It's harder to answer Subhan's challenge - to show directionality, rather than a random walk, on the meta-level.

Even if one is ignorant of what humans mean when they talk about morality, or what aspects of the environment influence it, it should be possible to determine whether morality-development over time follows a random walk empirically: a random walk would, on average, cause more repeated reversals of a given value judgement than a directional process.
For performing this test, one would take a number of moral judgements that have changed in the past, and compare their development from a particular point in human history (the earlier, the better; unreversed recent changes may have been a result of the random walk only becoming sufficiently extreme in the recent past) to now, counting how often those judgements flipped during historical development. I'm not quite sure about the conditional probabilities, but a true random walk should result in more such flips than a directional (even a noisy directional) process.
Does anyone have suggestions for moral values that changed early in human development?