Vote purchasing with convex costs

What if votes had a cost? In a voting mechanism initiated by Glen Weyl and mentioned by Steven Levitt at Freakonomics, individuals participating in an election would get the chance to vote as many times as they’d like, with each vote having equal weight toward determining the winner. The catch is that each vote is successfully more costly. As Levitt explains:

… each extra vote you cast costs more than the previous vote.  Just for the sake of argument, let’s say the first vote costs you $1.  Then to vote a second time would cost $4.  The third vote would be $9, the fourth $16, and so on. One hundred votes would cost you $10,000.  So eventually, no matter how much you like a candidate, you choose to vote a finite number of times.

The upside? Well, first,

People end up voting in proportion to how much they care about the election outcome.  The system captures not just which candidate you prefer, but how strong your preferences are.

Additionally,

This voting scheme can work in any situation where there are multiple people trying to choose between two alternatives — e.g., a group of people trying to decide which movie or restaurant to go to, housemates trying to decide which of two TV’s to buy, etc.  In settings like those, the pool of money that is collected from people voting would be divided equally and then redistributed to the participants.

But there are a couple of possible downsides, including an appearance to favor rich voters and the potential to lead to vote buying (since if I have already voted, it’s cheaper to buy someone else’s vote for $1 than for me to vote again). Nevertheless, interesting and alternative voting systems are good to get us thinking about democracy.

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