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It saddens me but it seems to fit life so well.
Thanks for posting this! Although citing the "80/20" rule is somewhat ubiquitous in engineering and moreover project management circles, Pareto is still much underrated, imho.
“Not only are intelligence and aptitudes unequally distributed among the members of society, but the residues as well.“

Maybe it’s just early in the morning here, but I’m having trouble parsing this sentence. What does “the residues” mean in this context?

It's not just you. I'm not familiar with this usage of the term.
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I think it refers to downstream effects of intelligence and aptitudes. For example if I'm really smart, and I make a lot of money and leave my children a generous inheritance, their privilege is a residue of my gifted aptitude.
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I sort of read that as 'residuals' which is still used to describe some types of benefits.
Pareto made a distinction between 'residues' (psychological bases underlying social action) and 'derivations' (rationalizations by members of society as justifications of those actions). It might be used in that sense here.
The little things which are left, but here's a throwback to "Cauchy's residue theorem"[0] to make this more fun.

You can also think of power spectrum analysis, not all frequencies have the same "power".

Though in a time-frequency representation, not all frequencies have the same energy at every moment.

- [0]: https://en.wikipedia.org/wiki/Residue_theorem

Can anyone ELI5?
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TLDR: after the revolution will have come and gone, you still won't be in charge.

Regime changes, whether forced by outside circumstances or from within a single society, just change one group of elites with another while the middle and lower classes stay mostly the same. Pareto (the originator of this theorem) thinks this is a basic conclusion from the fact that most people won't have the right combination of wealth, connections, intelligence, ambition and luck to take advantage of societal upheaval when opportunities present itself.

China had an emperor surrounded by an impenetrable bureacracy of "elites".

Then they had a communist revolution, overthrew the government, executed all the elites.

Now they have a chairman, surrounded by an impenetrable bureacracy of "elites".

I'm not the biggest fan of CPP, but I have to admit they seems to have improved the life's of most Chinese.
In the past 40-ish years, yes; in the previous 40 years, they inflicted a lot of suffering on the country.
I'm midway through reading "Why Nations Fail" and the book makes a case very early on that the replacement of elites with other elites is exactly what happens even when something akin to a coup or revolution happens. Case in point, Latin America, where extractive political and economic institutions have been passed from regime to regime, from the days of Spanish conquest all the way up through the CIA backed coups and the modern regimes.
> The role of ordinary people in such transformation is not that of initiators or principal actors, but as followers and supporters of one elite or another.

Hmm. I saw a fun talk years back. Ottoman Egyptian farmers using strikes to discipline local elites. If say a dominant local family was abusing power to general dissatisfaction, people would leave the village, staying with kin in nearby villages. The drop in village production would bring an Ottoman official to town, with little patience for local elites: "you will fix this, or else". So differential support of overlapping elites is perhaps richer in possibilities than that quote suggests.

At least lately, it seems way more relevant to watch second-order effects of a short/mid- term play come back to bite the homogenized class of elites in the ass.

E.g., fruit rotting on the vines in Alabama back in 2012 or so because they passed a law essentially deputizing all police to be ICE agents. Turns out it's lucrative to scream "they took yer jobs" on cable news all day long, but not so lucrative to accidentally energize a bunch of racists into taking action on it. And you can bet that if "ordinary people" hadn't been completely on board, they'd have burned down the statehouse before letting "Boss Hogg" restrict what the "Duke Boys" can do on their own farms. (Granted, Dukes of Hazzard was Georgia, but you get the drift.)

Also-- "circulation of elites" seems more fitting to describe what happens when you see someone like David Frum start appearing regularly on MSNBC instead of Fox News.

I could be wrong, but despite the astute analysis by Pareto that explains the persistence of elites through "revolutions," he doesn't have too many ideas about how the perfect social mobility that would make societies efficient (governed by the most qualified) can actually be achieved. As I found when covering the revolutions of 1989 in Eastern Europe, the former Communist elites just transformed into the new post-Communist elites, and in many places (Hungary, Poland, Slovenia, etc) they are literally the same people. Or as the great moral philosopher Peter Townsend once said, "meet the new boss, same as the old boss."
As Tomasi di Lampedusa wrote in his masterpiece “il Gattopardo”: everything has to change so that nothing will change.

But let’s be fair to Pareto: he was actually a great intellectual of his age, a Renaissance man. You can’t really complain that he didn’t have a magic wand to fix all the problems he identified- if anything because nobody else ever did either.

This is the theory described in the "book within a book" in Orwell's "1984". In it "Emmanuel Goldstein" (roughly equivalent to Trotsky) describes how revolutions occur when the Middle co-opt the Low to displace the High. The new High then push the Low back where they came from. Over time a new Middle emerges, and the cycle repeats.
On reading this, I feel Bioleninism is a concept which everyone should read upon. A brilliant concept which starts making a lot of sense given the times we live in.
Could you give a bit more detail? Like, why you think it's relevant?
This also happens with invasions. For example, The Roman and Norman invasions of Britain replaced the ruling class while leaving the bulk of the population intact. As opposed to the Viking and Saxon invasion/migrations, which displaced the population.
One thing that really lacks from Pareto’s thoughts on this, imho, probably because of his historical context, is the fact that population tends to expand. Even if it might be true that elites often simply get replaced by new sets of people who will in turn become elites, it’s also true that sometimes (particularly in the last couple of centuries) such new elites can end up being larger - sometimes as a result of demographic factors (population underneath grows, so elites have to scale up as well to ensure their management), sometimes of ideological factors (e.g. a government goes from centralism to federalism, generating a lot of new intermediate roles). Which is a good thing.

Pareto’s insights too often end up being used as a call for passive cynicism. IMHO they should be seen more as a statement of possibility: elites do fall, and if you really work to ensure that fall maybe you can be the next in line, because some elite will always appear at some point and this time it might be large enough to include you.

This Wikipedia page doesn't have a bibliography, but the russian version shows some works, namely: Pareto, V. 1916. Trattato di Sociologia Generale (Treatise on General Sociology).

which a cursory search indicates was also titled The Mind and Society in English translation.

This page about it seems good: http://www.eoht.info/page/Treatise%20on%20General%20Sociolog...