who gets to choose first is irrelevant – only number matter. it’s hard to think of an easy to understand example because very few relationships are bilateral and resource-limited in the same way as monogamous marriage. maybe think about it in terms of baseball players and teams: it doesn’t really matter who drafts who if you think about it. the current draft setup is a function of the disparity in number of players and teams, but if the quantities were to be reversed one could easily picture a world in which a players chose his team(s).
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