The matching algorithms and their results always make me question how models can be accurate interpretations of the real life…
Taking for example the Deferred Acceptance Algorithm in the heterosexual market with strict and transitive preferences, let me recall the given result where each woman is matched with a man and viceversa (assuming no one stays alone). However, what could happen if we assumed for a second that in this “Who gets who?” problem we are not supposed to be matched with only one person? We could still have strict and transitive preferences, not over individuals, but over groups of individuals.
In the US the estimation is that around 21-57% of married men cheat and 11-35% of married women do too. Is this a warning that our matching theories do not represent our real world or is something else is happening? The problem with the model might not be dealing with cheating (finding a blocking pair) or moving to another Pareto efficient equilibrium (either men or woman optimal), maybe what problem is the assumption of monogamy.
I found this video in one of my favorite science Youtube channels that explains a lot and I would like you guys to watch. As you will see, only 3% of all animals are monogamous. Is this assumption of monogamy in the matching theories a moral assumption? Or are we just trying to model what we observe in our real world? Would we see a stable equilibria in a non-monogamic society? Can a match still be called stable in a monogamic society where open relationships are morally acceptable?