Well, I have to clap, even though I think I still disagree at least part of what you said, because I was decisively wrong about at least one thing — you certainly do know quite a bit about economics, and you can make a convincing case.

And some extra claps for the photo with Arrow — that’s epic!

So my apologies there. Assuming people on Medium know nothing about economics has for years been a safe assumption, but clearly false in general.

(If instead of the bare numbers you had explained them, I would never have commented, mind you…)

It’s very unfortunate that I’m needing to work for the next few days, your response deserves a lot more.

I’m still not seeing, however, why Arrow’s Theorem is any worse w.r.t Condorcet voting than any other voting system. It’s always possible to come up with cycles — measuring the “goodness” of a voting system cannot be based on consistency as we know that’s impossible, so we need to look at real world edge cases and see how well they do.

Going back to the original article, I still have trouble with your equation, because as far as I know all taxation systems are simply a collection of piecewise linear segments with a terminal segment that ends up in a flat tax. By having an infinite convex-upward tail at the end, you put a huge amount of money into this equation that simply isn’t there in the real world.

Even more important, I would also say that the idea that all progressive taxation schemes are worse for the poor is obviously false, so I’m really having a tough idea understanding what the point of your work is.

Look at this quote:

What leaps out here is that the flat tax (red) is better than the progressive tax (yellow) for everyone under the 48th wealth percentile!

But I could easily tweak the two numbers in your equation to make that not “leap out” — or I could use a more realistic piecewise linear tax and do the same thing.

So I guess I’m back to the same thing — that you haven’t shown any universal behavior of flat vs. progressive taxes, but you’ve shown a single graph with two magic numbers and argued from that.

I hope to get back to this, but if I don’t, you can consider this a concession on anything I missed. And sorry again for “misunderstimating” you.