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Neat! I'm not surprised at the findings here. BlueSky (for the average user) is pretty much a drop in replacement for Twitter.

Despite the smaller total numbers in Mastadon, it's great to see that the ecosystem seems to be successfully avoiding centralization like we've seen in the AT-Proto ecosystem.

I suspect that the cost of running AT proto servers/relays is prohibitive for smaller players compared to a Mastadon server selectively syndicating with a few peers, but I say this with only a vague understanding of the internals of both of these ecosystems.

How would one measure old school federated contexts like IRC and NNTP in this way? I wonder would they would fare.
We're more decentralized in fedi but we're also not really consistent either. Which I think is the number one gripe for users who manage to get into the fedi.

I don't mind, I still think it's a huge leap forward, but it's important to set realistic expectations.

I think that thinking of "the fediverse" as one thing at all is a mistake. It's Gilbert Ryle's classic category mistake:

> A foreigner visiting Oxford or Cambridge for the first time is shown a number of colleges, libraries, playing fields, museums, scientific departments and administrative offices. He then asks “But where is the University?” .....

"The fediverse" is not a thing. There are many separate sites and the collection of all of them in total may be called "the fediverse", but that is not a thing by itself. They don't even all share a protocol in common. You cannot join the fediverse any more than you can join the game industry or the startup scene. You have to join a specific server, game company or startup (or more than one). And while from the outside you might have heard a lot of "the game industry is cut-throat" or "startups work together to innovate technology", once you are inside one of them, you'll find that it's a lot more fragmented than it at first appeared, and totally incohesive, and although from a bird's eye view it looked like you and your competitor down the hall were both making VR happen, they won't work together with you.

How do these metrics compare with usenet circa ~1989
Keep the needle pointing north. Towards the center of that dial.

Too decentralized, and you can't find anything. Nobody uses it.

Too centralized, and censorship takes over. Nobody can speak freely.

Mastodon has been great so far
I'd like to see Nostr added to this, since userbase concentration is always the thing they levy against the fedi model. It'd be a little weird to adapt because user identities don't live on single relays.
The honest truth is that:

Nobody outside tech cares about decentralization or federation.

At some point, everything converges to centralization.

No amount of Mastodon servers or any fediverse self hosted instances spun up will change that.

There is a reason that mastodon.social is the biggest instance and that they couldn't close registrations to promote decentralization.

Hell, I would even say that threads is the biggest mastodon instance.

I think this compares AT proto PDSes to Fediverse instances. In many ways this actually underplays just how grossly centralized AT proto currently is, since some of the components are 100% centralized still. (Whereas Fediverse instances, all downsides considered, are at least self-contained fully-independent instances.)
"Decentralization" isn't the end-goal so measuring it here isn't all that meaningful. Personally, I care about:

1. How hard is it to censor the network.

2. How hard would it be for some major player to enshittify the network.

Furthermore, while the fediverse has a single axis for decentralization, BlueSky has 3: number of "big index servers", number of PDSs, number of domain names (how many people own their handle):

1. Increasing the number of PDSs doesn't make it harder to censor the network when everyone still uses the same big index node.

2. BlueSky's primary defense against enshittification is user account portability. I'd love to see metrics on how many users have their own domain names. Having many PDSs is also a good defense here because it reduces the impact of BlueSky (the company) shutting off the firehose, but I still think account portability is the primary defense here.

TIL about the Herfindahl–Hirschman Index and I wanted to test it with a weird corner-case that I remember.

At one point in the late 1980's Microsoft had a GREATER than 100% market share of the Macintosh spreadsheet market.

How is this possible?

Market share (for a given period) is the participant's sales in the market divided by total sales. It just so happened that Lotus had more returns than sales of their failed spreadsheet, Lotus Jazz. So Lotus, had a negative market share and Microsoft had more sales of Excel than total sales in the market, resulting in a greater than 100% market share.

I don't remember the exact numbers and I believe there was at least one other competitor in the study. But let's just say the numbers were:

Microsoft: 102% Lotus: -2%

In that case the Herfindahl–Hirschman Index would be 102^2 + (-2)^2 = 10404 + 4 = 10408.

So, in this pathological case it is possible for the HHI to exceed 10,000.

Edited: Added (for a given period) above, for clarity.

> Market share (for a given period)

That's not a thing. Market share has no time period. It's an instantaneous measure of the state of things right now. How many of your company's units are out in the wild right now being used, vs. how many total units (sold by any company) are out there in the wild right now being used.

That number can and will be different at different points of time, as people buy and return your products, and buy and return your competitors' products[0]. You can certainly say that your market share increased by 300% or by -40% over a given period of time, but your actual market share is always a number between 0% and 100%.

> Market share (for a given period) is the participant's sales in the market divided by total sales.

No, that's a company's share of sales as compared to the industry/product category as a whole. Not market share.

[0] You also should take into account people who throw your product in the trash (or for software, delete it) without returning it. Depending on context, you might even want to take into account people who put your product in a box in their basement and never use it again. Assuming you could actually divine those numbers, which of course you likely can't.

