This post describes a system of voting/payments where you can make multiple votes, depending on how strongly you value your preferred outcome, but each vote costs more than the vote before.

Identity management and collusion are big issues with these systems, as the essay points out.

For programmers, one way to think about this is that each voter has a state, n, that tracks how many of times they've voted. And each vote is more expensive than the last. Eventually you either run out of money or you lack the desire to spend more money on another vote.

But if you can create a new voter account as easily as you can create a new Gmail account, then once n gets sufficiently high, you just switch to a new account to lower the price of your vote.

Or if a really rich voter with a high n-value pays someone with a low-n value to make a vote on their behalf, the system collapses as well.

Enforcing strict identity management (e.g. requiring valid state-issued ID cards) and implementing secret voting can help address these problems, but my guess is that if there is a strong enough incentive, people will try their hardest and come up with novel ways to thwart these safeguards.