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...this biass, though, perhaps, it may not appear in a few throws, will certainly prevail in a great number, and will cast the balance entirely to that side. (David Hume, Of the Rise and Progress of the Arts and Sciences, I.XIV.3)

The meaning of this sentence is clear. But is the style of “Cast the balance to that side” a very literal one? Can I use it in scholarly writing?

For example,

China has concentrated government, huge population..., but in her competition with America, she must be the loser, because democracy and freedom will cast the balance entirely to America’s side.

Is “Cast the balance to some/someone’s side” a standard usage or a figure of speech?

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It seems pretty standard though a bit archaic (used in Jeremiah Whitaker Newman's "The Lounger's Common-place Book" published 1838, in the "Commentary Critical and Explanatory on the Whole Bible" by Robert Jamieson, A. R. Fausset and David Brown, published 1871 etc).

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Well, it is a figure of speech because it isn't referring to an actual balance. However, the expression is absolutely standard. I wouldn't think twice about seeing it in the New York Times.

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Yes, you can use it, but "tilting the balance" is used more often.

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