As it turned out, the type of swaps that would be happening would be random swaps.
Anyone who swapped would retain their memories of everything as it was before the swaps began, but reality would change to accommodate whatever the changes that were caused by the swaps happened to be. For example, if Jon swapped with his little brother Mikey and either exchanged age, personality, or whatever, then anyone who hadn't swapped would think that Jon was supposed to be whatever he was as a result of the swap.