This method relies on the idea of a cost, most likely monetary, proportional to the choice. This is obviously incompatible with core principles of modern democracies.

This article reasoning compares the Brexit and Trump votes, and speculates that they might have had a different result by changing their voting mechanism, almost exchanging them. Rather than a good argument, this is exactly the reason why voting mechanisms should be dealt with carefully.

More generally, the idea of voting mechanisms using preferences is a few centuries old. There is an abondant literature analyzing its potential merits but also failures.