All persons whose land may be affected by any irrigation project provided for in this chapter may appear before the board of flood irrigation and fully express their opinion and offer evidence upon the matters pertaining thereto. Should two-thirds of the landowners whose land is subject to assessment for the construction of such project and who own at least one-half of such land petition the board of flood irrigation to have further proceedings discontinued, said board, by resolution, shall order all further proceedings in connection therewith discontinued.