A note on the non-emptiness of the stability set when individual preferences are weak orders

It is well known from the Nakamura's theorem [Nakamura, K., 1979. The vetoers of a simple game with ordinal preferences, International Journal of Game Theory 8, 55-61.] that the core of a voting game is nonempty for all profiles of individual preferences if and only if the number of alternatives is less than the Nakamura number. The aim of this note is to provide an equivalent result for the stability set introduced by Rubinstein [Rubinstein, A., 1980. Stability of decision systems under majority rule, Journal of Economic Theory 23, 150-159.]).