Julian pointed out that some planeswalkers might be saving up for the bang power, and thus there are some roles they might never be. If this is the case, I think that priest is better than pair investigator for day 1, and that pair investigator is probably better than splitter, even in the early game.
Expected results of being a priest before list sizes drop (randomly choosing people and with mafia randomly killing people): (6/25)*(5/24) = 5% chance of getting "one of 3 people made this kill", and (6/25) - (6/25*5/24) = 19% chance of getting "none of these 3 people made this kill." Pair investigators get a guaranteed "2 people didn't make this kill", a 50/50 chance of getting x2 priors on someone making the kill vs getting x4 priors on someone making the kill. However, note that priests get their results "per kill" while pair investigators get their results "per day."
I think this means that for day 1 (where we expect 3 kills), it's best for planeswalkers to be priest. I find it unlikely that serial killers would punt making a kill by a day (losing expected 1/3 of a kill) just for a couple of planeswalker priests.
Splitters can generate a maximum of 3 investigations per day; however, mafia may kill people in split sets, and people in split sets might be mafia, such that that I think the expected number of town investigations gained from a town planeswalker being splitter is probably less than the number of investigations town gets from a town planeswalker being pair investigator (generating guaranteed 2 investigations).
To be clear though, I think that town getting vigilante kills from planeswalkers is mostly useful in the late game. In the early-mid game, we aren't usually that limited in sketchy people to lynch. Furthermore, if people have noticed they are on the lynch block, they can say useful things before they die (e.g. about their suspicions, thoughts on game, role, etc), whereas they cannot if they are vigilante killed. Like, I objectively think that it is a generally bad idea for town to vigilante kill me, ksedlar, before the end game, because I would have a bunch of stuff I would say before getting lynched. So, I personally think it's better for planeswalkers who think they'll die before the end game to not save their points, and to instead use them for daily powers. Though people likely to live until the end game (new players and players who aren't living near other players) may want to save points for vigilante kills in the end game.
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