From the 12th Amendment of the Constitution (emphasis mine)
The person having the greatest Number of votes for President, shall be the President, if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice. And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President.
It is relatively well known that if no Presidential candidate receives a majority of electoral votes, the House of Representatives elects the President.
I have always looked at this as a barrier to a multi-party Presidential election, because with 3 or more strong candidates, the odds of receiving a majority of electoral votes drops dramatically. Even in an election with a clear "winner" (say 45%-30%-25%), the election still goes to the House.
If the entire House was elected every four years, this would not be an issue, as the the party of the "winner" in the hypothetical election above would likely also win the greatest number of seats in the House and would be elected there. But because this isn't the case (and possibly due to gerrymandering), there is no guarantee that the "winner" will make any significant gains and be elected in the House, and the electorate and/or strong third party candidates themselves choose not to take that chance.
Is this a common idea regarding US Presidential elections, or is there a logical mistake I'm making somewhere but just don't see it?