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I'm wondering whether red dots in the example scatterplot shown in the attached graphic can be used as an argument against reverse causation.

If the main effect was $Y \to X$, then we would assume that for high values of $Y$, we also get high values of $X$. However, $X$ appears to be assigned independently from $Y$, while $Y$ is not assigned independently from $X$.

Is the argument valid? If yes - how strong is it and can it be quantified? Is there literature on this?enter image description here

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    $\begingroup$ Why would you say that X "appears" to be assigned independently from Y and not vice versa? To me both directions provide equal amounts of information. $\endgroup$ – Pieter Feb 27 '18 at 8:57
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Detecting the direction of causality is an active area of research. The first thing you need to know is that this is impossible without causal assumptions.

Therefore, in order to proceed, you need to make assumptions not expressible in terms of the joint distribution of observables. For instance, some methods focus on the linear non-gaussian case, others have focused on "independence" conditions of the distributions and so on.

In terms of literature, you can check a recent review by Spirtes and Zhang here. You might find Chapter 2 of Pearl's Causality useful. Also, Peters, Janzing and Scholkopf have a new book out, Elements of Causal inference, the pdf is free and they do focus on causal direction problems.

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    $\begingroup$ I would add Hernán, M. A. and Robins, J. M. (2018). Causal Inference. Chapman & Hall/CRC, Boca Raton, FL. which is freely available in pre-print PDF after the link. $\endgroup$ – Alexis Mar 1 '18 at 6:59
  • $\begingroup$ @Alexis as far as I know, they do not cover causal discovery in the book. $\endgroup$ – Carlos Cinelli Mar 1 '18 at 7:00
  • $\begingroup$ The OP did not ask about "causal discovery" but about "reverse causation," which the cited text contributes to, as well as serving as a solid pedagogical reference for introducing and motivating formal causal reasoning. $\endgroup$ – Alexis Mar 1 '18 at 18:40
  • $\begingroup$ @Alexis finding out if x causes y or y causes x is refered to as causal discovery. $\endgroup$ – Carlos Cinelli Mar 1 '18 at 18:42

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