The word 'relative' gets thrown around a lot these days, especially when talking about morality. I'm constantly hearing claims that morality is relative, but people never seem to specify what exactly is relative about morality. More importantly, people have this idea that if morality is relative then there can be no objective morality. Realizing that the upsurge in the idea of relative morality and the more extreme idea of relative "truth" was largely a response to Einstein's theory of relativity makes this claim sound quite strange to the physicist who realizes that the theory of relativity is actually a very objective theory.
The problem is that morality can only be relative with respect to some variant. However, this could very easily lead us to an objective description of morality that takes that variant as an input. For instance, saying that morality is relative to a society's belief merely means that our objective description of morality needs to take "societal beliefs" as an input. The fact that an action can be good in one society and bad in another doesn't mean much for objectivity. It just means that our description of morality will be "Action X is bad in a society with belief set Y, and good in a society with belief set Z," and this description will still be objective.
Many people also fail to separate possible variants. Often the claim "morality is relative" is synonymous to the claim "morality is relative to pretty much every variant you can think of." This is problematic because it generates a false dichotomy. When I say morality is relative, people think I mean that morality is relative to every variant, including everyone's beliefs (in this way, 'relative' is basically interpereted as 'subjective'). But if I say morality is not relative, then people think I mean that morality is not relative to any variant whatsoever. It divides the positions into "If I believe X is right then X is right" and "X is right regardless of anything," and my position is neither of those.
When I say morality is relative, I mean that morality is relative to some non-belief circumstances. In other words, killing is usually wrong, but there may be circumstances that make it right (like self defense). However, given a single set of circumstances, either killing is right regardless of your beliefs or killing is wrong regardless of your beliefs. While I admit that the morality of an action must to some extent depend on the state of affairs in which that action is performed, I realize that this does not necessarily mean that one's beliefs about morality change morality. I can claim that murder is wrong here regardless of your beliefs without having to claim that murder is always wrong no matter what the circumstances; a morality that is both relative and objective.
Furthermore, even IF morality is relative to one's beliefs or society, this would not necessarily preclude a belief-independent means of choosing between possible actions. To demonstrate why this is so I will of course use a mathematical analogy.
Is 10 a big number? The answer to this question will vary depending on your frame of reference. 10 is a big number when counting the number of PS3s I own, but a small number when counting the number of seconds it's been since I last ate. To make a big/small system objective we'd have to input information about what it is we're counting.
Is 10 bigger than 9? The answer to this question is yes, and this answer does not depend on your frame of reference. 10 is bigger than 9 when counting the number of PS3s I own, and it's still bigger than 9 when counting the number of seconds it's been since I last ate. An objective bigger/smaller system does not need to input the items being counted.
So let's assume for a moment that good and evil depend on one's personal beliefs just as big and small numbers depend on what you're counting. Yet perhaps better and worse could function more like bigger and smaller, without any dependence on one's personal beliefs. While the statement "Action X is good" may depend on what bar one sets for counting as 'good,; the statement "Action X is better than Action Y" may not. So even if good and evil depend on personal or societal beliefs, better and worse could still be independent of those beliefs. And that's all we really need for an objective moral system.