@freemo @olamundo @design_RG I don’t think having a lower insularity than M.S is actually a meaningful comparison, as their user count is more than forty times greater than QOTO’s. It seems reasonable to expect that large instances will score higher measures of insularity, even given the same behaviour as small instances.
Quick aside: insularity is defined as the ratio of mentions of local users to mentions of all users.
Consider a Fediverse where all the users are instance-agnostic in their communications; that is, the likelihood any pair of users communicate is independent of whether or not they are on the same instance. Now imagine the limiting case, with just two servers, one a single-user instance and one a giant instance with everyone else. The small instance will have near-zero insularity (the only mentions of local users will be if the user names himself for some reason) and the large instance will have near-100% insularity (the only mentions not of local users will be conversations involving this one particular user). The insularity scores differ wildly, even though the users have the same behaviour - they’re just a function of where you draw boundaries to group users.
It seems like there ought to be a way to normalise this, something like (local mentions * all users) / (all mentions * local users), but quantifying the “all users” part seems hard. How would you qualify a user as potentially mentionable, how would you treat dormant accounts, etc. - such questions would affect the outcome. Absent such a normalisation, I think insularity scores should really only be compared between instances with similar numbers of active users.
@freemo Actually, thinking about it, peer count would have the reverse bias (i.e. large instances would seem better connected, while insularity favours small instances). If you have probability P of following a user, independent of his instance, the probability you follow someone on an instance with N users is 1-(1-P)^N. This likelihood increases with N, for 0 < P < 1, so large instances will have more remote followers, and in principle from more remote instances.
Unsurprisingly given the above, Mastodon.social outranks us by several hundred peers. This isn’t that much, given the disparity in size, but I don’t know if that’s because QOTO users are on average more interesting :-) or because QOTO’s followers already make up close to two thirds of the Fediverse, so it’s impossible to do better than about 150% of our count. I feel like this relationship is probably something like a logistic curve, where you get diminishing returns as your instance size approaches infinity.
@khird I think there is a subtle importance regarding what we measure… Are we trying to measure how popular our users are? Or are we trying to measure how many servers block us and what portion of the fediverse we federate with.
I was trying to measure how much of the fediverse we federate with more so than simple popularity. The point was to measure instance blocks and how common they may happen to be.
As such im not sure there would be a need to normalize the peer count. Sure M.S is expected to have more peers because they have more users. While that does say something, perhaps about how interesting we are as you say. If we really just care about how many servers are ferederating with us our prevalence for being blocked I’d say the raw peer count makes sense as was stated without any additional work to adjust for server size.
Insularity though I do agree with you, that needs to be normalized somehow to be useful.
@freemo Good point. I figured the primary motivation for following a QOTO user (thereby making your instance a peer of QOTO) is because you think the guy you’re following is interesting enough you want to see what he posts. But maybe the connection between the two is more tenuous than that, and my assumption was unjustified.
@khird It is certainly a factor that plays a role here. But that would probably only be an effect seen on smaller servers in relation to us, consider…
If a instance is sufficiently large then it is garunteed that at least one user on the instance would want to follow one of our users, especially since we are a large instance. If you are less interesting you might get 1 follower instead of 100 from a server of 100,000, but 1 or 100 makes no difference WRT federating. So for large servers if we federate or not is going to be almost entierly determined by if we are blocked or not.
It would only play a role if a server is small enough that popularity has a significant effect on if a server has that one user.
So its going to play a role for sure, but I dont think its going to be the majority of the effect at play.
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Agreed, to me insularity isnt as meaningful as peer count.