Variant criteria have a priority. When determining what objects to publish, Author-it checks variant criteria in order of priority, starting from zero.
For example, a primary object could have two variant objects. The first variant object has a location variant criteria: Australia. The second variant object has a Product variant criteria: X1000. The Location variant criteria has a priority of one, and the Product variant criteria has a priority of ten. If an author published a book with this object and selected Australia and X1000 as the Country and Product variant criteria, the selected variant criteria would meet the requirements of both variants. Author-it would publish the first variant object, because it has the matching variant criteria with the highest priority.
Library administrators determine the priority that each variant criteria has. Authors can view the priority of variant criteria in Author by going to File > Manage Variables.