algorithm - Calculate comparative rank of things compared two at a time -

how calculate weights of 10 things express person's relative preference when input data follows:

the list of 10 things presented in random pairs (ignoring order, vs b might shown, or b vs a, not both; , not item itself);

a better b d better f h better b c better j 

etc.

is there way rank or weight 10 items data this? , there way shorten sequence 10! / (2! (10 - 2)!) =45 questions.

you're making dangerous psychological assumption here: assume "better than" relation transitive, from

a > b b > c 

directly follows that

a > c 

that is, without loss of generality, not case humans preferences. puts whole approach in questionable light.

however, if can justify assumption, yeah, breaks down sorting problem. there's truckload of sorting algorithms out there, rely on existence of ordering relation ">". weight position in sorted list.

every real-world programming language out there has library contains @ least 1 sorter algorithm; languages have way of specifying function call compare 2 elements, boils down calling sorter function unsorted list , function call when comparing 2 things.

if assumption "better than" relation transitive cannot made, things lot more complex. basically, can build directed graph , try find paths through it, graph might not cycle free, , there might no definite possibility assign weights.

there's decades of psychological method research on how test such things; i'd recommend finding university offers psychology programmes , asking people there.