I often get the sense that these games are broken for enlightened players, the way to win is to coordinate
Sounds like this should be true for the group as a whole but not necessarily for every individual in the group. That is, a coordinated group could make 5 out of 6 players win, but Alice might believe that she’s a very skilled player and personally has a greater than 5⁄6 chance of winning if people play “normally”, and thus believe it’s in her personal interest to discourage coordination.
This still implies that someone is making a mistake, because the players can’t all have >5/6 chance, but it doesn’t require that everyone is making a mistake.
(Also note it should theoretically be possible to assign probabilities of being the scapegoat in such a way that every player is at least as well-off as if you hadn’t coordinated, but that doesn’t help Alice unless she can convince the rest of the group to actually assign her that probability.)
Sounds like this should be true for the group as a whole but not necessarily for every individual in the group. That is, a coordinated group could make 5 out of 6 players win, but Alice might believe that she’s a very skilled player and personally has a greater than 5⁄6 chance of winning if people play “normally”, and thus believe it’s in her personal interest to discourage coordination.
This still implies that someone is making a mistake, because the players can’t all have >5/6 chance, but it doesn’t require that everyone is making a mistake.
(Also note it should theoretically be possible to assign probabilities of being the scapegoat in such a way that every player is at least as well-off as if you hadn’t coordinated, but that doesn’t help Alice unless she can convince the rest of the group to actually assign her that probability.)