Created attachment 275739 [details]
screenshot

What does

gsettings get org.gnome.desktop.notifications application-children

say ?

['abrt-applet', 'evolution', 'org-gnome-software', 'gnome-music', 'transmission-gtk', 'birdie', 'gnome-network-panel', 'vlc']

On my Fedora 20 + GNOME 3.12 Copr I get even more doubles.
Twins for Polari, Software and ABRT.

there gsettings...applications children gives me:
['org-gnome-software', 'mozilla-thunderbird', 'empathy', 'transmission-gtk', 'gnome-abrt', 'sparkleshare', 'org-gnome-polari', 'gnome-music', 'gnome-network-panel', 'tomboy', 'evolution', 'abrt-applet']

Looks like "org-gnome-software" vs "org-gnome-Software".

Reassigning to gnome-control-center. This seems to be a bug with the notifications panel that considers "org-gnome-software" and "org-gnome-Software" as different identifiers.

gnome-shell runs the desktop file ID-s through the following function before saving them in application-children:

    _canonicalizeId: function(id) {
        // Keys are restricted to lowercase alphanumeric characters and dash,
        // and two dashes cannot be in succession
        return id.toLowerCase().replace(/[^a-z0-9\-]/g, '-').replace(/--+/g, '-');
    },

commit ea66f828eb8207fb8741decd68bb9851e73d55d2
Author: Bastien Nocera <hadess@hadess.net>
Date:   Tue Jul 1 16:23:55 2014 +0200

    notifications: Fix duplicates in application list
    
    When saving applications in the "application-children" list, gnome-shell
    will lower-case the whole canonical application ID in _canonicalizeId().
    
    Match _canonicalizeId()'s behaviour, and lower-case the canonical
    application ID so we don't try to load "org-gnome-Software" from
    GNOME-Software's desktop file in addition to the already saved
    "org-gnome-software".
    
    https://bugzilla.gnome.org/show_bug.cgi?id=729447

commit 45183a89b5caf2d593abc8a731a05b9fec7f5fc3
Author: Bastien Nocera <hadess@hadess.net>
Date:   Tue Jul 1 16:23:11 2014 +0200

    notifications: Add better debug for saved apps
    
    So we can see the apps for which there already are saved settings.

*** Bug 732797 has been marked as a duplicate of this bug. ***