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Check shoulder, signal, maneuver (if it's safe to do so).
If all you're doing is signalling (in a large and obvious manner) and maneuvering then you're abdicating responsibility for your actions and placing it in the hands of other road users, just the same as looking at your phone whilst stepping out to cross a road.
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I agree - that said any driver should be overtaking wide and at a decent, safe speed (meaning that the will not hit someone turning right unless they do it suddenly) or driving a safe distance back so that they do not hit an idiot who onl signals and does not check.
As an individual I try to cycle as well as I can and both signal and look, because not looking is dangerous. As a member of the cycling community I believe that signalling and moving slowly to the right without looking would be perfectly safe if ever driver drove as they should.
What?
Surely if you are not going to look over your right shoulder (which itself is a form of indication that you might wish to turn right) then you have a much greater need to indicate before turning right?
Are you advocating not signalling properly because lots of bad cyclists indicate properly? To a large extent indicating properly is what you do to ensure that there is a safe space to move into as the moment you indicate you are obliging everyone behind you to stay back and not overtake? (Obviously looking over your shoulder is a f'ing good idea too).