I not sure what you mean exactly by "causal reduction" as opposed to a magnification. Surely the rules governing neural activity are simpler than descriptions of thoughts - even if the number and complexity of these neural interactions have little hope of human comprehension.
In Zombies! Zombies? Eliezer mentions that one aspect of consciousness is that it can causally affect the real world, e.g. cause you to say "I feel conscious right now", or result in me typing out these words.
Even if a generally accepted mechanism of consciousness has not been found yet are there any tentative explanations for this "can change world" property? Googling around I was unable to find anything (although Zombies are certainly popular).
I had an idea of how this might work, but just wanted to see if it was worth the effort of writing.