I would say "The Western World's answer".
When to use the Saxon Genitive (the possesive "'s") is a common problem. A common answer to many such problems in English is which one is quicker and easier to say, but there are certain rules for the Saxon Genitive. I think it's something to do with whether the subject is a person or a thing. For example:
"It's Peter's restaurant." is fine,
but we don't usually say
"Peter is the restaurant's owner"
instead we say
"Peter is the owner of the restaurant"
In the case of your sentence I believe we can think of the Western World as a large collection of people, therefore "Western World's owner".
I know I haven't expressed the rule very clearly because I don't remember it very well but I'm sure it's very simple to understand if someone can explain it better than I have.