Basing causal discovery on cause-effect pairs may help fighting against the “curse of dimensionality” by avoiding to perform extensive conditional independence tests, which are very data hungry. 

University of Michigan - Ann Arbor

Why considering only pairs of variables?

There are multiple justifications to embrace the cause-effect pair setting. 
 - Practical (the primary justification)
 - Fundamental Scientific Interest
 - Low Dimensionality

However, what is gained on one side might be lost on another and ultimately, so it is better to think of pairwise methods as complements to multi-variate graphical model methods that help orienting edges left un-oriented in Markov equivalence classes.

Justifications to Embrace the Cause-Effect Pair Setting

 Isabelle Guyon, Alexander Statnikov, Berna Bakir Batu (2019)
Cause Effect Pairs in Machine Learning (The Springer Series on Challenges in Machine Learning)
https://www.amazon.com/Effect-Machine-Learning-Springer-Challenges/dp/3030218090

Cause Effect Pairs in Machine Learning

Cause-effect pair methods might extend the potential outcome framework to resolve cases with no a priori on causal direction X → Y or X ← Y . All is needed is to first condition P ( X , Y ) on known potential confounders Z (e.g. age, gender, etc.) or adjust with a propensity score to get P ( X , Y | Z ), then address edge orientation as a cause-effect pair problem. 

The setting of cause-effect pairs, making no a priori assumption on causal orientation nor on the presence of hidden confounders, lends itself to applications in areas like epidemiology, when it is unclear which variable is the “treatment” and which one is the “outcome”, e.g. X = diabetes_consumption and Y = drinking_diet _soda .

Practical (the primary justification)

One may argue that the cause-effect pair problem is of fundamental scientific interest. Indeed, it is the smallest problem addressing the issue of finding asymmetries in joint distributions of variables that are potentially revealing of causal relationships, and it cannot be resolved using Markov properties (conditional independence testing). 

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