Tax cuts we can all understand

Suppose that every day, ten men go out for dinner.  The bill for all ten comes to $100.  If they paid their bill the way we pay our taxes, it would go something like this:

The first four men - the poorest - would pay nothing.
The fifth would pay $1.
The sixth would pay $3.
The seventh would pay $7.
the eighth would pay $12.
The ninth would pay $18.
The tenth man - the richest - would pay $59.

The ten men ate dinner in the restaurant every day and seemed quite happy with the arrangement - until one day, the owner threw them a curve.  “Since you are all such good customers,” he said, 
“I’m going to reduce the cost of your daily meal by $20.”  So now dinner for the ten would cost only $80.

     The group still wanted to pay their bill the way we pay our taxes.  So the first four men were unaffected.  they would still eat for free.  But what about the other six - the paying customers?  How could they divvy up the $20 windfall so that everyone would get his “fair share?”  The six mean realized that $20 divided by six is $3.33.  But if they subtracted that from everybody’s share, then the fifth man the sixth man would end up being “paid” to eat their meal.

     Unable to resolve the conflict, the restaurant owner suggested that it would be fair to reduce each paying man’s bill by roughly the same percentage - 20%.  Everyone was hungry so they agreed.

So the first four men would continue to eat for free
The fifth would now eat for free
The sixth would pay $2 - a reduction of $1
The seventh would pay $5.50 - a reduction of $1.50
The eighth would pay $9.50 - a reduction of $2.50
The ninth would pay $15 - a reduction of $3
The tenth would pay $48 - a reduction of $11

Each of the six men was better off than before.  And the first four continued to ear for free.  But once outside the restaurant, the men began to compare their savings.  “I only got a dollar out of the $20,” declared the sixth man.  The Seventh man shouted, “I only got $1.50 out of that $20.”  The ninth man screamed, “I only got 3 dollars but he - pointing to the rich man - got $11, over half of the money we saved!  The wealthy get all the breaks”   “Wait a minute,” yelled the first four men in unison, “we didn’t get anything at all.  The system exploits the poor!”  Then the nine men surrounded the rich man and beat him up.

     The next day, the rich man didn’t show up for dinner, but the other nine ate without him.  When it came time to pay the bill, the men discovered they were $48 short.  “Who is going to pay the rest of the bill?” demanded the restaurant owner, as he picked up the phone to call the police.