For the purpose of holding any general, primary, or special election in this State, the voting precincts and voting places in the several counties of the State shall be designated, fixed, and established by the General Assembly. Nothing in this chapter prohibits a county election commission from establishing multiple polling places within a precinct, provided that voters are assigned to these polling places alphabetically or geographically as determined by the county election commission and approved by a majority of that county's legislative delegation. A voter must be notified in writing of his transfer to a new polling place and the location of the new polling place.