Como é que se diz isto em Inglês (EUA)? The consequences of interaction can be difficult to foresee because they are subject to academic backgrounds of both parties. Here what does "subject to" mean?

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"Subject to.." Can mean two things;

1. Having the tendency/likeness to be affected by something that is usually unpleasant.
i.e, "The country's economy is subject to decline in the next couple of years." = this sentence implies that "the country's economy" has the probability to fall …in the next couple of years.

2. Roughly like, "Determined by.." — means what was mentioned is reliant on (something.)
i.e, "The proposed laws are subject to the approval of the president." = this implies that the "proposed laws" are relying on the "president's approval".

It seems to me that in your sentence, "…subject to.." means the latter.

"The consequences of interaction can be difficult to foresee because they are subject to academic backgrounds of both parties." = this implies that the "consequences" are difficult to anticipate because they are being determined by/reliant to the "academic backgrounds"