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<p>I'm sorry, I'm still not able to understand this particular point you're trying to make. You say that you want to give all people the opportunity to improve their financial status, start everyone at the same line (in a race). </p>

<p>But don't we make sure everyone starts at the same point to make sure that potentially everyone has the opportunity to finish quickly (barring intrinsic qualities such as strong legs, etc.). In this case, so that everyone can potentially be well off (financially), except for those who don't deserve to be.
So when this potentiality has been attained, we have achieved income redistribution have we not?</p>