All proceedings undertaken by any chartered city, or by any chartered county or by any chartered city and county for the construction of any public improvement, or the acquisition of any property for public use, or both, where the cost thereof is to be paid in whole or in part by special assessment or other special assessment taxes upon property, whether the special assessment will be specific or a special assessment tax upon property wholly or partially according to the assessed value of such property, shall be undertaken only in accordance with the provisions of law governing: (a) limitations of costs of such proceedings or assessments for such proceedings, or both, in relation to the value of any property assessed therefor; (b) determination of a basis for the valuation of any such property; (c) payment of the cost in excess of such limitations; (d) avoidance of such limitations; (e) postponement or abandonment, or both, of such proceedings in whole or in part upon majority protest, and particularly in accordance with such provisions as contained in Sections 10, 11 and 13a of the Special Assessment Investigation, Limitation and Majority Protest Act of 1931 or any amendments, codification, reenactment or restatement thereof.

Notwithstanding any provisions for debt limitation or majority protest as in this section provided, if, after the giving of such reasonable notice by publication and posting and the holding of such public hearing as the legislative body of any such chartered county, chartered city or chartered city and county shall have prescribed, such legislative body by no less than a four-fifths vote of all members thereof, finds and determines that the public convenience and necessity require such improvements or acquisitions, such debt limitation and majority protest provisions shall not apply.

Nothing contained in this section shall require the legislative body of any such city, county, or city and county to prepare or to cause to be prepared, hear, notice for hearing or report the hearing of any report as to any such proposed construction or acquisition or both.