How does the Borda count work?

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I was watching this video. about ranking a bunch of proposals by dividing the full list in to sub lists and each person that submitted the proposals gets one of these sub-lists and ranks it. The lists are then combined to produce a global rank.

To understand it better I tried working through a simple example, 6 people each who have written a paper. So person A writes paper 1, person B writes paper 2... for example.

Then I decided to make the sub-lists have size 2, so there are 6 choose 2 possible sub lists, i.e., 15 sub lists. But for any given person, 5 of the lists has their own paper in it, so any one person can be given one of 10 sub lists.

What I'm confused about is how you can fairly decide who gets which lists? In my example I could have a sub list with paper 5 and paper 6 in it, and just not give that list to anybody - doesn't that then have an impact on what 5 and 6s global rank will be?