The default metaphor is a village of people who can extrajudicially murder those among them with sufficient democratic consensus, on suspicion of being part of a secret group of people who murder others at night, either as members of organized crime, or a werewolf pack.
The default metaphor sucks a little bit for a few reasons:
1) Some alternatives might fare no better, but they sometimes require some of suspension of disbelief. If the villagers don't care about rule of law anyway, why don't they torture one Mafiosi to learn the others? Why don't they use a jail cell in place of death to keep this option on the table? Heck, why don't they volunteer to sleep in a jail cell if the odds of getting murdered at night is so high? With Werewolves, why not put them in shackles, verify they are werewolves when they transform, then kill them? And why don't multiple werewolves have multiple kills per night? (the mafia is an "organization" and gets somewhat more of a pass, there).
2) Group extrajudicial murder is bad in principle. In practice historically it has been used in accordance with prejudices rather than a tool that punished crimes (with an ultimate punishment that is now controversial or condemned even judicially). Nightly individual murder is also bad, creating a game with no protagonists. "Tragic heroes" in art can be well done, but this is not that.
3)
The metaphor poorly reflects the win conditions of the game
. It is likely the case that the metaphor accurately reflects the game's older, commonly understood win condition, or even what you can encounter that some casual party game players perceive as the win condition: that only living players can win. Well, now I'm not sure, chicken or the egg, on whether the metaphor leads to that misconception, or a previous conception led to the metaphor. But saying a dead townie has "won" is a bit presumptive about his/her/their moral code, some people are in it for themselves. Similarly, organized criminals often betray loyalty to avoid jail time, let alone death, so it is confusing for a dead Mafiosi to be considered a winner (though, with the level of fanaticism implied by "Cults", this works much better).4) It's maybe kind of violent. Does everything have to be violent? This one's a bit more subjective.
I like hearing of and thinking about other metaphors for mafia. My last mini theme I ran, I used very different explanations for why each player lost their voice and their vote, and it grew on me pretty rapidly. "Purgatory" has its own metaphor, with less of the details on how the democracy works but a gratifying finality to decisions.
I'm hoping to hear people's ideas and brainstorms for how they've made metaphors that work or fit well (used and unused in game). Most metaphors won't fit perfectly one way or the other, but coming up with ways they can fit the mechanics is fun.