Say I want to produce a ranked list of a population’s favorite foods.
My idea is to give them a list of 50 or so possible food options to choose from, and let them list their favorites in order of how much they like them. The responder can choose any number of responses as they want, as long as they are ranked in order of favorite. Each person’s response would be given the same weight, for example think about each responder having 10 “points” to “spend” on their rankings, and an algorithm then taking those 10 points and distributing them amongst their choices based solely off of their rank in the list. The mathematical relationship between subsequent rankings is what I'm confused about though. I was considering an X^n distribution where each subsequent rank is weighted at X% of the previous, then using these ratios between ranks to assign points so that the sum of the individual choice’s “points” adds up to 10. Then the “points” for each choice option could simply be averaged across all responses to make a guess about the population. I have included an example in which I use X=80%, but this number is basically pulled out of my ass, and has a large effect on the final ranking for the population. Possibly an X^n distribution for subsequent ranks isn't even accurate, although I think it is. Even so, how would I find this X value so that it produces the most accurate ranking for the population?
I considered literally giving the responders 10 points to spend on their favorites and allowing them to organically distribute them amongst any number of their favorite foods, but this seems much less user-friendly. This could be the most accurate (or only) way to get meaningful data however.
My idea is to give them a list of 50 or so possible food options to choose from, and let them list their favorites in order of how much they like them. The responder can choose any number of responses as they want, as long as they are ranked in order of favorite. Each person’s response would be given the same weight, for example think about each responder having 10 “points” to “spend” on their rankings, and an algorithm then taking those 10 points and distributing them amongst their choices based solely off of their rank in the list. The mathematical relationship between subsequent rankings is what I'm confused about though. I was considering an X^n distribution where each subsequent rank is weighted at X% of the previous, then using these ratios between ranks to assign points so that the sum of the individual choice’s “points” adds up to 10. Then the “points” for each choice option could simply be averaged across all responses to make a guess about the population. I have included an example in which I use X=80%, but this number is basically pulled out of my ass, and has a large effect on the final ranking for the population. Possibly an X^n distribution for subsequent ranks isn't even accurate, although I think it is. Even so, how would I find this X value so that it produces the most accurate ranking for the population?
I considered literally giving the responders 10 points to spend on their favorites and allowing them to organically distribute them amongst any number of their favorite foods, but this seems much less user-friendly. This could be the most accurate (or only) way to get meaningful data however.
