Consider attempting to remove the insideousness of money in political campaigns by changing from "one man, one vote" to "one dollar, one vote", essentially (cynically) making explicit what is implicit now. You cast your ballot by giving as much money as you want toward (not to) your candidate.
Sarcastically, "what could possibly go wrong?"
In order to avoid the game-theoretic craziness of the All Pay Auction, you need to get your money back if your candidate loses.
In order to permit anonymous voting, you can designate someone else, perhaps a charity, to get your money if your candidate loses.
Obviously, there will no longer be problems with vote buying. Are other types of coercion possible? Instead of having a special set of laws and law enforcement agencies about election fraud, we can lump them with all other types of fraud where a man gets cheated out of his money: economy of scale in law enforcement?
Even though you can designate someone else to receive the refund, if you don't, then it becomes possible to prove you voted for a non-winner (though not which non-winner). Does this have bad consequences?
Of course, this would be a good way to raise money for the Treasury.
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