I see one problem with my math already.
Krypsyn: The chance of other Lover's Pairs containing Mafia:
1 - (5/7 * 3/5) = 57.14%
This means that each person in the other Pairs has a 28.57% chance to be Mafia, individually.
This has a bad assumption: that your partner won't ever be selected as Mafia.
Thus, it should actually read:
The chance of other Lover's Pairs containing Mafia:
1 - 2/3(5/7 * 3/5) - 1/3(5/7 * 4/6) = 55.56%
This means that each person in the other Pairs has a 27.78% chance to be Mafia, individually.
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However, this is all total gibberish anyway, if this is taken as a pure Monty Hall Problem.
The odds before knowing your own alignment that each Pair, including your own, will have Mafia is 50%. Thus, everyone has an equal 25% chance. However, if you are town, then you are revealed as having 0% chance to be Mafia. Each Pair
still has a 50% chance to contain Mafia, cumulatively, so your partner must then make up the difference in your Pair. This makes his/her probability to be Mafia 50%.
drealmer7: What did I do?!
Nothing.