Method for ranking multiple items based on a population of rankings?

[KingNothing]

Imagine that I want to rank the top 3 foods of all time. I want to ask ten different people to answer this question. So I get answers such as:

Mashed Potatoes > Artichokes > Carrots
Beef Jerky > Mashed Potatoes > French Fries

...etc. Is there an established method or algorithm for compiling these rankings together? It's clear that you can't simply ask everyone for their 'one favorite', because if everyone says Beets, the results say nothing about the second best food.

This sort of thing has a lot of applications in sports statistics, ranking teams, players, etc.

 

[EnumaElish]

What do you mean by "compiling these rankings together"?

Not knowing the exact question, here's something that might be useful to look at: http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem

 

[John Creighto]

What do you mean by "compiling these rankings together"?

Not knowing the exact question, here's something that might be useful to look at: http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem

Interesting. I guess no ranking system is perfect. However, we could still rank them. For instance:
-what percentage, chose the item as their first choice, their second choice and then their third choice?
-another option: assign a given point value to each choice. The point value could be equal for all choices, or the first choice could be given a higher point value.
-or maybe some kind of relative ranking. Whenever x>y then x goes up an equal amount that y goes down.

Here might be an interesting value, initially, rank items by one of the first two methods, then use some kind of Monte carlo competition, where you randomly select a given preference, then change the items relatively based on that preference (simmillar to the third method). Or alternatively, randomly select two people, and if they each have the same item on the list but ranked differently then adjust the overall rank based on that.