The problem with a no party election is that it allows several candidates to have a legitimate chance at winning; which sounds good, except that an election with more than two candidates is mathematically unfair. The more candidates there are, the greater the chance that the person elected would have been less popular than the runner-up if they were campaigning only against one another, because candidates that do not win can still have an effect on the outcome of the election- particularly under the rules of the electoral college, wherein a third-place candidate might win one state by a small margin where the candidate who won the national popular vote won second, thereby costing him all of the electoral votes that would otherwise have been his. But even under a pure popular vote, a third candidate can take votes away from another a la Ralph Nader. Of course, this is something of a problem as it is, but with parties to give the dominant two candidates a boost, the effect is less significant. Primaries, naturally, are not fair under this model, but the differences between candidates are usually less marked and therefore the problem is less critical, even where there is more potential for unfairness.