I have a hunch you'd get better policy results if people were paid to consciously abstain from voting – so that the least-informed, now making their decisions based on last-minute TV ads or mass-mailers with crude messages, voluntarily opt-out – delegating the choice to others.

I too miss the days when only landowners could vote.

Sounds fantastic. But I can already see a problem of poor people being disproportionately incentivized not to vote. Maybe the payment would be a tax reduction instead that affects everyone proportionally to their income.

Let's temporarily assume for the sake of argument that 'poor people' could wind up significantly better off under the decisions of a system where low-information, low-motivation voters are discouraged – but not disenfranchised. There'd be fewer (Hugo) Chavez- or Trump- type winners.

If under such a system, the 'voluntary, compensated abstentions' are disproportionately 'poor people', what principle is being violated? Is the option-to-vote or the actuality-of-voting the more important value?

Is maximal voting participation a religious goal, to be pursued even if it delivers poor results, such poor results sometimes including the collapse of democratic-processes entirely? Or is voting just one part of a system to be evaluated based on how well it delivers welfare and protects rights?

I think it's arrogant to assume that you know better than (other) voters. If you believe a demagogue is bad, what happens if he turns out to be just what was needed (Churchill perhaps?). Some people say Trump is good for poor people by wanting to reduce welfare which would pressure more people off their ass and into work. Welfare does have that incentive problem so there is a tradeoff and it's not obvious how much welfare is the optimum amount. If you believe democracy itself is too important to leave up to the will of the people, what happens if that turns out to be wrong? China is doing fine without it, while South Africa is going down the gurgler with it and Egypt fell on its face attempting it.

I would lean a little bit in the direction of actually voting being more important than being able to vote. Anything less than 100% turnout is bound to have some bias in how the non-voters are selected, even if they're self selected.

I'm not sure about solving the other issues you mentioned, but I've often thought that a ~$100+ payment for voting in a national election would fix the voter turnout problem.

Interestingly, that solution would motivate the rich less than it would motivate the poor.

Even more American? make it a tax deduction.