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Let me expand past Rand. The French Revolution purported to enshrine Reason at the center of society. Two years later the revolution was devouring its devotees in the Terror. Karl Marx claimed to have scientifically analyzed society. We know where that led, too.
Logic and rationality ex ante don't necessarily provide you with good road maps of how society can be organized on a macro level. Yes, they are useful in making individual small-bore decisions, but even then things break down because humans are complex and unpredictable. Logic and rationality will help you with societal organization ex post - once something happens and you see how people react, you can evaluate why and figure it out. But trying to predict it is a hit-or-miss affair.
That's why I'm a big believer in the scientific method: quantitative analysis and experimentation. The only way to know what works is to test it and see what happens, then test it again, then test it again -- just like any scientific experiment. If it's replicable consistently and the result is roughly what was sought, then it "works." To my mind this is the way rationality should work, because it recognizes both the possibilities and the limitations of reasoning.
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