No, I was using marginal utility to demonstrate that the relationship between total wealth and the utility provided by that wealth is non-linear.
To complete the full thought: Marginal utility is the first derivative of utility. If marginal utility is constant, then overall utility is linear. If marginal utility trends downward then the overall utility is non-linear. Since we appear to agree that marginal utility tends to decrease, then calculus forces us to agree that the utility that someone derives from wealth has a non-linear relationship with that wealth.
> "what if the poor people you're helping through harming others don't use the money wisely"
I think it's a fair question, but it seems hypocritical to ask immediately after asking: "why would anyone else have the right to decide how their property is allocated or used".
However, every study I've seen done on this issue has shown that unconditional cash transfers to impoverished people tends to be used reasonably well[1]. Certainly there will be some people who choose not to use redistributed income well, just as there are some people who have lots of capital who choose not to use their income well.
> "why would anyone else have the right to decide how your property is allocated or used"
This one you'll have to take up with the Supreme Court, Congress, the United States Treasury, and the Internal Revenue Service who all take it as a given that the United States Government has the right to decide how your property is allocated or used.
Again, as mentioned in our other comment thread, since you seem to be advocating for zero taxes and zero government spending, I don't think we can come to any meaningful resolution on these issues in a text-format over the internet.
I think this is the critical point of our disagreements over UBI — you find all government spending to be theft and morally wrong. This isn't an argument against UBI, but an argument against the entire system of governance that the world has adopted. That's totally fine, but it's not an argument that I'm prepared to consider on this particular forum. If you want to continue this discussion, let's do so in person or over the phone sometime.
[1] One example of a study showing gains from unconditional cash transfers: http://www.princeton.edu/~joha/publications/Haushofer_Shapir...