I understand that the social preference relation need not be an ordering. But is it also not necessary that it be complete? I have read conflicting viewpoints on this.
We haven't been taught what the exact functional form of a SCR is supposed to be, just that it is a function of the individual preference relations, so it seems to me that if we are allowed to use piecewise functions, we could construct a function from the individual preferences that could be incomplete, but I am not sure how to go about that.
Please help me understand this.