After all, to whom should an identification be assigned to?
To who studied and proposed the identification of the species, or to who agreed with the identification?
In the case of the observation
inaturalist.org/observations/63131439
an insect with few references in the literature, without records in iNaturalist or GBIF, was identified by @luiscarlosrodrguezmndez through the British Museum’s Catalog of Phalaenae Lepidoptera, who then presented its identification;
later on, @guillaume_delaitre, who had proposed another identification, agreed with the identification made by @luiscarlosrodrguezmndez;
now, on that taxon’s page,
inaturalist.org/taxa/980634-Diospage-rhebus
@guillaume_delaitre appears as the identifier.
My understanding is that, in this case, @luiscarlosrodrguezmndez was the identifier of the taxon.
What are the criteria for assigning identifiers?
Note: @guillaume_delaitre is a very active identifier for many of my observations.
If you click for the full leaderboard, it will display both of them as having one ID. I am not sure why the preview chooses one person over the other; might it be as simple as alphabetical order?
For example, this one suggests the order is alphabetical, and indeed the other two people didn’t actually ID the species, they said “plants” and “angiosperms” on the observation I then identified to species.
In my database I save only one identifier, only the first who, cronologically, suggested the species that became RG
I don’t think the “top identifier” that iNaturalist offers when no one has offered more than one ID for the taxon is determined alphabetically, or I wouldn’t currently be called the “top identifier” of Poa cenisia. I suspect that, in case of a tie, they may offer the person who offered the most recent ID as the “top identifier”, which is the only way I could think of for how I became the top identifier, among only 3 people that offered an ID for that taxon. Tangentially, I had to laugh when iNaturalist designated me the top identifier of that species in the world, after agreeing to one identification of that species.
I’m not 100% sure what the question is asking, but as far as I know, anyone who submits an ID on an observation has that ID counted for 1 ID. So if two people ID as species A, both will be considered IDers as species A. There’s no priority accounted for.
Right now, for the purposes of the taxon page calculation, every identification counts the same. However, if you look at the observation page, you can see that in some sense luiscarlosrodrguezmndez is getting more “credit” for the ID because the ID is labelled Improving, meaning “First suggestion of this taxon that the community subsequently agreed with. This identification helped refine the community taxon.”
There has previously been some discussion about whose name should be displayed as the top identifier on the taxon page if there are multiple people with the same number of IDs (e.g. here), but I believe that it’s currently alphabetical and no one has yet submitted a request to set it to something else.
Edit: it’s not alphabetical, nor is it in order by user id number. 
If this a question to how a determination should be assigned in context of say a specimen, it is a bit complicated. Bugguide handles things differently, but almost all the main identifiers are entomologists or very experienced “amateurs” who are known in their field. Given that, the person who offers the ID I usually designate on the “Det label”.
In iNaturalist I’m not really sure. I would have to say I would say that if an experienced person in the area agreed, I’d designate them, unless the person who posted it was such an expert. While is unfair to a lot of people on the assumption that they can’t be trusted without a pedigree, for scientific purposes it’s best to have an authority weigh in and have them as the confirming person on a Det Label. Most of the specimens I’ve uploaded have determinations already made by people who know the group and I include them. It’s less of an issue with more common things, but when you get something really obscure and rare, it starts to matter.
My two cents, presented from the point of an entomologist who has taken this approach if needed.
Oh and I forgot to mention that if an observation is exported to GBIF, the first person to add the ID that it’s exported as is listed in GBIF as the identifier.
For example:
In this case, because there are so few identifiers, Guillaume’s name appears probably because he identified the species most recently. However, if you look at higher level taxa or taxa with much more identifications, the “top identifier” that appears on the taxon page is the person who has given the most IDs of that particular taxon or lower, and from my observation and understanding, these are not just “research grade” observations and include observations whose community IDs are at a higher level than that taxon, but still have that taxon or lower suggested by the user. As long as that taxon or lower was suggested, it will add to the person’s ID count for that taxon
It would be interesting to see how GBIF does it. I’m a Bugguide editor as well and I simply meant how I make det labels based on who identifies things rather than an actual function of Bugguide.
While we’re on this subject, I’ve also always thought it unintuitive that a user’s own observations of a taxon don’t count toward their tally of identifications of said taxon. Saying you observed a species implies that you identified it! And if you’re trying to check the leaderboards to see whom to ask for advice on IDs, the people who felt confident enough to identify their own observation as such seem like a pool that should be included.
For example, I’ve always thought it was odd that other people (i.e., agreers) show up as the top identifiers for some robber flies where I’m literally the only person to submit any observations of it! (For example, https://www.inaturalist.org/taxa/823751-Lasiopogon-coconino)
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