Hi Nick,
Deriving the side from the family (if one is provided) is exactly what people attempt to do with each DNA match, before contacting them and hoping for a reply. I understand that some sites now attempt to automate this (Ancestry’s “ThruLines” and MyHeritage’s “Theory of Family Relativity”), but I haven’t used them.
Otherwise, the only information a person receives about their matches limited to things like the following (the columns from a csv file provided by FamilyTreeDNA):
“Full Name”,“First Name”,“Middle Name”,“Last Name”,“Match Date”,“Relationship Range”,“Suggested Relationship”,“Shared cM”,“Longest Block”,“Linked Relationship”,“Email”,“Ancestral Surnames”,“Y-DNA Haplogroup”,“mtDNA Haplogroup”,“Notes”,“Matching Bucket”
In that case, the “Relationship Range” are “Suggested Relationship” are about the distance of the relationship, not which side it’s on. The “Matching Bucket”, however, predicts whether a given match is on your maternal or paternal side, but only to the extent that you have already mapped sufficient other matches onto your tree. Here’s an explanation of that Family Matching feature.
On GEDmatch, people use the Triangulation feature to relate matches. (That link might not be available unless you sign in.) Again, it’s only helpful if you’ve already figured out one of them.
Even if you had another user’s raw data (the file containing hundreds of thousands of SNPs) and compared it directly with your own, you wouldn’t know whether the matching segments were maternal or paternal unless you had first “phased” your data by comparing it with that of one or both of your parents. In the raw data file, the two letters that appear for each SNP do represent the maternal and paternal values, but they are not in that order; rather, they are ordered alphabetically (for example, you will find “AG” but not “GA”). In fact, you wouldn’t be sure whether the matches were really matches (see examples here).
Just as our chromosomes don’t have numbers stamped on them (the traditional numbering is simply according to decreasing length), so also they don’t have “maternal” and “paternal” stamped on their component parts.