Ah, well, yes, looks like I was right, too, though.

Unless I'm mistaken (and that's possible, I've changed my opinion twice now), my example outlined above is

- conceivable, and

- has 85% accuracy (85 people correctly identified as liars, 85% x 9900 = 8415 correctly identified as non-liars, thus a total of 85+8415=8500 of 10k total "accurately" identified), and

- still only 5% or 6% of flagged liars are actual liars.

EDIT to add:

And if the system is tweaked as you suggest, to very rarely fail to flag a liar:

- suppose it correctly flags all 100 liars as liars

- suppose accuracy is still 85%, thus 8500 people in total classified correctly

- thus 8400 non-liars flagged correctly, and the remaining 1500 non-liars flagged incorrectly

Now still only 6.25% (100 of 1600) of people flagged as liars are actually liars. Thus, even with the tuning you suggest, this remains.

(Note to self: 1. think 2. write)

FWIW, I think you are totally correct if you take accuracy at face value.

You really have to compare precision and recall values to know if the accuracy statement holds true. You could have have 100% precision and low recall and still have 85% accuracy (meaning you could never flag someone as lying and be wrong while missing a bunch of liars and still have 85% accuracy).

but if everything is totally evenly distributed, then 85% accuracy means 85% accuracy and your first statement is correct.

The real issue is that accuracy is only one piece of the puzzle.