[dylwil3]

Yep, see Eckmann for a generalization and precise characterization: https://core.ac.uk/download/pdf/82385648.pdf

[contravariant]

Awesome, always nice to see my mathematical intuition still works. Also an interesting piece of mathematics.

My main takeaway was the following conclusion

> [E]xcept for the contractible case either no social choice function can exist on P, or if it exists for all n then unexpected properties turn up.

[ykonstant]

The notion of "space with mean" from that paper seems to be of independent interest; nice.