Ayn Rand's philosophy is that of a free economy that stresses the importance of the individual. A democracy is a political institution that stresses the rule of the majority. Rand idealized the self-sustaining individual. A democracy by definition cannot be sustained by one individual. So, it's a difficult analogy to make.
A better analogy would be like saying that a king has a right to abolish his monarchy.
Also, it is only self-defeating if the original goal was only to amass the wealth.
To continue the analogy to this point, a king abolishing his monarchy would only be self-defeating if his only goal was to be a king. However, if his goal as king was to make life better for his country, then abolishing his monarchy in favor of a democracy would be a very good move and not self-defeating at all.
Likewise, if the person's original goal was to produce and then dispose of the rewards as he wished, then doing so is not self-defeating. It's only self-defeating if his original goal was to simply have wealth.
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The other part of Rand's argument is that the individual has the right to dispose of their wealth however they please, because they produced it and they own it. A democracy would only have a right to dispose of itself provided it was the democracy that created itself in the first place.
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That's a pretty fatalistic argument. I think meritocracy has merit and I don't want it to self destruct. That's why, like other principles, this one needs exceptions as too.
Set theory is very useful but it needs an exception to survive Russel's paradox. You can't let useful things become useless just to uphold some moral rule.
