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# Are you a shoplifter?

## Question

You are conducting a survey where the question is somewhat embarrassing: have you shoplifted within the past 12 months? You realize that it might be difficult to get honest answers, so you ask your friend the psychology student for advice. He tells you the following trick: Ask each person to flip a coin and tell them that if the coin land heads, they should answer the question with a lie, if the coin lands on tails, they should answer 'yes'. As the person agrees to this before the outcome of the flip is revealed, people would be more likely to participate in such questions.

## Recommended Posts

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Assuming you all people follow this method honestly, and you ask enough people the question then you can get useful information from this method. Anybody who claimed to not shoplift must be lieing as they didn't answer yes (since you lie or say yes (inclusive or)), and a shoplifter as they are denying it. As ~50% of people will get tails and answer yes regardless of whether they did/didn't shoplift, this means that if you ask enough people then you can deduce that the number of people who shoplifted is ~ twice the number of people who answered no

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Is the OP correct?

With the coin setup, it should either change to be (a) answer the truth for heads or change to be (b) respond 'no' for tails. Otherwise, it doesn't make sense from a psychology standpoint that the person would feel at ease participating, there will be no doubt when they answer about shoplifting.

For example, if you go with (b), then if they shoplifted, they will be comfortable responding "no" (a lie) as there is a 50% chance they are only responding because the coin dictactes it.

With the given example, if they respond "no", you will no for sure that they shoplifted. Who would be amenable to that?

Edited by vinay.singh84
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Is the OP correct?

With the coin setup, it should either change to be (a) answer the truth for heads or change to be (b) respond 'no' for tails. Otherwise, it doesn't make sense from a psychology standpoint that the person would feel at ease participating, there will be no doubt when they answer about shoplifting.

For example, if you go with (b), then if they shoplifted, they will be comfortable responding "no" (a lie) as there is a 50% chance they are only responding because the coin dictactes it.

With the given example, if they respond "no", you will no for sure that they shoplifted. Who would be amenable to that?

To answer your first question, yes. The op was intended to be written this way.

Does the researcher knowing or not knowing the result of the flip matter?

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I think Nins_Leprechaun has it. Nice puzzle.

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Is the OP correct?

With the coin setup, it should either change to be (a) answer the truth for heads or change to be (b) respond 'no' for tails. Otherwise, it doesn't make sense from a psychology standpoint that the person would feel at ease participating, there will be no doubt when they answer about shoplifting.

For example, if you go with (b), then if they shoplifted, they will be comfortable responding "no" (a lie) as there is a 50% chance they are only responding because the coin dictactes it.

With the given example, if they respond "no", you will no for sure that they shoplifted. Who would be amenable to that?

You have a point. The trick in the OP wouldn't really work since saying "no" is pretty much a confession.

Edited by gavinksong
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Is the OP correct?

With the coin setup, it should either change to be (a) answer the truth for heads or change to be (b) respond 'no' for tails. Otherwise, it doesn't make sense from a psychology standpoint that the person would feel at ease participating, there will be no doubt when they answer about shoplifting.

For example, if you go with (b), then if they shoplifted, they will be comfortable responding "no" (a lie) as there is a 50% chance they are only responding because the coin dictactes it.

With the given example, if they respond "no", you will no for sure that they shoplifted. Who would be amenable to that?

You have a point. The trick in the OP wouldn't really work since saying "no" is pretty much a confession. But changing the coin setup in the way you described wouldn't work either. The only honest way to make it work would be to tell the surveyee to lie or tell the truth based on how the coin lands, but that wouldn't give you any useful data.

I disagree. This is actually a classic setup that many psychologist use. Since the participant has the security of the coin flip (if it is secretive toss) the psychologist can calculate using some simple statistics the rate at which one shoplifts (in this case)

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Is the OP correct?

With the coin setup, it should either change to be (a) answer the truth for heads or change to be (b) respond 'no' for tails. Otherwise, it doesn't make sense from a psychology standpoint that the person would feel at ease participating, there will be no doubt when they answer about shoplifting.

For example, if you go with (b), then if they shoplifted, they will be comfortable responding "no" (a lie) as there is a 50% chance they are only responding because the coin dictactes it.

With the given example, if they respond "no", you will no for sure that they shoplifted. Who would be amenable to that?

You have a point. The trick in the OP wouldn't really work since saying "no" is pretty much a confession. But changing the coin setup in the way you described wouldn't work either. The only honest way to make it work would be to tell the surveyee to lie or tell the truth based on how the coin lands, but that wouldn't give you any useful data.

I disagree. This is actually a classic setup that many psychologist use. Since the participant has the security of the coin flip (if it is secretive toss) the psychologist can calculate using some simple statistics the rate at which one shoplifts (in this case)

If you follow the current setup, saying "no" is a full confession that you are a shoplifter and saying "yes" means that you may be or may not be. If you change the setup in the way vinay described, saying "yes" means that you are not a shoplifter and saying "no" means that you may or may not be (thus you never have to fully confess that you are a shoplifter).

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