it is again with a solution.
The shy voter conundrum
Imagine an election with two candidates, say Trump and Harris. Many voters are ashamed to admit who they are voting for.
You are a pollster, go door to door. You have a coin in your pocket. Your goal is to find the percentages that will vote for each candidate.
Can you think of a voting method that makes voters comfortable giving their honest preference, even if they are embarrassed to admit their preferred candidate to you?
The method should result in a reasonably accurate poll, although it may not be 100 percent accurate.
Solution It’s all about the coin.
Ask each voter to privately flip the coin twice. There are four equally likely outcomes: TH, HT, TT, HH.
(Am I the first person to notice that in this toss-up election, one of the candidates is T and the other is H?)
Tell the voter the following: if you flip TT, say you will vote for Trump. If it’s HH, Harris says, and if the outcome is TH or HT, give your honest preference.
This method gives the selector plausible deniability. If the voter responds that they will vote for Trump, they have flipped TT or they are responding honestly, and the pollster doesn’t know which. Similarly, if the voter responds that they will vote for Harris, they have flipped HH or they are responding honestly, and the pollster does not know which. If you’re a shy voter, you’ll be less shy about giving your true preference because you can always deny that what you told the pollster is your preference – it could just be the coins!
If you ask all voters to flip the coins in this way, at the end of the process about 25 percent will have flipped TT and about 25 percent HH. So, if the final tallies are X percent for Trump and Y percent for Harris, you subtract the ‘coin’ votes from the rights to get the final total. The actual ratio of Trump to Harris voters is X-25/Y-25.
The method is a technique – called ‘random response’ – that has been used since the 1960s for surveys on sensitive issues, such as drug use or sexual preference, although I’m not aware of pollsters doing this for presidential or general elections. If any pollsters are reading this, could they let us know in the comments below how common the method is, or if it has been used in a political context?
I hope you enjoyed the puzzle, I’ll be back in two weeks.
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