Two answers:
1. If you're going to be doing a filter based on UI selection then the CollectionViewSource is the way to go as Graeme_Grant mentioned.
2. If the person you're looking for is an existing relationship to the person, then the most appropriate implementation is modifying the PersonViewModel to contain references to that person.
public class PersonViewModel
{
public PersonViewModel EmergencyContact { get; set; }
...
}
Then bind the button to a command and pass the desired property via CommandParameter.