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ninalanyon Not quite: you can have three or more parties (as does the UK and some European countries) but by people,
not ballots, forming those parties.
If the elections become dominated by only two it is only because the others are insufficiently attractive to enough voters.
Britain has largely been dominated by Labour and Conservative for nearly a century, but has had one or two Liberal ones. Their successor, the Liberal Democrats, does attract votes but not enough to win many seats because behind the electioneering, it doesn't offer much the others don't. Similarly with the Green Party though many of its demands may be too extreme to be very popular anyway; and they have yet to gain sufficient, proven Parliamentary experience. The separatist parties of course, have their own, self-selected franchises.
Between them, England, Scotland and Wales have something like five parties.
The simple majority-count system
does work: others methods tend only to create messy coalitions wobbling vaguely around some undefinable centre-ground. That could be dangerous, ripe for some far-out party to spot something the others miss among the electorate's apparently-coherent wishes, and exploit it.
What is far more harmful is the wasted vote - which is
not one for a "losing" party, as some seem to imagine; but is one wilfully not cast, or on a spoilt ballot-slip, or in some insincere "tactical" move by a voter unable to spell "abstain".
(Have you noticed how those wanting that option, call it "None of the above" [candidates / parties], not "Abstain? If they don't know the correct word I doubt they'd understand even a village-hall committee!)
The American situation is that they really only have two parties!