Until the early 19th Century, Stalemate was a win for the party stalemated. Fact.
So who would win in a situation of a double stalemate? Would that game be scored 1-1?
I'm not sure how a 'double stalemate' is possible, any more than a double checkmate, but it would be the guy who was to move, but couldn't, who would win.
#323: The motivation for changing stalemate doesn't need to be low rated players making errors. It could simply be that we want to see more definitive outcomes and fewer draws in higher rated games.
If your goal is to eliminate draws then the US Chess forum had a couple of topics from a decade back for how to do that:
http://www.uschess.org/forums/viewtopic.php?f=23&t=15972
http://www.uschess.org/forums/viewtopic.php?f=23&t=16369
That also takes care of the issues involving the 50-move rule, repetition of position, insufficient mating material (lone K vs lone K is no longer a draw), etc.
A simple rule saying that inflicting stalemate is a win would mean that a lone king IS sufficient mating material as long as the opponent has an a or h pawn (final position could be that everything else is captured and the pawn is one square from promoting with that player's king immediately in front of it while the opposing king is on the same row but two files away). Eliminating stalemate can result in the lone king winning on time. (and it would be even easier if the rule was changed to say that inflicting stalemate was a loss).