Suppose we have a society where there are three voting blocks of equal size: low, middle, and high income. The low income voters have 0 income, the middle voters have 6 income, and the high income voters has 21 income.
The low income voters propose to levy a tax of 10 on the high income voters and split the tax revenue with the middle income voters, which would leave the income distribution as:
Low income = 5
Middle income = 11
High income = 11
(A rule of this game is that the overall plan of taxation and redistribution can never give leave any group with more than it leaves the high income voters with.
The reason is that if the taxation and redistribution left the low or middle income people with more income than the original high income, the former low or middle income people would be the new high income group and would be the ones to be taxed.)
The high income voters make a counter-offer to the middle income voters, volunteering to pay a tax of T and give all the revenue to the middle income voters, which would give the following income distribution:
Low income = 0
Middle income = 6+T
High income = 21-T
What is the maximum value of T that the middle income voters can demand and hope to get the high income voters to accept?