Right. The Pareto principle is the observation that large amounts of resources tend to consolidate in a few 'hands'. It's observed in natural systems as well as human created ones.
So, back to your original point. You seemed to be saying that in order to reduce inequality (a good thing), you must trample of the rights of people, specifically the wealthy (a bad thing). But then you admit that it's largely luck which determines whether or not a person is wealthy.
I don't think it would be a big problem to redistribute a small portion of their wealth. Or, similar to what you said in a nearby comment, if society as a whole decides to redistribute a portion of your wealth then "tough luck" (although remember that you are still better off than most when considering how "tough" your luck is). So the original problem with reducing inequality seems to have been solved. It is not a great trespass on the rights of the wealthy to redistribute some of their wealth.
I don't think it would be a big problem to redistribute a small portion of their wealth. Or, similar to what you said in a nearby comment, if society as a whole decides to redistribute a portion of your wealth then "tough luck" (although remember that you are still better off than most when considering how "tough" your luck is). So the original problem with reducing inequality seems to have been solved. It is not a great trespass on the rights of the wealthy to redistribute some of their wealth.