Suppose you want to find out how many people support Policy X. A standard polling approach is to just ask N many people whether or not they support Policy X, and take the fraction of people who say yes as an estimate of the probability that any one person supports the policy. Suppose that the probability someone supports the policy do not know. Let py be the number of people polled who supported the policy, divided by the total is p, which you number of people polled N. However, 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, or whatever people are sensitive about), they may be reluctant to answer honestly. A potential solution to this is the following: 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 answer honestly, but if it comes up tails answer 'YES' regardless of what the truth is. This gives people plausible deniability about
Suppose you want to find out how many people support Policy X. A standard polling approach is to just ask N many people whether or not they support Policy X, and take the fraction of people who say yes as an estimate of the probability that any one person supports the policy. Suppose that the probability someone supports the policy do not know. Let py be the number of people polled who supported the policy, divided by the total is p, which you number of people polled N. However, 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, or whatever people are sensitive about), they may be reluctant to answer honestly. A potential solution to this is the following: 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 answer honestly, but if it comes up tails answer 'YES' regardless of what the truth is. This gives people plausible deniability about
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Suppose you want to find out how many people support Policy X. A standard polling approach is to just ask N
many people whether or not they support Policy X, and take the fraction of people who say yes as an estimate of
the probability that any one person supports the policy. Suppose that the probability someone supports the policy
is p, which you do not know. Let îy be the number of people polled who supported the policy, divided by the total
number of people polled N.
However, 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, or whatever people are sensitive about), they
may be reluctant to answer honestly.
A potential solution to this is the following: 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 answer honestly,
but if it comes up tails answer 'YES' regardless of what the truth is. This gives people plausible deniability about
why they answered yes, if pressed. Again, let pN 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 again,
we have that the expected value of pN is p, but we are actually interested in measuring q.
Transcribed Image Text:If both YES' and 'NO' are potentially embarrassing or stigmatizing, you could change
the polling procedure in the following way: flip a coin, if it comes up heads answer honestly, if it comes up tails, flip
the coin again to decide whether to answer yes or no. Repeat the above analysis with this new polling paradigm. Do
you need to poll more people or fewer people to guarantee the same level of accuracy?
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