Dropdowns have a displayName and a value. When referring to a SharePoint list, the displayName is typically some human-readable field, and the value is typically the ID of the list item. This is especially important if you have lookups.
What you do is you have a second field in your schema (it could be hidden and not displayed in the canvas). You'll set up rules to set the value of that field to store the displayName (because, remember, the dropdown is storing only the ID). Then you can use that new field (displayName) however you need: as a promoted property, in a qRules mapping, etc.
Hilary's blog post on the qRules command includes lookups in her example, so that might be a good reference if you're trying qRules.