Using the current traffic-light hardware (green, yellow, red lights), we can provide more information about how much time a driver has to get through an intersection. Rather than having one intermediate stage (yellow) between "go" and "stop", we can have three: green+yellow, yellow, and yellow+red.
Yellow lights currently give the driver just enough time to decide whether to stop or go. Giving more information will allow the driver to have more confidence in his decision and allow the driver to dedicate more attention to things other than the traffic light.
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...or simply install a black numeric countdown with in the yellow light like the countdowns used for walk/don’t walk/run signs…..
The problem with staging multiple color lighting or countdown lighting is that there are already too many people in too big of hurry who already don't care that yellow really means stop if you can safely do so. These are the same people who floor the pedal when the light turns yellow instead of braking.
The real solution is for drivers to keep a two second gap between their car and the one in front of them so they have room & time to make these critical judgements and act accordingly.
In Sweden, they have lights that turn yellow for both green and red - thus, a green yellow means it's about to turn red and a red yello means it's about to turn green. It works great, but I think that's because getting a driver's license here takes more than $50 (more like a $1000) and you get better training than in the US.
And we recently changed the system to green-yellow-red for the exact reason hyenuf pointed out above.