> This page measures the concentration of the Fediverse and the Atmosphere according to the Herfindahl–Hirschman Index (HHI), an indicator from economics used to measure competition between firms in an industry. Mathematically, HHI is the sum of the squares of market shares of all servers.

I had not heard of this metric before - it’s neat and simple to understand. If you scaled it down to 0-100 (by dividing by 100), I think it would make the numbers more immediately understandable. I’d even consider inverting it (so 0 = centralized and 100 = decentralized), since the website title implies measuring progress ‘towards’ decentralization.

mastodon is the equivalent of bsd code, but for user generated content.

Microsoft and apple would just reach for bsd tcp stack etc. today bluesky just "federate" to mastodon and instantly had millions of active users, until they don't need to federate anymore, when they will blame the other instances to not migrating to some crazy protocol or something, never they will just "shut the door".

I thought Bluesky was federalized? How is it not?
Wonder how one could calculate email concentration.
Can someone explain how Fediverse instances or any decentralized platforms deals with most obvious issues of decentralization? Like if I join some node then one day it's offline and all my data lost. I mean surely instances usually don't disappear without notice but it still a totally possible thing. Or what about those times when entire instances get involved in dramas and end up defederating? I don't want to lose my connection with potential friends from such instance just because of something like that. I even remember some time ago when there were news about Threads being federated some people deliberately gathered "signs" across lots of instances to collectively defederate from Threads and it's just ridiculous to me that this even happened. What all this talk about fighting censorship while actively engaging in constant "self-censorship" making own echo-chamber as tight as possible?
Sadly, and fortunately, there is no such thing as "avoiding centralization", the evidence is overwhelming:

== Politics & Sociology (power concentrates in organizations)

- Robert Michels, Political Parties (1911) origin of the "iron law of oligarchy": even democratic groups tend to end up run by a few: https://en.wikipedia.org/wiki/Iron_law_of_oligarchy

- Jo Freeman, "The Tyranny of Structurelessness" (1970/72): leaderless groups develop informal, unaccountable elites unless they make structure explicit: https://en.wikipedia.org/wiki/The_Tyranny_of_Structurelessne...

- Max Weber, bureaucracy & rational-legal authority: why modern societies gravitate to rule-bound, hierarchical administration: https://en.wikipedia.org/wiki/Rational-legal_authority

- James G. March & Herbert A. Simon, Organizations (1958): classics on bounded rationality and why attention/decision bottlenecks yield hierarchy: https://www.amazon.se/-/en/James-G-March/dp/0471567930

== Economics & Political Economy (why markets/platforms centralize)

- Ronald Coase, "The Nature of the Firm" (1937): firms exist (and grow) when internal coordination is cheaper than market exchange: https://onlinelibrary.wiley.com/doi/10.1111/j.1468-0335.1937...

- Oliver Williamson, Markets and Hierarchies (1975): transaction-cost economics: asset specificity & opportunism push activity into hierarchies: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1496220

- W. Brian Arthur, "Increasing Returns and Lock-In" (1989): small early advantages + network effects => path-dependent monopolies: https://www.jstor.org/stable/2234208

- Katz & Shapiro, network effects (1985/1994): compatibility and standards help explain winner-take-most dynamics: https://faculty.haas.berkeley.edu/shapiro/systems.pdf

- Thomas Piketty, Capital in the Twenty-First Century (2014): when r > g, wealth concentrates; proposes progressive wealth taxation https://en.wikipedia.org/wiki/Capital_in_the_Twenty-First_Ce...

== Networks, Complexity & Information (why hubs and hierarchies emerge)

Albert-László Barabási, Linked (2002): preferential attachment makes networks develop hubs (central nodes) http://networksciencebook.com/chapter/5

Herbert A. Simon, "The Architecture of Complexity" (1962): complex systems often become hierarchical because modular hierarchies are easier to evolve and manage https://faculty.sites.iastate.edu/tesfatsi/archive/tesfatsi/...

W. Ross Ashby, "Law of Requisite Variety" (1956): controlle...

I just wanted to thank you belatedly for an excellent set of resources and references. I'm familiar with several, others look like worthwhile exploration.
So why not just wordpress and rss?
It would be great to add nostr, but nostr doesn't really match this model. Nostr doesn't need a single server to hold your identity, your app connects to many "relays" at the same time.
would be awesome if they added nostr to the list, too.
So we are not decentralized. Git was a good attempt, but it kind of got centralized around GitHub, GitLab, and other variants. BitTorrent was decentralized, except tracker sites were the natural centralization points. Bitcoin was also decentralized, but still had Coinbase and other sites. Even SMTP is de facto centralized due to the spam problem.
I think git is a successful attempt despite existing centralized hubs. git over ssh just works. Decentralized does not mean federated
Including Threads with Fediverse might have an interesting impact.
One of the nice things about mastodon is that the total lack of centralization and the absence of the dreaded algorithm means you don't have reputation farmer accounts posting bloviating nonsense the whole time. Its really great there.

Mastodon is social like a quiet pub. Twitter and Bluesky are social like a crowd at a concert.