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Random manual recounts are done on a statistically significant portion of paper ballots. Additionally, paper ballots allow for manual recounts in contested contests (e.g. a legal challenge).

E.g. see https://twitter.com/SFElections/status/534405668258594816 and https://twitter.com/SFElections/status/535541022915186688

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And here is a video of the random selection process for last week's election (the two tweets above are from last year):

http://sfgov2.org/index.aspx?page=4938

This took place this morning (Tuesday, November 10). I'm the lone member of the public who showed up and rolled the dice the first few times (5:15 into the upper video). :)

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