A problem with polling is whether or not people are willing to answer honestly. If a question might be viewed as shameful or embarrassing (about politics, sexual activity, etc.), they may be reluctant to answer honestly. A potential solution to this is the following: let's suppose that 'YES’ is the embarrassing or socially shameful answer. Give the people you are polling the following instructions: flip a coin privately, and if it comes up heads, you must answer honestly. However, if it comes up tails, you must answer 'YES’ regardless of what the truth is. This gives people plausible deniability about why they answered yes, if pressed. Again, let p, be the fraction of people who said 'YES’. Let p be the probability that a randomly selected person says YES’. Let q be the probability that a person’s true answer is 'YES’. Note A again, we have that the expected value of p, is p, but we are actually interested in N measuring a

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A problem with polling is whether or not people are willing to answer honestly. If a
question might be viewed as shameful or embarrassing (about politics, sexual activity,
etc.), they may be reluctant to answer honestly.
A potential solution to this is the following: let's suppose that 'YES’ is the embarrassing
or socially shameful answer. Give the people you are polling the following instructions:
flip a coin privately, and if it comes up heads, you must answer honestly. However, if it
comes up tails, you must answer 'YES’ regardless of what the truth is. This gives people
л
plausible deniability about why they answered yes, if pressed. Again, let p,
be the
fraction of people who said 'YES'. Let p be the probability that a randomly selected
person says YES’. Let q be the probability that a person’s true answer is 'YES’. Note
л
again, we have that the expected value of p,, is p, but we are actually interested in
N
measuring q.
Transcribed Image Text:A problem with polling is whether or not people are willing to answer honestly. If a question might be viewed as shameful or embarrassing (about politics, sexual activity, etc.), they may be reluctant to answer honestly. A potential solution to this is the following: let's suppose that 'YES’ is the embarrassing or socially shameful answer. Give the people you are polling the following instructions: flip a coin privately, and if it comes up heads, you must answer honestly. However, if it comes up tails, you must answer 'YES’ regardless of what the truth is. This gives people л plausible deniability about why they answered yes, if pressed. Again, let p, be the fraction of people who said 'YES'. Let p be the probability that a randomly selected person says YES’. Let q be the probability that a person’s true answer is 'YES’. Note л again, we have that the expected value of p,, is p, but we are actually interested in N measuring q.
What is the relationship between q and p?
Transcribed Image Text:What is the relationship between q and p?
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