I think "One person, one vote" is to blame, not democracy in general. A different voting system should be developed that weighs how much people care about a particular issue, and how much they know about it.

To weigh how much people care about an issue, you could:

• Charge people a nominal sum to vote on an issue; or even let them buy as many votes as they want. I know everyone's first reaction is to say that this would favor the rich. I think it might favor the working classes. The rich already buy votes, and very cheaply relative to their market value. The working are unable to, because they are uncoordinated, and the barriers to entry are very high. It would at least drive up the price of buying votes for the rich, and reduce the deficit.
• Give every voter a limited number of votes per year, which they may distribute among different issues as they see fit.

To weigh how much people know about an issue, you could:

• Have voters choose areas of expertise from a menu; they will then be allowed to vote only on issues in those areas.
• Award more votes to voters who: complete high school, complete college, complete an advanced degree, serve in the military, complete a government-authorized test on the subject area, score well on standardized tests created by the Dept. of Education
• Require literacy tests. I am aware that literacy tests were historically used to deny voting to blacks. Times have changed. If someone in America can't read today, they shouldn't blame racial discrimination.
• Have a short factual test at the polls. Voting weight will be proportional to number of correct answers.
• Have Congress draw up a list of things to predict each year. Each voter must make their own predictions. Next year, Congress votes on what the answers to those things were. Voters have weights proportional to the correctness of their predictions. Alternately: Apply this to members of Congress.

You could frame legislation not as a binary pass-or-fail proposition, but as having a parameter that varies from, e.g., 0 to 1000, and have people vote on the parameter value, and take the average or median.

I am aware that these ideas have problems. It is not helpful to respond to ideas by immediately dismissing them because they don't work perfectly out of the box. There is a powerful bias toward de-emphasizing the problems with existing social arrangements. The problems with one-person one-vote are vast; and IMHO any of the above ideas, while problematic, would be less problematic.