Is there any available/feasible/practical way to make a Cardinal Voting both Incentive Compatible and Secret?
A method to make a cardinal voting incentive compatible would be to force them to put their money in the place of their mouths. Making them pay the cost for their decision. As such a Vickrey-Clarke-Groves auction applied to a Cardinal Voting would provide incentive compatibility. My problem is that a public vote would make the voters take into account the Society so the voting will reflect the person's opinion of society and their fears.
Unless the vote is public I do not see how they could be identified so as to pay the Clarke Tax. Preferably I would want the voting power of each individual to be inversely proportional to their wealth to. The preference they declare would be divided by their wealth but the Clarke Tax would be multiplied by their wealth. I want to adjust voting for the wealth effect. Rich people are frivolous and I want to pose a incentive for them not to declare extravagant preferences just because they have the money to pay the clarke tax.