While browsing various social media platforms, I encounter this upvote, likes button that shows an ambiguous count for the aforementioned things.
Is there a name for such a pattern ?
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"First-order approximation is the term scientists use for a slightly better answer. Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given ("the town has 4×103 or four thousand residents"). In the case of a first-order approximation, at least one number given is exact."
Maybe they determined that the exact number is not important for the majority of users and an estimate fulfills the role just as well. As you said, knowing the exact number won't add that much to a user's experience, e.g. 3000+ vs. 3845.
But on the other hand, I wonder if it really "saves" them anything. Because personally, such things instantly make me feel manipulated or make me wonder "what are they trying to persuade me for as a user here?"; and I'm sure that's not only me.
It feels like someone made the decision that it would be too complex for you to view detailed numbers.
Anyway, your question was about the name and it seems there is no definitive name or pattern for it out there yet. Not really a fan of "optimistic count", as it doesn't really represent what it means. I actually feel like the term you used, ambiguous count, fits very well.
I am interested to see if there is a more specific terminology for this, but in general anything that exists on a social media platform which encapsulates the behaviour of a group of people contributes to the concept of social proof.
Therefore, any terminology derived from the interactions that utilizes or is caused by social proof should have some consistency in wording.
I would argue that these are perhaps 'social proof' counters? And if you want to be specific then each of them could be named based on the type of social proof it is counting or reflecting, so upvote or reputation social proof counter, and share link social proof counter (except perhaps for the comments since it is a more direct metric of engagement).
Sounds a bit wordy but hopefully a good starting point.
I'm not sure if there is an actual name for this other than an approximate count but I believe there may be two reasons why it was implemented this way.
Firstly, an accurate number doesn't really provide much benefit to the user. The average user is probably not going to spend time analysing exactly which post has more likes than another post and only really cares about relative popularity which this approximation gives. Using this format provides an easier to parse representation of popularity that doesn't take space away from other UI components.
Secondly, (and more likely the actual reason it is shown in this way) they likely cannot provide an accurate value immediately. Most social services are now provided on distributed platforms meaning votes and comments will likely be stored on multiple servers across the globe and would require synchronizing before an accurate count could be determined. It is easy to estimate these values by adding the local totals together but is much harder to verify an accurate total count as each vote counted needs to be synchronized with the main server to ensure votes aren't duplicated across servers.
I like "First-order approximation", but it's a bit technical. Another one could be "unbounded range", but again it's a little technical sounding.
I might call it a "lower-bound threshold count" since it's likely based on a defined set of thresholds. There could be one threshold (100+), or they could be 100+, 1000+, 10000+, or they could be 100+, 200+, 300+, 500+, 800+, 1300+, etc.