A Parity Cop is a player who can investigate other players at night to determine which faction they belong to: different alignments give different results. However, the assignment of results to factions is effectively arbitrary, and the Parity Cop will thus not initially know which results will correspond to which alignments. As such, the role effectively just allows the Parity Cop to determine whether or not two players who they have investigated (at some point in the game) have the same alignment as each other.
Typically speaking, Parity Cops cannot self-target, as it would be too easy a way to learn the result given for their own alignment (typically Town), and thus deduce by elimination that all other results were for anti-town factions.
An alternative version of a Parity Cop can target two people per night, and are told whether or not they have the same alignment (as opposed to being given a codeword for the factions they're in). This variant is rarely used due to being too powerful to easily balance around.
The Parity modifier could in theory be used for other investigative roles; for example, a Parity Neapolitan would get one result on Vanilla Townies, and a different result on players who were not Vanilla Townies, but not know which result was which. Roles such as Parity Tracker, while meaningful, are likely too weak to be usable (while the Tracker might eventually deduce what result corresponded to "no action", they would be unlikely to establish which results corresponded to which players.)
Use and Power
If a Parity Cop wastes an investigation on a player who has a known alignment, they effectively become equivalent to a Novice Cop, a fairly strong role. However, the role is probably more powerful when used on players who are hard to read, like a regular Cop is; if at any point any of the investigated players die, then the alignment of all the others will retroactively become known, and Cop-type information is generally almost as useful even if it's significantly delayed in arriving.
Note that in all cases a Parity Cop is useless unless they get at least two investigations off. As such, it should be seen as a late-game role that rewards its owner for surviving for a long time.
The variation that targets two players per night is less than twice as powerful as a standard Parity Cop (as it does not allow comparison of results from different Nights). However, it's still much more powerful than a regular Cop, especially outside multiball; discovering that two players are the same alignment normally makes it obvious what alignment that is, and if the alignments are different, town will often be able to discover which is scum (and thus confirm the other as town in the process).
- The Cop of unknown sanity is similar to a Parity Cop. (In fact, a Cop who is known to be either Sane or Insane, but not which, is exactly equivalent in a two-faction game.)