The owner of a building and the insurance company or agent shall each file with the Commissioner a list of not less than three disinterested persons competent to act as appraisers of the building described in the notice. The Commissioner shall select one person from each of the lists so submitted who shall together act as appraisers of the property, and, in case these two cannot agree, he or she shall select a third competent and disinterested person who shall act as third appraiser only as to matters regarding which the two appraisers first appointed cannot agree.