Firstly, I really like this kind of thing and enjoyed you analysis.
One thing I think it misses out on Marek’s choice of who to inspect.
Liberal!Marek chooses without knowledge of who is fascist and who is liberal so has a 50:50 chance of selecting a fascist or a liberal. So if he is a liberal there is a 50:50 chance of him selecting a fascist, outing them and getting into this argument. (I’m ignoring the possibility that Marek will just say nothing)
Fascist!Marek already knows who is fascist/liberal and looking at the party membership card is a charade for him. He has 4 options:
1. Choose liberal, claim liberal
2. Choose liberal, claim fascist
3. Choose fascist, claim fascist
4. Choose fascist, clam liberal
On the surface option 3 doesn’t seem likely. Options 1 and 2 are the options investigated in the OP (but assuming liberal was chosen by chance). Option 4 also seems like it might be used.
If we set option 4 to 0% then Marek is guaranteed to choose a liberal and assume the 50:50 bold/timid split for 1&2 then fascist!Marek has a 50:50 chance of getting into this argument—the same as liberal!Marek so this provides no evidence either way.
If we say split the probabilities of option 1,2 and 4 in 25%:25%:50% then we return to the result in the OP. If option 4 is between 0 and 50% likely then the argument happening is somewhere between 0 and 1 bit of evidence in favour of Marek being liberal.
***
Of course fascist!Marek makes the choice between the 4 options in the knowledge that everyone already thinks he’s probably a fascist (although he’s probably not Hitler). This will effect his choice as he may be extra keen to send a signal that he isn’t a fascist, so would ideally like to not accuse anyone in the knowledge that everyone will probably side with the person he accuses. He might choose option 1 as this will increase that person’s trust in him and also cast doubt on that person in the mind of everyone else. Even option 3 might be appealing—it might harm Marek but it makes the person he accuses look very liberal.
But everyone knows that Marek is in this position and Marek knows that everyone knows so this begins to hurt my head and is also why this kind of game is amazing!
Harry, smiling, had asked Professor Quirrell what level he played at, and Professor Quirrell, also smiling, had responded, One level higher than you. - HPMor
Firstly, I really like this kind of thing and enjoyed you analysis.
One thing I think it misses out on Marek’s choice of who to inspect.
Liberal!Marek chooses without knowledge of who is fascist and who is liberal so has a 50:50 chance of selecting a fascist or a liberal. So if he is a liberal there is a 50:50 chance of him selecting a fascist, outing them and getting into this argument. (I’m ignoring the possibility that Marek will just say nothing)
Fascist!Marek already knows who is fascist/liberal and looking at the party membership card is a charade for him. He has 4 options:
1. Choose liberal, claim liberal
2. Choose liberal, claim fascist
3. Choose fascist, claim fascist
4. Choose fascist, clam liberal
On the surface option 3 doesn’t seem likely. Options 1 and 2 are the options investigated in the OP (but assuming liberal was chosen by chance). Option 4 also seems like it might be used.
If we set option 4 to 0% then Marek is guaranteed to choose a liberal and assume the 50:50 bold/timid split for 1&2 then fascist!Marek has a 50:50 chance of getting into this argument—the same as liberal!Marek so this provides no evidence either way.
If we say split the probabilities of option 1,2 and 4 in 25%:25%:50% then we return to the result in the OP. If option 4 is between 0 and 50% likely then the argument happening is somewhere between 0 and 1 bit of evidence in favour of Marek being liberal.
***
Of course fascist!Marek makes the choice between the 4 options in the knowledge that everyone already thinks he’s probably a fascist (although he’s probably not Hitler). This will effect his choice as he may be extra keen to send a signal that he isn’t a fascist, so would ideally like to not accuse anyone in the knowledge that everyone will probably side with the person he accuses. He might choose option 1 as this will increase that person’s trust in him and also cast doubt on that person in the mind of everyone else. Even option 3 might be appealing—it might harm Marek but it makes the person he accuses look very liberal.
But everyone knows that Marek is in this position and Marek knows that everyone knows so this begins to hurt my head and is also why this kind of game is amazing!