At the end of the game, an 'Electoral Tie' is defined as any situation wherein no party has received the required number of Electoral Votes (152+). Under US law, the election is then "thrown" to the House of Representatives, where each state is allocated one vote. From the top three candidates in terms of Electoral total, the player with the most states will then be assumed to have won the necessary support in Congress, and can claim victory.

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If EVEN THIS is a Tie, then the election will be won by the party with the largest Electoral Vote total.

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Example:

It's the end of the game. The Republicans, Northern Democrats, and Southern Democrats are the top three finishers in terms of Electoral Votes, but none of them have the necessary 152+ to win the election.
Normally, the election would then be resolved by collecting vote totals. Unfortunately, the Republicans and Southern Democrats have eleven states each, which means that neither of these parties has the necessary strength to force a win in Congress.

Therefore, the parties must now compare electoral vote totals. The Republicans have 120, the Northern Democrats 60, the Southern Democrats 55. As such, the election is given to the Republicans, who control 120 electoral votes and, as such, have presumably worked their way toward a bargain with the members of Congress.