How about a point system? Allow everyone to vote for a 1st choice, 2nd choice, 3rd choice, then assign 5 points to 1st, 3 points to 2nd, 1 point to 3rd. Add up the total points and whoever scores highest wins.
Or simply continue with the primary process as we have now, but do away with the general elections altogether. Instead, on election day, put all the candidates in a dark room, toss in a knife and close the door. Whoever survives gets the White House for the next 4 years.
That’s known as the Borda system. For more information, see Mr2001’s most recent post above.
A point system can mean that a person preferred by a majority does not win. For example, take a 2-way contest:
A gets 51 votes
B gets 49 votes
Clearly, A should win.
But suppose the B party adds another candidate C, to split its votes, but knowing that candidate C will be the last choice of party A. So you get:
A gets 51 #1 votes, 0 #2 votes and 49 #3 votes
B gets 40 #1 votes, 60 #2 votes and 0 #3 votes
C gets 9 #1 votes, 40 #2 votes and 51 #3 votes
With a #1 vote worth 5 points, a #2 vote worth 3 points, and a #3 vote worth 1 point:
A gets 304 points
B gets 380 points
C gets 216 points
So B wins (unless the A party strategically gives some of its #2 votes to candidate C, who they hate more than candidate B).