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That probably is too 'practical' question so I will be happy to re-formulate it in more abstract terms if needed.

I have a list of n items (say, 30) and an audience, larger than n (say, 200). I am interested to know what are the most popular three items among this audience. What is the most correct and efficient way of doing it?

I realize of course that there can be the case of a draw, or some other peculiar distribution of preferences that won't allow me to draw any conclusion. But apart of these unlikely situations, if we assume there are top three most preferred items, what could the way to ask the audience the least amount of questions (i.e. efficiency) to these three items with the highest probability (i.e correctness)?

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  • $\begingroup$ Point for clarification: ¿what is the response scale for the $n$ item? $\endgroup$ – Gregg H Apr 21 '18 at 2:38
  • $\begingroup$ well, for ranking we don't need the response scale if I get it right? we just need to sort them from 'most preferred to least preferred'. But if we need some scale it can be "on the scale from 0 to 5 how do you like item n" $\endgroup$ – David Pekker Apr 21 '18 at 3:07
  • $\begingroup$ I'll rephrase: ¿are you asking respondents to pick their top three (or some other number) from the $n$ choices? or ¿are you asking respondents to rate the entire set of $n$ choices on some scale? $\endgroup$ – Gregg H Apr 21 '18 at 3:44
  • $\begingroup$ Or, are you asking participants to rank their favorite items from 1 to 30? $\endgroup$ – Mark White Apr 21 '18 at 4:11
  • $\begingroup$ no, I intend to ask them to choose 3 most liked items out of 30 $\endgroup$ – David Pekker Apr 21 '18 at 13:25

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