In Stereotype Accuracy, Clark McCauley describes a fascinating Ideological Turing Test from 1972:

Dawes, Singer, and Lemons (1972)… recruited students who were “hawks” and “doves” with regard to the Vietnam War and asked them to write opinion statements that the typical dove on campus as well as the typical hawk on campus would endorse.  Then they recruited a second group of hawks and doves, asked the hawks to agree or disagree with the hawk statements written by hawks and doves, and asked doves to agree or disagree with dove statements written by hawks and doves.  Hawks rejected more hawk statements written by doves than hawk statements written by hawks, and doves rejected more dove statements written by hawks than dove statements written by doves.  Both hawks and doves rejected statements mostly on the grounds that they were too extreme.

However:

The degree of exaggeration was… neither large nor consistent.  Hawks rejected as too extreme 16 of 40 statements written by doves and 11 of 40 statements written by hawks; doves rejected as too extreme 9 of 40 statements written by hawks and 8 of 40 statements written by doves.  Thus, doves significantly exaggerated the extremity of the typical hawk, but hawks showed only a weak tendency to exaggerate the extremity of the typical dove.

Interpretation:

Dawes et al. (1972) recognized two possible explanations of their results.  One is the information-processing version of exaggeration theory: We disregard information indicating moderation or neutrality because this information is more difficult to assimilate.  The other possible explanation… is motivational: Exaggerating the position of our opponents reduces the force of their arguments.

A well-designed Ideological Turing Test reverses the latter temptation – the more accurate your description of your opponents’ position, the more credible your rejection of that position.