Because Permission Granted has problems in some environments, many folks choose to authenticate users before allowing them to edit wiki pages. The most common form of useful authentication is to have some reliable check that the edit is being performed by a member of the community responsible for the wiki.
Turn on the edit permission checks for your wiki. Then make sure some mechanism is set up that can correctly identify editors as members of the community. For example, perhaps they need to know a secondary password, are issued authenticators by a central authority, or merely have accredited themselves appropriately on a password-protected account.