Assume for the sake of argument that the policy of the "third" party is just like that of the "second" of the two "main" parties. In that case, it's true that the second party could be eliminated in the initial round of voting. However, all its votes would then transfer to the third party. In that case the third party very well could beat the "first" party, satisfying supporters of both the second and third parties.

It's true that third parties would be unlikely to map to the current political spectrum in such a "pure" fashion. However, that just means that voters reject the political choices currently on offer. Voters really should have that option.