I'm not worried that much about software bias - I feel that a lot of good could be achieved with software clear enough for all sides to accept it represents their interest in an ok-ish way.
What I'm worried about is this: technology has always been a force multiplier for those who wield it. For now it's us (maybe in the future it will be a superintelligent AI, maybe not). Even if we manage to write a pretty unbiased governing software, how are we going to ensure that it isn't subtly manipulated by some interested party? And can we ensure that while also making the system extensible, so that it can cope with the demands caused by the impact of ever-progressing technology on our societies? It seems to me that the two goals - a system above humans and a system that can evolve with us - are fundamentally incompatible.
Two problems: One, do we really get unbiased software? Or do we get software that's claimed to be unbiased, but has actually been quietly biased according to the authors' prejudices (and all attempts to criticize it get shot down because "it's really unbiased, so the problem is with you")? Or do we really get a good-faith attempt to write unbiased software, that winds up biased in ways and for reasons that we don't understand?
Second, how are you going to make this happen? It's going to involve taking power away from the existing powers-that-be. And you don't sound like you're going to do it by democratic means, since you see democracy as broken. How do you propose to do it? ("Bottom up" isn't enough of a plan. At each step, it's going to be a war against entrenched interests. How are you going to win?)