Explorations of self-selective social choice functions

In this study, we analyze self-selective social choice functions focusing on whether one can escape dictatoriality. Two ways are examined: In the first attempt, the set of social choice functions is restricted to tops only. With this restriction, selfselectivity turns out to be equivalent to dictatoriality. In the second, the set of prefence profiles restricted to single-peaked ones. Here we show that there are some self-selective social choice functions which are not dictatorial.