The board of supervisors of a county of the first class as described by Sections 28020 and 28022 may, by resolution adopted by a majority vote, increase the amounts of the death benefits payable pursuant to Sections 31760.1, 31765.1, 31781.1, and 31785, with respect to a death occurring on or after the date this section becomes operative in a county, up to the amount of the monthly allowance to which the deceased member was or would have been entitled as of the date of his or her death.