re: Why hasn't the independent party become powerful?

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Why is that?

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Well the United States uses a first past the post electoral system which means winner takes all.

Duverger's Law goes into why this system tends to favor the emergence of a two party system.

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Duverger laid out two paths by which plurality voting systems lead to fewer major parties: the "fusion" or alliance of weaker parties into more effective factions, and the "elimination" of weak parties as voters gradually desert them because they have no chance of winning and influencing governance.

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Now it's not an absolute rule but it seems to hold decently well. The link has more information.