stl ordering - strict weak ordering

Question

Why does STL work with a comparison function that is strict weak ordering? Why can't it be partial ordering?

Answer 1

A partial order would not be sufficient to implement some algorithms, such as a sorting algorithm. Since a partially ordered set does not necessarily define a relationship between all elements of the set, how would you sort a list of two items that do not have an order relationship within the partial order?

Answer 2

You can implement it for example by combining std::multimap/multiset with own predicate, overriding std::less.

Answer 3

You cannot perform binary search with partial ordering. You cannot create a binary search tree with partial ordering. What functions/datatypes from algorithm need ordering and can work with partial ordering?