'automatic assumption' is a correct and usable phrase in written English.
You can use it to refer to an assumption that is made without thinking or being aware of it. For example, "The public had an automatic assumption that the government was not to be trusted."
In particular, given what happened in Libya (among many other examples) after the U.S. helped overthrow Libya's government, shouldn't we question the automatic assumption that U.S. overthrow of a government automatically leads to an improvement in the human rights situation in the country from the point of view of the country's residents?
"Our automatic assumption is something real has changed," Mr. Eibach said.
"That needs to be a question rather than an automatic assumption," she said.
But so does any automatic assumption in genteel society that silence is continuing virtue.
But the automatic assumption that supermarket wine is better value really doesn't stack up.
For most violinists in these works, Romantically soaring lyrical lines are an automatic assumption.
The system also makes some automatic assumptions, like excluding gift-wrapped items.
This world view is founded on such chauvinism that Americans, with our automatic assumptions about equality, might fail to notice it.
He is good at imagining the details of these hypothetical lives - not only the food and the rituals, but the moral atmospheres and the automatic assumptions.
"If I did, I'd be sitting in Los Pinos [the President's office] now," he said sharply, unwittingly revealing the automatic assumptions of America's power to influence everything here.
Not a terrific record for one who had had infinite leisure to rethink the automatic assumptions of the less polished element of the ruling class, and a multimillion-pound overdraft with which to finance, had she wished it, her education.
