Today, the nation has no draft, and relies instead on dire economic necessity and a lack of gainful employment for encouraging young people to man its legions. Still, there's no reason we can't reductio TB's logic ad absurdum to its eventual conclusion.
The proportion of rich people to the general population is so low that exempting them from a mandatory draft is not going to measurably affect military manpower levels. Consequently, they should not be required to register for the draft, or be inducted into the armed forces. In fact, since these people are obviously superior to the rest of us, and represent the nation's reservoir of work ethic, creativity, ambition, and other entrepreneurial virtues, it would be a criminal waste to put their lives on the battle line when they could be at home Creating Jobs instead.
During the Civil War, exactly such a policy was in effect. You could avoid military service by simply paying some poor slob to do your fighting for you. Someone who could afford to do this was called a "Fortunate Son". You will recall this was not only a song by Creedence Clearwater Revival, but was George W Bush's nickname during the Viet Nam era.
Fortunately for the nation, America's rich, (until fairly recently, anyway), felt a certain noblesse oblige, a sense of community duty and public service that even though they felt exempt from paying their fair share of war taxes, still had enough shame left to volunteer their sons to fight in times of national emergency. The fact they felt their children were more expendable than their discretionary cash tells you a lot about the propertied class and their middleman minions and how they got that way.
I would like to add my own amendment to the Buffett Rule. I think retired Cuban amateur astronomers who know celestial navigation should also have a reduced tax rate because there can't possibly be enough of them in the country to make any difference to the national debt. (Not to mention the vast reservoir of priceless knowledge they represent for future generations!) They should be exempt from not only paying taxes, but from any possible future military draft, since there can't possibly be enough them to make any difference in any future conflict.
People need to pay for this country to the extent which they have benefited from it. Those who feel they are exempt from this are worthless parasites and should be considered with the contempt they deserve.
