My personal take on this question is that it would follow that we are living in "the best of all possible worlds" if God were a utilitarian, that is, if we viewed God as an agent making decisions based on a Utility or Goodness function. This would allow God to assess possible worlds and make comparisons of the form:
- Goodness (possible_world1) > Goodness (possible_world2)
- Goodness (possible_world1) < Goodness (possible_world2)
- Goodness (possible_world1) = Goodness (possible_world2)
Thus, upon creation God essentially solved an optimization problem, by actualizing one specific world (the one we are living in right now) among all possible worlds that maximize the Goodness function. However, at least in Christianity, viewing God as utilitarian is debatable (see Can the Christian God be a Utilitarian?). That makes me think that perhaps you don't need a utilitarian God to still believe that this is the best of all possible worlds that could have been created.
Under what conceptions of God does it follow that we necessarily live in "the best of all possible worlds"? Are there more options besides a Utilitarian God?