If there is a stop light, you should be turning at different times, so the person turning right would have to wait for the green arrow. Otherwise, I would assume it's the person turning left, since the person turning right is turning across a lane of traffic. Might not be the case though, there are others who know the rules of the road far better than myself.
This is Japan we are talking about here right? I didn't know there were traffic rules??? It was my understanding that it is everyone one for themselves once they give that little plastic thing called a licence.
Just a run down on basic rules here in the Kansai region.
Traffic signals:
Green means go.
orange means go, but get across the intersection as quick as possible.
Red means go, but just be careful when doing so.
Also as a general rule, if the car in front of you runs a red light, than it is pretty safe to say that you can too.
Other rules:
pull in front someone so they have to slam on the brakes.
When pulling out into traffic only look the way you are intending on going.
Never ,ever use indicators, this will only confuse the motorists around you.
Your horn is used for telling people that you are not going to stop at stop sign marked intersection.
Ignore pedestrian crossing when ever possible.
If you are a high school student you are automaticaly given the right to ride a bicycle two sometimes three abreast with you school mates, even though the road is as narrow as one way street at home.
Well, now to answer the question seriously. As NiceGaijin said, the person turning left has right of way when all signals are taken out of the equation.
Let me guess people in the other postion try to turn in front of you?