If at or prior to the final confirmation of any special assessments the owners of privately owned real property to be assessed for more than 50% of the cost of an improvement or in the case of paving or similar improvements the owners of more than 50% of the frontage to be assessed for any such improvement shall object in writing to the proposed improvement, the improvement shall not be made by proceedings delineated by this chapter without a 2/3 vote of the members-elect of the City Council. This section shall not apply to sidewalk construction.