Cheating and Elections

If you cheat in a game and are caught, you lose.  In forfeiting, your opponent wins.  But in elections, it is different.  If you break election laws, even ones that would have had a decisive effect on the election results, you pay a fine, go to jail, have to resign your post, or suffer some other penalty, but the candidate who suffered the harm as a result of the cheating is left out in the cold.  If it is, say, a governor who is removed, it is his personally selected lieutenant governor who takes over.  It may be a penalty for the person himself, but not for his agenda.  The crime was a person and a political one, but there is only a personal and not necessarily a political price to be paid.

One possible solution is to appoint the loser from the last election if the office holder is removed for election fraud, but what if it is somewhere like the district of Columbia where the general election is a foregone conclusion, but the primary is the big fight?  Do you go back and hold a new general election with the candidate who was cheated in the primaries getting his turn?

Can this be done fairly?