A question tag reverses the polarity of its statement: positive takes negative, negative takes positive.

The tag exists to invite confirmation, so it must offer the other possibility. A tag that agrees with the statement asks nothing.

She has signed it, hasn't she? She hasn't signed it, has she?

each tag reverses its statement

She has signed it, has she? She hasn't signed it, hasn't she?

polarity repeated instead of reversed

Where it bites

Where the statement's negative is hidden in a word rather than in 'not' — see the card on hidden negatives.