The real point is that some members of society are more productive than others. Apparently, tall people are more productive than short people. What we want to make equal (from a utilitarian point of view) is income per unit effort. If you're from a disadvantaged background, but put as much effort as a person from an advantaged background, then you would make the same after-tax income.
He's demonstrating that this point of view is impractical in reality.
I think this misrepresents the notion behind progressive taxation. I'm no expert, but I understand it like this: because of declining marginal utility, the same % of income may mean much more to the poor than to the rich. If my yearly income is 10k, then 10% of it might mean the difference between making rent or not. If I make 100k, 10% of it may mean forgoing some luxury, but needn't substantively impact my overall quality of life.
In that sense, the subjective impact of money is not fixed by its objective value; it's more important to those that have less of it. This is borne out by research. Money significantly impacts happiness until you make enough to basically get into the (lower) middle class, and then it has little impact.
So, if you buy the above intuition and want to use taxation to help maximize happiness (utilitarianism), then you would want some form of progressive taxation in order to alleviate the negative impact of poverty. This doesn't mean "making everyone equal."
To test our intuitions about this subject, I like philosopher John Rawls' conception of a "Veil of Ignorance." Rawls would ask: would you rather live in a society with, say, 1% billionaires and everyone else in poverty, or one more evenly distributed around a middle class -- without knowing in advance where you would end up in this society? The answer may well depend on one's level of risk tolerance, but I'd wager that most people wold opt for the latter.
Except that that's not the choice that we're faced with.
Instead, we're faced with "lots of billionaires, a huge middle class, and poor people with 2 cars and 4 TVs" vs "nasty, brutish, and short". Oh, and the former gets better over time much faster than the latter. If you're really going to be serious about the ignorance thing, you should be ignorant of when you live.
If I make $100K it's entirely possible that my rent or mortgage is ten times that of a person making $10K, as well as my other costs of living.
If you doubt the veracity of that comparison, take a look back at property prices in the few years prior to 2008 and do the mortgage calculation yourself. It is not at all uncommon to find $5,000 p/month mortgages, and I know you can find rooms to rent for no more than $500 p/month.
So, if you buy the above intuition and want to use taxation to help maximize happiness...
What does happiness have to do with it? No-one in this country is guaranteed happiness. It's not the government's responsibility or right to make people happy, or even to try. Their charter ends at making sure people have the right to pursue happiness, that is all.
The article isn't about progressive taxation. It's about utilitarian taxation.
central planners can not be objective under any circumstances unless it is literally a god AI with perfect knowledge of determinism.
Or, having (fallible!) humans doing the hiring has created certain inefficiencies in the labor market; inefficiencies which could be exploited/corrected by someone clever.
edit: His final claim -- that the tax on height is an explicit consequence of a utilitarian approach -- is simply flawed (or irrelevant, actually) because we do have a tax on height. A progressive income tax is meant to approximate what would happen if we accounted for all of these variables, but without actually accounting for each one explicitly, as that would be impractical.
Now, I'm not saying that the utilitarian method is the end-all. If it is flawed (which I think it is), this is simply not the flaw.
This is clearly untrue. If I have $2M US in the bank, it takes me no effort at all to earn $40K/year. This is part of the rationale behind a progressive tax, that money begets money with little effort, like a snowball rolling downhill. That's why only a fraction of the wealthiest 5% started life outside the top 15%. They love to tell the rags-to-riches story, but the riches-to-more-riches story is about 20 times more common.
So while height taxing a more blunt instrument than income taxing, it doesn't distort people's choices in the same ways and avoids some of the deadweight losses. Unfortunately it probably will end up distorting people's choices in new and creative ways that we'd probably only find out about later.