In the UK, at Barnet Council (one of the London boroughs) the Leader of the Council (party leader of the ruling political group), does regular sessions in different parts of the borough and then that content (video and/or transcript) is posted here: http://leaderlistens.com/ Folks who were or weren’t in attendance can contribute to the discussion.
There’s also a growing list of examples here: http://sandbox.dius.gov.uk/digitalgovuk/ though not all are local government.
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