If the party finishing 2nd and 3rd had more votes than the party finishing 1st and 4th, they wouldn't be the minority party. I find it more likely that the 3rd and 4th places would be taken by third parties, and you'd have something like this:
1st: Republican
2nd: Democrat
3rd: Green
4th: Libertarian
...in which case the Dems would be the minority party, but the left in general would still hold a majority of the votes (assuming 2nd + 3rd > 1st + 4th).