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Comment by tovej | Hacker News Reader

That's because it is the average of the "time to earn 1$" per individual.

So let's say you're Elon Musk and it takes you a negligible enough time to do this that we can say that t_Elon = 0.

Now say you are way below the poverty line and earn 6000$/year. This means t_Poor = 87 mins.

If we average 80 t_Poor and 20 t_Elon we find we get 0.8 x 87 mins = 67 mins. Even when the average income in this case would be 0.2 x income_Elon. Something like 7 billion $/year.

I hope this shows why you can't just take the inverse to get the average income. The only way that was true was if everyone earned the exact same income.

Why is this a better metric?

The average income is biased towards big earners, while this metric is more centered around the mode of the distribution (poor people).

It captures the income distribution much better than average income.

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Well, Average is indeed a worthless metric, and that's why everyone is using median for these statistics unless they're arguing in bad faith

If you do want to use average, you'd at least need to remove 10% both from the top and bottom before calculating it, but it's still gonna be super untrustworthy.

Not sure what to take away from your comment, I'm still unsure what kind of metric you're pitching and why it'd be a valuable thing to track

I'm not pitching any metric. I'm describing the metric being discussed.

The average is certainly not worthless. The average gives the expectation, which is more meaningful than the median, which is just the arbitrary line at the 50th percentile.

So if we're trying to find the expected value of how rich someone is, the average income is the answer. And if we want the expected value of how poor someone is, this new metric (average poorness) is the answer.

If we want to learn about poverty, obviously the poorness is more important.

But of course, you could also calculate the median poorness in this case, but that would actually just be the inverse of the median income, so no new information would be gained.

this metric is more centered around the mode of the distribution (poor people).

It's focused on the very poorest, who are not the mode. (Income distribution is approximately lognormal; see https://www.researchgate.net/figure/The-lognormal-distributi...).

Say you have 10 people: one making $800/year, 8 making $80k/year, and one evil billionaire making $800 million. Their times to earn $1 are respectively 10 hours, 0.1 hours, and essentially zero. If you take the arithmetic mean of that you get 1.09 hours, and that's dominated by the single poor person. If you double that person's income to $1600, then they're at 5 hours to earn $1, and the overall average is nearly cut in half to 0.58. Meanwhile you can reduce the income of all the middle class people to $40k and not much changes; the average time to $1 would be (5+8(0.2)+0)/10=0.66.

It captures the income distribution much better than average income.

Not really, and certainly not better than median income which is what people typically use. It tries to measure exactly how little income the very poor make, which is not normally what people mean when they talk about inequality or poverty, and also hard to measure at the accuracy that you need when small changes produce huge swings in the result. In particular I don't believe he's correctly accounted for government benefits; hardly anyone in the US is consuming less than $8000/year.

He is not proposing to do away with the median income measure (or other quantile measures), but to add to them.

The median income is not a very good measure at all, you would need more quantiles to capture the distribution.

This metric is much better at capturing the distribution than the average income.

It's true that the mode is not at the very bottom of the distribution, but it is much more aligned with the lower tail than with the upper tail.

And I don't know why you mistrust this figure so much, it's based on this World Bank dataset, which you can verify yourself: https://datacatalog.worldbank.org/search/dataset/0064304/100...

Thanks for the comment, I was trying to parse the meaning of "time needed to earn $1" for a bit. This just boils down to what countries have the highest floor for their poorest members.

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