Why ref and out are not sufficient to disambiguate overloaded in C#?

Question

For example, why this method Max(ref int x, ref int y) is not considered overload of Max(int x, int y)? Why is the same with out?

Answer 1

This question presupposes a false premise.

 Max(int x, int y)
 Max(ref int x, ref int y) 
 Max(out int x, out int y)

are all overloads of a method named Max. However, note that only one of the last two may be present in any given class definition. From the specification §3.6:

The signature of a method consists of the name of the method, the number of type parameters and the type and kind (value, reference, or output) of each of its formal parameters, considered in the order left to right. For these purposes, any type parameter of the method that occurs in the type of a formal parameter is identified not by its name, but by its ordinal position in the type argument list of the method. The signature of a method specifically does not include the return type, the params modifier that may be specified for the right-most parameter, nor the optional type parameter constraints.

[...]

Although out and ref parameter modifiers are considered part of a signature, members declared in a single type cannot differ in signature solely by ref and out. A compile-time error occurs if two members are declared in the same type with signatures that would be the same if all parameters in both methods with out modifiers were changed to ref modifiers. For other purposes of signature matching (e.g., hiding or overriding), ref and out are considered part of the signature and do not match each other. (This restriction is to allow C# programs to be easily translated to run on the Common Language Infrastructure (CLI), which does not provide a way to define methods that differ solely in ref and out.)