Democracy is hailed as the holy grail of modern civilized culture. Most modern cultures agree that it's the best form of inefficient government.
The degree of corruption in a government is the degree that the actions of government reflect the will of the population at large. Unfortunately even if the population directly influences decisions, this government is going to be average at best due to sheer statistics of the people.
In every other faculty of life we are able to find experts who complete tasks for us with a greater efficiency than if we were to try on our own. Our whole modern economy is based on this principle of specialization, but when it comes to the marketplace of governance we have settle for the idea that one person should have one vote, regardless of the vote topic. I think that specializing voting power in the way we specialize the economy would allow for something greater than the sum of the parts. For votes that pertain to tax law, you would assume that an accountant should have more vote power than a carpenter.
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Since governance for large amounts of people requires immense amounts of time and computational effort, we elect representatives who ideally work on these issues full-time so the citizens can focus on their respective specializations. The people who represent us can't be experts in every field, yet we trust them to find experts in every field. Breaking down governance into specialties allows a group to avoid having umbrella representatives and divides the effort to a larger array of people.
If every citizen was limited to 1 or 2 specialities, then perhaps we can scale direct democracies in a way that lets people govern the field of their specialty and not rely on a single leader to make all decisions for them.