Why use “b < a ? a : b” instead of “a < b ? b : a” to implement max template?

C++ Templates - The Complete Guide, 2nd Edition introduces the max template:

template<typename T>
T max (T a, T b)
{
  // if b < a then yield a else yield b
  return  b < a ? a : b;
}

And it explains using “b < a ? a : b” instead of “a < b ? b : a”:

Note that the max() template according to [StepanovNotes] intentionally returns “b < a ? a : b” instead of “a < b ? b : a” to ensure that the function behaves correctly even if the two values are equivalent but not equal.

How to understand "even if the two values are equivalent but not equal."? “a < b ? b : a” seems have the same result for me.

std::max(a, b) is indeed specified to return a when the two are equivalent.

That's considered a mistake by Stepanov and others because it breaks the useful property that given a and b, you can always sort them with {min(a, b), max(a, b)}; for that, you'd want max(a, b) to return b when the arguments are equivalent.