Changing Lanes in an Intersection (Colorado)

I have been curious for a while about this:

If I am turning left at a green light onto a multi-lane road, I should turn into the left lane. If someone is simultaneously turning right (they also have a green light) onto the same road, they should turn into the right lane. That being said, if the second person were to turn into the left lane and cause a collision, would the fault lie on them for changing lanes recklessly, or on me for not giving the right-of-way to the person turning right (as it would be if turning onto a single-lane road)?

Changing Lanes in an Intersection (Colorado)