gistfile1.rb

class Qualification
  include Mongoid::Document

  field :name
end

class User
  include Mongoid::Document

  references_many :departments,    :stored_as => :array, :inverse_of => :users
  references_many :qualifications, :stored_as => :array, :inverse_of => :users

  field :name
end

class Department
  include Mongoid::Document

  references_many :users, :stored_as => :array, :inverse_of => :users, :inverse_of => :departments do
    def qualified
      ???
    end
  end

  references_many :required_qualifications, :class_name => 'Qualification', :stored_as => :array, :inverse_of => :departments

  field :name
end