A service, that would work on principles of LinkedIn, of 1st, 2nd, and 3rd line of connections, and provide anonymous prompts for the middle man whether he wants to recommend the renter.
Have it draw everyone you have on emails as your contacts in order for it not to have the hassle of adding and accepting people for yet another platform. You can then just go over the list and tick untick people you want to associate with or not. Completely optional though. They need to install the app too in order for them to appear on your listing, of course.
The renter sends out a signal that he is looking for an apartment, and sets out filters that he is looking for.
The landlords who are in search for a reliable renter, put their apartment on the app as well, fill in the description according to the filters. But the apartments are not public on the app, nor photos, nothing. They just need to be screened for quality by the app's employers.
In case of a first connection match, the app just notifies the two parties.
In case there isn't a direct match, the app can find any mutual connections between the renter and the landlord and annonymously ask them whether they are ready to recommend the renter to the landlord. They can be able to view the appartment's photos before giving the nod.
You don't get to see anyone's else connections for this principle of anonymity to work. So that people won't get mad if you're not willing to recommend them for an appartment.
If the sides complete the deal, the identity of the middle man gets revealed to the parties.
The question is, what makes the middle man want to be on the app? They can be incentivized by getting a small percentage of a month's rent, after six months. That is if the recommendation he gave held the test of time. But helping someone with such a big thing like finding a great place to live would be satisfying in itself and would earn social points.
A social media platform like Facebook or LinkedIn could just extend their business model to automatize this process. But there is a way for a new app to do this.