The main oppositions to direct democracy seem to be that it would be too cumbersome and that people simply don't know enough about the issues to cast an intelligent vote. If we accept those complaints as being valid, then I have a proposal that would solve both.
It assumes, of course, that voting would be done via your personal computer, that there is a national voting website and that every registered voter would have a personal voter page that he could access. Special voting kiosks would be made permanently available to those without their own computer.
One way you could do things would be to manually cast your ballot on every piece of legislation as it came up for a vote. This would be subject to the two complaints above, however, and I suspect very few people would want to do that. So there are a couple of ways around the problem.
On the national voting webpage, there would be any number of individuals or groups that would give their endorsement for, or against, any piece of legislation. I could check the ACLU endorsement, for example, and vote according to their recommendation without having to read all the legislation myself. Or I could check the endorsements of several groups and vote accordingly.
But this still leaves me having to vote on every piece of legislation. The way to make that more manageable would be to tag your vote to a certain group, or groups, on your voter webpage. I could set it up so that my vote is automatically cast according to the ACLU endorsement. Or I could set it up to check the endorsements of several different groups and automatically vote whichever way has the most endorsements. If there were a tie, I'd get an email notice alerting me that I'd need to manually cast my ballot.
To prevent people from tagging their vote and then forgetting about it forever, your settings would expire after, say, three months and would have to be manually reset. You'd have to go back in at least four times per year and recheck your settings, otherwise your vote would not be cast.
So there you have it. Once again I have solved another of the world's problems.