You articulated the main issues in an excellent manner. You are right, there will be many logistical issues, Would the best option just might be to make a formal apology for historical conduct?
issues i see
1. proving the decendants
2. proving the original slave was not compensated when they were freed
after all having kids while slave was not a massive thing to happen. so the decendants would usually have been birthed after the slave was set free and probably compensated.
yes there were many cases where decendants were the result of master/slave rape and yes that should be compensated. but trying to gather evidence from over 100 years ago of what actually happened and if the slave was previously compensated fairly. makes this new policy hard to determine
things like DNA tests of the white decendants of the original master to compare lineages may need to be involved.
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for the non master/slave rape situations, but for the unfair freedom compensation situations. this is hard to prove. masters could have wrote they paid x and only paid 0.x but legally the only proof is of x being paid.
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i dont think that the policy will just pay out all claims just because they say they are the great grandchild. it wont be that simple