They shall submit to the people of the county at any regular or special election any question involving any extraordinary outlay of money by the county or any expenditures greater in amount than can be provided for by the annual tax, or whether the county will construct any courthouse, jail, or other public buildings, or aid or construct any road or bridge, and may aid any enterprise designed for the county, whenever a majority of the people thereof shall authorize the same as hereinafter provided. Provided that, for the purposes of this section the term “public buildings” shall include, but not be limited to, a county rest home, which shall be defined as any home, establishment, or institution owned and operated by the county in which there is offered or provided personal care and supervision to persons who are unable to care completely for themselves.