The thing about the value of money being roughly logarithmic sent me on a google exploration where I ended up on a suggested "logarithmic flat tax plan". The gist is, you figure out how many times the poverty rate you make, take the log-base-10, and multiple by some flat constant that is the same for everyone - the result would be your tax rate. Right now in the US that constant would be around 9, assuming the same tax scheme would apply to companies that make billions in profits like Apple and Exxon.
So Alice earning 10x poverty pays 9 (somethings), while Bob earning 100x poverty pays 18 (somethings)? Note that poor Carol earning 1x poverty pays nothing. I'd expect Alice to be rather unhappy with this system.
(Also, if someone ever manages to earn 0 in a year, you'll have to give all of the world's wealth to him/her. ;-) )
Alice pays 9% of her $117k income. Bob pays 18% of his $234k income. Those are lower tax rates than the present, so not sure why Alice would be unhappy with it. Carol pays nothing. Floor is the poverty rate, so no one makes infinity.
I've always believed the most common responses to St Petersburg Paradox felt incomplete. The biggest miss is not looking at the other side of the transaction. What's the lowest that the casino offering the game would be willing to charge to play it?
I think the gap between what a person would be willing to pay to play this game and what a casino would be willing to charge is the reason that no one plays it.