- Mon Aug 26, 2019 12:46 pm
Great (and interesting) question about circular game scenarios!
To give you a specific example of what Dave means, the most pertinent example of a circular game scenario where it could be advantageous to depict the mirrored versions of a "block rule" (a rule stating two variables must be arranged consecutively) is the fourth game on the October 2003 exam, which arranges 8 seats around a table. The third rule in that game states, "Ingrid sits immediately next to, and immediately clockwise from, Olivia." On the right side of the diagrammed circle, O will appear just above the position in which I appears. On the left side of the diagrammed circle, O will appear just below the position in which I appears. Notice this "mirroring" diagramming is required because of the fact that O and I's positions relative to one another are fixed, and the fixed placement looks different on different sides of the circle.
If the rule dispensed with the "immediately clockwise from" requirement, the position of the two variables would not be relatively fixed, and you wouldn't need the mirroring form of diagramming.
There have been so few disclosed circular games in the history of the test that this "OI" block rule is the only instance I've uncovered of a "block rule" where mirroring was necessary to capture the implication of the block relationship. Are there other wordings of the rule that are possible? Yes. In the game above, imagine the seats had been numbered 1 through 8. A rule that said, "Ingrid sits immediately next to, and in the next highest numbered seat from, Olivia," would require mirroring. A rule that said, "Ingrid sits immediately next to Olivia," would allow the two be on "either side" of each other and therefore not require mirroring.
I hope this helps!