if no Person have a Majority, then from the five highest on the List the...House [of Representatives] shall...chuse the President. --U.S.Const. Art. II, Sec. 1, Cl. 3.
You would need a constitutional amendment to implement your idea.
> You would need a constitutional amendment to implement your idea. <
Yes, I agree. The section of the Constitution you referenced only applies if there is no overall (national) electoral majority. The problem with third parties is that they upset the apple cart within individual states.