In our society, which, if I remember correctly, 10% of the population control 90% of the wealth, AP would only lead to 10% of the population being able to screw the remaining 90%. At least as it is, it takes a simple majority.
As for the murder of the rich, here is a scenerio.
A collection of poor pool their capitol to have a tyrant killed. The tyrant assembles a counter-wager saying that anyone able to prove thier ability to kill him without harming him, and who can show they got through will get 110% of the poor's bid. The household is told that a standing bounty has been placed with a collection of individuals, on the head of the trigger man involved in the tyrants murder. The poor can not hope to match the tyrants bid as they only have 10% of the wealth, the household knows that thier participation in an attempt on the tyrant will get them killed. Even if the attempt was successful. The people from the outside who would benefit from the bounty benefit more by taking the tyrants offer and then trying again, i.e. tiger teams.
I think a hole in your thinking is to assume that the assasins have no motive other than financial gain. I would submit that there are those that have the skills, training and a political agenda coherent with the wagerers, lacking only the financial incentive to make the risks acceptable. These wetworkers won't consider accepting the bribe of the rich/powerful --Steve