When Lincoln was elected in 1860, there were 4 major political parties. Whigs, Republicans, Northern Democrats and Southern Democrates. He didn't win the electoral college to win the first go round. The dropped the lowest number of electoral votes, which was the Whigs. Then voted again. This time the Northern Democrat party had the fewest electoral votes so they were dropped. Then it was the Republicans vs the Southern Democrats. Lincoln won the electoral votes and the rest is history.
Well, that being said, it isn't impossible to start or have a third party or a 4th party. Wish we had that option today. Dems could split between the moderates and far left. GOP could split between the Wall Street types and the middle class Tea party. Then everyone run, then sort it out. There would have to be some compromising then. Maybe people would study the issues more then.
I hate to say this, but when women didn't vote, there was more issue based voting among men. Chaisma and good looks didn't matter. Women mostly vote emotion. Men vote more logical. When our country was founded only land owners could vote. Thus one reason the push west to stake claims on land and get territories settled to become states. Later, all free men could vote, then all men after the Civil War. Women didn't vote until the 1920's. Most women voted the way their husbands voted until about Kennedy. As divorce and single women increased in the adult population, without a husband, a woman needed help with day care, health care, food stamps, etc. They are more dependent. If young men would man up and pick one woman to love and cherish, and take responsibility as husband and chief provider, the middle class would return and there would be fewer government dependents.