People are mostly only semi-conscious when driving.
Over years of driving they learn to automatically react to certain stimuli like how Pavlov's dogs salivated to the sound of a bell.
They subconsciously see you gaining on them in their side mirrors and unconsciously speed up because you initiated their learned response of "keeping up with traffic".
This is also why it seems like people change lanes when you do.
One early morning I took advantage of this knowledge and swerved my car indicating a right turn to the vehicle in front of me. This caused them to not only blinker, but to pull into a right turn lane for a neighborhood. They realized their mistake and merged back behind me.
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