Sorting a set of objects by a user's preference

Question

Given a set of n objects in no specific order (n = 5 in this example):

{
    apple,
    orange,
    banana,
    cherry,
    cabbage
}
         


        

Answer 1

You don't need to compare every item against every other item. That would require you to ask the user 15 questions to sort 5 items. It's been proven that you can get a total ordering of 5 items in 7 comparisons.

You can accomplish this with a sorting network. For any N, you can create a series of comparisons and swaps that will sort the items. There are known optimum sequences for sorting up to 16 items. Beyond that there are algorithms that will generate sorting networks (see Constructing sorting networks in the linked article). Although those networks are not proven to be optimum, they're probably more efficient than a general-purpose sorting algorithm.

Your larger problem, which I think you gloss over too easily, is the very real possibility of circular logic. Transitivity typically doesn't hold when it comes to user preferences.