I feel like you have this backwards. In the assignment Y:=2X, each unit of Y is caused by half a unit of X. In the game where we flip a coin at fair odds, if you have increased your wealth by 8× in 3 tosses, that was caused by you getting heads every toss. Theoretically establishing causality is trivial.
The problem comes when we try to do so practically, because reality is full of surprising detail.
> No bias: The association between X and Y is not affected by a third, omitted variable, Z.
This is, practically speaking, the difficult condition. I'm not so convinced the others are necessary (practically speaking, anyway) but you should read Pearl if you're into this!
The problem comes when we try to do so practically, because reality is full of surprising detail.
> No bias: The association between X and Y is not affected by a third, omitted variable, Z.
This is, practically speaking, the difficult condition. I'm not so convinced the others are necessary (practically speaking, anyway) but you should read Pearl if you're into this!