The Gentleman's Agreement

Someone posted the following thing on Facebook.

Suppose that every day, ten men go out for beer and 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.
So, that's what they decided to do.
 The ten men drank in the bar every day and seemed quite happy with the arrangement, until one day, the owner threw them a curve ball. “Since you are all such good customers,” he said, “I'm going to reduce the cost of your daily beer by $20”. Drinks for the ten men would now cost just  $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 drink for free. But what about the other six men ? How could they divide the $20  windfall so that everyone would get his fair share?
They realized  that $20 divided by six is $3.33. But if they subtracted that from  everybody's share, then the fifth man and the sixth man would each end  up being paid to drink his beer.
So, the bar owner suggested that  it would be fair to reduce each man's bill by a higher percentage the  poorer he was, to follow the principle of the tax system they had been using, and he proceeded to work out the amounts he suggested that each  should now pay.
And so the fifth man, like the first four, now paid nothing (100% saving). 
 The sixth now paid $2 instead of $3 (33% saving). 
 The seventh now paid $5 instead of $7 (28% saving). 
 The eighth now paid $9 instead of $12 (25% saving). 
 The ninth now paid $14 instead of $18 (22% saving). 
 The tenth now paid $49 instead of $59 (16% saving).
 Each of the six was better off than before. And the first four  continued to drink for free. But, once outside the bar, the men began to  compare their savings.
“I only got a dollar out of the $20 saving,” declared the sixth man. He pointed to the tenth man,“but he got $10!”
 “Yeah, that's right,” exclaimed the fifth man. “I only saved a dollar  too. It's unfair that he got ten times more benefit than me!” “That's  true!” shouted the seventh man. “Why should he get $10 back, when I got  only $2? The wealthy get all the breaks!”
“Wait a minute,” yelled the first four men in unison, “we didn't get anything at all. This new tax system exploits the poor!”
The nine men surrounded the tenth and beat him up.
 The next night the tenth man didn't show up for drinks so the nine sat  down and had their beers without him. But when it came time to pay the  bill, they discovered something important. They didn't have enough money  between all of them for even half of the bill!
And that, boys  and girls, journalists and government ministers, is how our tax system  works. The people who already pay the highest taxes will naturally get  the most benefit from a tax reduction. Tax them too much, attack them  for being wealthy, and they just may not show up anymore. In fact, they  might start drinking overseas, where the atmosphere is somewhat  friendlier.
David R. Kamerschen, Ph.D. — Professor of Economics.

Okay, first of all, I realize he's trying to talk about how taxes work in his perception of the world view of progressive people, but the example kind of sucks because it's both overly complicated and overly simplistic at once. The overly complicated part is that the fictitious bar owner would have never tried to divide the bill that way. With the bill being exactly 20% less than it was before, he merely would have just taken 20% off of everyone's portion. It would be the fair and most direct way to handle it, because it's a bill and not a tax system. It's also not adding in all of the other factors that alter how taxes would get paid.

In the way that it's overly simplistic is that the example doesn't address that currency is never just about money. People don't repeat a situation over and over again if it has no value and value is measured in more than just money.  Everyone is getting something out of this.  Now, the four men who are drinking for free . . . okay, their motivation may be just to drink for free, but everyone else has more complicated reasons.

They have to. In our society, we still have pretty strict social classes and often people of different socio-economic groups would never mix like this . . . unless they had very good reason for it. The richest man would only pay the lion's share of everyone's drinking if he was gaining from them in other ways. Perhaps he is in a position of political power and the other men have the largest influence over the voting habits of their various groups. Perhaps the four poorest men are in a position to bring him information about one of his projects. Perhaps they are highly entertaining and he figures paying for their drinks is worth the cost.

The other men who are paying are either trying to gain access and influence with the richest man or feel a sense of smug satisfaction from being, daily, in a situation where they know they are better than others. Even the man paying the least amount can still feel more powerful than the four who depend on everyone else. They still get to make connections with the other men. All of this is important to them, probably far more important than what they are paying, especially when you consider that they are only paying what they can afford.

With all of this in mind, why, under any circumstances, would they be angry because suddenly the richest man is paying ten dollars less? They're all paying less and are all STILL receiving the benefits that brought them into this agreement in the first place. There is no logical reason why things would end this way.