Definition
Fixed Pair (COMSOC)
A pair of distinct alternatives
is fixed in a non-empty profile if either Here
is the multiset of all voters’ submitted strict rankings, with one occurrence per voter. For in tuple notation, let The double braces denote a multiset: identical ballots from different voters remain separate occurrences. Thus
keeps precisely the ballots that rank above , and keeps those ranking above . Equality with means that every ballot is retained. A fixed pair therefore has unanimous agreement on its order. In terms of the pairwise support function,
, so the condition is equivalently or .