https://twitter.com/#!/rags/status/166967947607293953
Before you read on. Take a moment to stop and think about the options. You are running a survey and decided to use raffle and not pay-per-response method to get your target customers to respond to your survey. The question then is which raffle, for the same amount, will get you better response rate?
You do not have resources to run both. You are going to pick one method.
Have you made your choice? and written it down?
Let us do the math first to see which option offers better expected value to your respondents.
Assume 100 customers.
Option A: The chances of winning is 1/100. So the expected value of $250 prize pot is $2.5.
Option B: There are 10 chances to win (no duplicates). The prize port remains $25 for all 10 chances but the probability changes.
For the first chance it is 1/100.
For the second it is 1/99
For the 10th it is 1/91
The expected value is $2.62, a tad more than$2.5.
If your respondent were presented with these two options and asked to pick then they might choose Option B.
But notice that your respondent does not get to see both options. They either see 1/100 chance to win $250 or a little better than 1/100 chance to win $25.
We are not good in math and in case of handling probabilities we tend to focus on magnitude of the prize pot over the chances of winning. You can see this behavior when Power Ball or other lottery pot rises past $50 million.
So a 1/100 chance to win $250 will look more attractive than the $25 option even if its expected value is higher.
You will most likely receive better response rate by giving all the $250 to one lucky respondent than splitting it over 10 people.
You think otherwise? I am happy to run this test for you. I just need $500 for the prize pot and $500 for my fee.
Iterative Path 
I don’t think the math in this article is correct. If the total reward and total participants are the same then the expected value of participating shouldn’t differ; if it does then some money is appearing out of “thin air” so to speak.
Assuming a total rewards sum of $250 and 100 participants:
One reward of $250; 1 winner, 99 losers: 1/100 chance of winning * $250 = $2.50 expected value
Ten rewards of $25; 10 winners, 90 losers: 1/10 * $25 = $2.50
You can also see this following the math in reverse as well – calculate the chance of losing on all ten drawings:
99/100 * 98/99 … * 91/92 * 90/91 = 90% chance of losing, or in other words a 10% chance of winning $25.
None of which, of course, contradicts the main point in the article; people are probably more likely to enter if the overall pot size is larger.
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Leo
Did you mean self-selection bias (only those attracted by raffle take the survey?). That requires to be weeded out with better survey design and filtering answers that follow the pattern of those taking it only for the raffle.
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When I saw the post’s title, I thought you’d address the issue of bias when using a raffle… What do you think about that?
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Denominator neglect!
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Ryan
Another good case to test. the lotteries do state the probabilities of winning (albeit in fine print). I believe we give more weight to prize pot increases than probability increases.
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Also, if there is no indication as to the size of the survey, the perceived difference in the probability of winning 1 of 10 prizes vs 1 prize may be negligible.
What do you think would happen if option A was 1 in 100 win $250 and option B was 1 in 10 win $25?
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