2

I want to create a "game" that aims at supporting the decision making. The user has to consecutively select one out of two random items. Each item belongs to one of X sets.

My question is how many different choices are required to be sure which set is the preferred one.

Example:

  • 3 sets of food: "German", "Italian", "Mexican".
  • First screen: potatoes (german) vs spaghetti (italian). User selects: potatoes
  • Second screen: taco (mexican) vs bratwurst (german). User selects: bratwurst
  • …

How many selections are required to be sure that user selects the German food with a probability of 70% over Italian or Mexican food?

Greeny
  • 21
  • 1
    Do you know the strength of the preferences? Will the user in the example always prefer German food over Italian food? If not, how often? Without that information, the question is meaningless. – joriki May 01 '16 at 13:51
  • I'm not sure if this is a good question for the Mathematics SE, because there is no mathematical statement "Person likes ... more". A possibility could be "If A selects German food over 70% in the cases, then ...". Depending on the requirement you're stating this question is mathematically founded or not. – Jasper May 01 '16 at 13:51
  • @Jasper: We can set the threshold to "[…] over 70% in the cases". Can you tell me the sufficient sample size for this case? – Greeny May 03 '16 at 11:26
  • We need to know how consistent people are. If they only choose probabilistically, then you are fitting a categorical distribution...but, you will never be 100% sure. –  May 05 '16 at 04:59
  • @Bey: If the user has a strong opinion (which I will assure) then he will always pick the item from his preferred category. But unfortunately, if the user has to choose between two items from italian vs. mexican food (and he prefers german), he has to choose at least one item from another category. – Greeny May 06 '16 at 15:01
  • @Greeny what I am asking is that does there exist an absolute preference, like German>Italian>Mexican, so Italian will always be selected over Mexican, and German over either of them? –  May 07 '16 at 00:29
  • @Bey Yes. Each individual user has his/her own absolute preference (and this is what I want to know). To be clear: I want to know the sample size that each user has to fulfill so that I "know" his/her absolute preference. – Greeny May 08 '16 at 07:30
  • Wouldn't it take N-1 pairwise questions? Then you could deduce the preference? What does probability have to do with this? –  May 08 '16 at 16:37
  • @Bey I want to be sure about this. Maybe the user is "unsure" about the category of the item he selected - so to be sure I want the user to at least double-select each category. – Greeny May 09 '16 at 11:02
  • @Bey Can you present me the model and roughly explain the blanks in their? – Greeny May 10 '16 at 08:13
  • @Greeny see below. –  May 10 '16 at 12:00

0 Answers0