Normally at package install time we try to detect a good default instance for creating SQL Server databases automatically. If an instance called SQLEXPRESS isn't available we usually try to detect LocalDB instances.

Apparently this logic depends on a naming convention that used to work in the LocalDB databases installed by VS 2012 and VS 2013, i.e. there is always a database called (localdb)\v11.0 if LocalDB v11 is installed. Once we find that v11.0 of LocalDB is installed we create the appropriate entry for a default connection factory:

    <defaultConnectionFactory type="System.Data.Entity.Infrastructure.LocalDbConnectionFactory, EntityFramework">
      <parameters>
        <parameter value="v11.0" />
      </parameters>
    </defaultConnectionFactory>

But as soon as you install the SQL Server 2014 version of LocalDB in a machine, the logic will start creating invalid entries in the config, because the instances automatically created don't follow the same naming convention, e.g. the entry will look like this:

    <defaultConnectionFactory type="System.Data.Entity.Infrastructure.LocalDbConnectionFactory, EntityFramework">
      <parameters>
        <parameter value="v12.0" />
      </parameters>
    </defaultConnectionFactory>

But the only LocalDB instance created in the machine by default is called "ProjectsV12".

Note that the actual instances are located in the file system under %LOCALAPPDATA%\Microsoft\Microsoft SQL Server Local DB\Instances. Not sure if there is a corresponding registry entry.