Can we (is it reasonable to) apply auction theory and the various incentive compatible mechanisms to elections and guarantee cardinal voting?
I am thinking specifically of VCG auctions and particularly the Clarke Tax.
I am interested in weighted (inverse of wwealth) voting (a person who holds twice the wealth can easiliy pay twice the tax so I would expect him to pay twice as much for his vote to have the same effect).
First scenario where the N persons with the highest score (the most cardinal votes weighted with the inverse of wealth) are elected.
People all vote and assign their subjective value for each candidate who the gets divided by their wealth given that if their vote causes a person who would otherwise be elected not to be or causes a person who would otherwise not be to be pays the difference multiplied by their weatlth (he is a pivotal agent and pays the clarke tax)
Second scenario with Parties and Proportional Representation
People all vote for parties who then get seats proportionally to their score and anyone who makes a party lose or win a seat pays the difference (this is more complicated so it can be weighted or not).