An indifference relation over the information state {w_pq, w_qr, w_pr} necessarily contains all reflexive world-pairs, and possibly one, two, or three non-reflexive pairs.

The problem with the system of Groenendijk (2009) and Mascarenhas (2009) is manifested by the fact that this issue cannot be represented by means of an indifference relation. An indifference relation over the information state \(\{w_{pq},w_{qr},w_{pr}\}\) necessarily contains all reflexive world-pairs, and possibly one, two, or three non-reflexive pairs. In either case, however, the resulting issue does not correspond to the one depicted in Figure 1.