I have a process by which people must compare a bunch of items against each other in pairs. For now, let's say we're comparing two at a time from a set of six items. The problem is that people end up having to make 15 comparisons to compare everything (n choose k), which is tedious. However, let's say that "assuming" one degree of accuracy is okay. That is, we can say that because A > B and B > C, that A > C, and because B > C, and C > D, that B > D, and so on. Is this the only (and best?) way to use assumptions for this combination? Does anyone have an idea about how to compare things like this?
2026-03-26 09:40:06.1774518006
N choose K and assumptions.
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You have to define the range of items and how pairs are compared. Each item might correspond to two characteristics, so we can represent it as an ordered pair. If the two values for the two items are just added, you can collapse the two characteristics to the sum and you get the transitive ranking you are hoping for. If you multiply the corresponding values of the pair and add the products this will not work. Maybe A is $(10,1)$, B is $(1,10)$ and C is $(4,3)$. Just adding the two values would lead you to choose A,B, but that is the worst you can do as it only scores $20$ while B,C scores $34$ and A,C scores $43$.