With this set up, would you be willing to answer the pollster's questions honestly? Why or Why not? **Title: Addressing Honesty in Poll Responses with Randomized Response Techniques****Main Text:**A significant challenge with polling is determining whether individuals are willing to provide honest answers. When questions are perceived as potentially shameful or embarrassing, such as those related to politics, sexual behavior, or other sensitive subjects, respondents may hesitate to respond truthfully.**Proposed Solution:**An effective strategy to enhance honesty in polling involves the use of a randomized response technique. Consider a scenario where answering 'YES' is potentially embarrassing. Participants are instructed to flip a coin privately. If the coin lands on heads, they should answer truthfully. However, if it lands on tails, they should answer 'YES', regardless of the truth. This mechanism provides respondents with plausible deniability about the reason behind their 'YES' answer if questioned.Let \( \hat{p}_N \) represent the fraction of individuals who reported 'YES'. Define \( p \) as the probability that a randomly selected person actually says 'YES'. Let \( q \) denote the probability that the true answer is 'YES'. It's essential to note that while the expected value of \( \hat{p}_N \) is \( p \), the primary interest lies in accurately measuring \( q \). This approach maintains respondent privacy and improves data accuracy by reducing the impact of social desirability bias. 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 \( \hat{p}_N \) be the number of people polled who supported the policy, divided by the total number of people polled \( N \).

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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.

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.

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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