(My take on the two cows metaphor. Here’s how each political ideology plays checkers.)
A conservative plays by the traditional rules and follows conventional, time-tested strategies. Don’t expect an exciting game.
A progressive keeps putting back captured pieces to give them another chance, and also refuses to king anyone, because that would create inequality. There are no winners or losers. The game keeps going until the players get bored and leave.
A libertarian gets his friends to each control a separate piece, so that they can move as individuals, not as a collective. Then they refuse to coordinate and fail to win even a single election game.
An objectivist does the same thing as a libertarian, but is more self-righteous about it.
An anarchist plays by their own rules, regardless of which rules their opponent is following. The board quickly becomes a chaotic mess.
An anarcho-capitalist does the same thing as an anarchist, but has a different opinion about what the result will be.
A social democrat, instead of actually playing, asks everyone in the room who they think the winner should be.
A communist wipes off the pieces and rips up the board, because competition alienates the masses. If their opponent is angry, it’s only because they’ve been brainwashed by the bourgeois.
A monarchist chooses one special-looking piece at the beginning of the game, and then makes sure that it’s the only piece to get kinged.
A theocrat waits for God to tell them what to do.
A fascist doesn’t allow any piece to stray too far from the others. They must move as a group.
A Nazi shoots the loser. They are not contributing to the checkers champion master race.
A centrist doesn’t play at all, but tells everyone else what an awful job they’re doing.