For me day one is tricky because we're trying to find a balance between a random lynch without discussion and a day-one-from-last-game clusterfata. Even discussion and disagreement on how to go about the first lynch can become useful when looking back in the future.
The only problem I see with random lynch based on (least) favorite characters is that it can also be influenced by the mafia. A few extra votes on one character from them would be enough to tilt it in their favor.
That said, I would be more in favor of lynching a less active poster, perhaps in a couple days time to be fair. The counter-argument is of course that mafia could add in a few random thoughts here and there to boost their post count and avoid the lynch. But, until I hear or think of a better strategy, that's my line of thinking.
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