I saw a few threads that touched on this, but to avoid thread necromancy I'm going to submit my own question.

I'm trying to make it on my site where an applicant can apply privately (to avoid any issues with their current guilds, obviously). I've set the applications up as "Private" and made a rank of Applicant which I assign whenever an applicant creates an account on the site.

But... it doesn't seem to be allowing them to see the application. It could be that they create the account (and are prompted to) after the application, or it could be that Applicant is not my lowest rank (Non-member is).

However, I don't want to make Applicant the lowest rank, because then non-members can see and vote on the application, which in effect makes the application non-private, since I can't prevent non-members from seeing the application. Plus, I'm already letting more people than I'd like to view the application have access already (I'd like it to be between my officers and the applicant).

So, I guess what I'm looking for is a way for an admin to add a name to the access of an application manually, like we can do with other private threads. That way, we can set the security of the applications to the correct level while still being able to give the applicant access to view their own app.

The way an application works today is that it is not visible to the person that created. It is created under the Generic Account Applicant. With the settings set to private thread when the application is created it makes it readable to accounts that exist at the privilege level of the thread and the generic account Applicant that the thread was created.

If I understand you correctly you want a system in which you must create an account on the system before you can create an application for the guild.

I think a plausible solution to that would the following. This is something Chops would need to develop.
You need a setting on your page under applications that says something like "Requires Account to apply". Then the system would have the user create an account and then take them to the application. The account would them be temporarily approved based on the acceptance of the application. While in this temporary status they only get what non members see and the application they filled out. This would mean a slight change in the application system in that if the application was filled out by a logged in user it would use that user as the sender and not the generic account. Accepting or Declining the application would also either fully authorize their account and automatically promote them the the lowest rank on your site or if declined it would delete the account and provide feedback via an email message that the application was declined. Prior to declining this would give you the time to converse via the application thread with the applicant to ask the questions you needed to make a good decision. I would also suggest though that if you use a polling system that the applicant should not be able to see the poll on the account.

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Egg Shen: Wind, fire, all that kind of thing!

Correct. The applicant doesn't get to see their own application, because they can't log in as the generic account Applicant that is given access to see it. Thus, the person who puts in the private application never sees it.

Your solution would be ideal. It would take automate a lot of the stuff that we do manually, and would give the applicant a way to interact with us during the review process.

In the meantime, some way to simply add an account to the list of allowed users on a particular application once they create their account would help achieve the interactivity we're looking for.

Though your solution is spot on. That would be the ideal solution.