By vote of a majority of the qualified electors voting thereon in each county affected, any contiguous counties, not exceeding ten, may join in performing any common function or service, including the purchase, construction and maintenance of hospitals, almshouses, road machinery and any other county property, and by separate vote may join in the common employment of any county officer or employee common to each of the counties. The county courts shall administer the delegated powers and allocate the costs among the counties. Any county may withdraw from such joint participation by vote of a majority of its qualified electors voting thereon.