Section 1A. The majority of the members of the board shall constitute a quorum for the transaction of its business. For purposes of this section, temporary members shall not be counted for purposes of a quorum, and shall not vote on board matters other than upon specific cases to which they are assigned by the chairman. A single member of the board may decide the following types of cases:
(i) cases on appeal from a board of assessors where the assessed value of the property involved does not exceed $500,000;
(ii) cases on appeal from a board of assessors where the assessed value exceeds $500,000 but does not exceed $750,000 when the appellant and appellee gives written consent to a decision by a single member;
(iii) cases heard under the informal procedure in which the assessed value is less than $1,000,000 as provided in section 7A or the small claims procedure as provided in section 7B.
In any such appeal, upon request and upon the filing of such written consent the appeal shall be advanced for speedy hearing.
Such decision shall be signed by the single member of the board who presided at the hearing, and such case shall be attributed to said single member for tracking and evaluation purposes.