By effective, I mean a clean election that produces a winner who can act with the consent of the governed, including those who didn't vote for him.
You don't have to believe there is cheating in order to support reforms. You only have to accept that a lot of other people believe there is cheating and that this is bad for the country.
Many kinds of cheating have been alleged. A major kind of cheating involves the actual vetting and counting of the ballots, the kind of cheating Lyndon Johnson did to get into the Senate. In recent elections it takes longer and longer to count the votes, for no apparent reason, which creates suspicions of widespread ballot-count cheating.
What to do? There's an old trick used in technical organizations when a critical decision depends on a complex calculation. The trick is to have two groups do the calculation and make sure they get close enough to the same answer.
In an election, roughly speaking, you would divide the vote-counters into Team A and Team B. The teams would be sequestered like juries and then would independently gather the ballots, decide which ones are legal to count, and actually count them.
If the two counts agree within say 10% of the margin of victory, then the winner is declared. If not, then they go back and count again. The teams are not told how big the discrepancy was or in what direction, only that there was a discrepancy. They have to keep trying until agreement is reached.
All of the individual counts would be made public in the end, and there would be a report listing the discrepancies so they could be prevented in the future. (This in itself would greatly increase confidence in elections.) The teams would be given immunity from prosecution for election fraud, because any discrepancies under this system would be "made honest".
This idea only fixes the counting process itself, but that's the part that is causing the most controversy now. It's just a simple and cheap improvement on the current system. Even if the vote-counters were totally corrupt, splitting them into two teams means each team would have to be independently corrupt in almost the same way. And remember that it's not just the count itself that has to agree; the teams also have to agree on which ballots are legal.
I feel this is nearly foolproof on paper, but some people are incredibly creative when it comes to cheating. The political parties would probably recruit champion blackjack or roulette players to count votes. But let's try to make it as hard on them as we can.
I'm uncomfortable with any election where the counting takes longer than 24 hours or results in a margin of victory of 1% or less, and I don't think I am alone in this. The two-team method would totally resolve such questions in my mind.
I'm aware that something like this method is used informally in some places, but what I'm suggesting is that it be written into the law. The federal government seems eager these days to tell the states how to run their elections, so if they're going to impose rules they may as well impose good ones.
This is one option. Another option is to say: raising the question of cheating does more harm than good, many courts agreed that the elections are clean, and so we're going to go on doing it the old way no matter what anyone thinks. It does not take a political scientist to realize the second option invites disputes, riots and recriminations, and I suspect there are people who are fully aware of this and consider it a feature rather than a bug. But that's another post.