Uh, have you read the 12th Amendment?
The Amendment applies to elections of the Executive — President and Vice President. We were talking — it seemed to me — about legislatures — where in the US two parties dominate, but in other countries there is a wonderful tapestry of multi-partyism.
So, if 3 candidates are in the running, one gets 10%, one gets 45% and the other gets 45%, no one wins.
I don't believe, this ever happened. Somebody would usually get at list slightly more votes than the other. Ross Perot — the most recent remotely-viable 3rd-party candidate lost not because Congress didn't like him, but simply because he came a distant 3rd.
I have not voted for a party, ever, in my life
I meant legally. Though many people (not you, Ok) vote on straight party-tickets, legally they all vote for people, not parties. Yes, it may be, that all a voter knows about a particular candidate is his (likely) party-affiliation, but the vote — in the US — is still for the candidate, not his party.
In many other countries it is the opposite — people might know, who the party is likely to appoint upon winning, but they vote for the parties, not individuals. The parties then allocate seats (in the legislature) according to their own whims and preferences.