Mark's answer is correct but could use a bit more explanation.
The problem is indeed due to a subtle difference between how method groups are handled and how lambdas are handled.
Specifically, the subtle difference is that a method group is considered to be convertible to a delegate type solely on the basis of whether the arguments match, not also on the basis of whether the return type matches. Lambdas check both the arguments and the return type.
The reason for this odd rule is that method group conversions to delegates are essentially a solution of the overload resolution problem. Suppose D is the delegate type double D(string s)
and M is a method group containing a method that takes a string and returns a string. When resolving the meaning of a conversion from M to D, we do overload resolution as if you had said M(string). Overload resolution would pick the M that takes a string and returns a string, and so M is convertible to that delegate type even though the conversion will result in an error later. Just as "regular" overload resolution would succeed if you said "string s = M(null);" -- overload resolution succeeds, even though that causes a conversion failure later.
This rule is subtle and a bit weird. The upshot of it here is that your method group is convertible to all the different delegate types that are the second arguments of every version of Sum that takes a delegate. Since no best conversion can be found, the overload resolution on method group Sum
is ambiguous.
Method group conversions rules are plausible but a bit odd in C#. I am somewhat vexed that they are not consistent with the more "intuitively correct" lambda conversions.