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The questions method of the API returns the number of delete votes among other kinds of votes: sample query.

But the answers method does not have a delete_vote_count field available in the filter:

filter

This could conceivably be a design decision, but is more likely an oversight.

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    "Delete votes" on answers are a very different beasty. They don't work the same as for questions and, IIRC, they are only available for 20K users and moderators -- and only if the A has a negative score, for the former group. – Brock Adams Mar 12 '15 at 0:02

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