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But what causes the connection between ideology and consumer behavior?

As presented, “system justification” is what philosophers of science call a pseudo-explanation. That is, it labels a correlating effect but does nothing to explain why the effect exists to begin with.

There is a well-established factor on the personality level that might point to an explanation:

Conservatives score higher on the “conscientious” dimension of the best established personality model, called the Big Five or “OCEAN” model. Conscientious people are dependable, disciplined, act dutifully, and can be seen as stubborn.

In contrast, liberals are much higher than conservatives on the Openness dimension of the same personality model. Openness reflects independence and a willingness to pursue new things, even at risk to oneself.

Complaining about a product or service could be seen as rude, abandoning one’s duty as a consumer to politely take what is offered, and then stubbornly refuse to take action when unsatisfied.

On the other hand, liberal high-openness might be expressed as a willingness to step outside of one’s comfort zone and risk being seen as rude or otherwise inconsiderate.

I’m afraid that “system justification” is simply another correlate with conservatism, only incidentally related to this particular consumer behavior. Maybe the researchers should try repeating the study and control for OCEAN personality factors.

Both effects, system justification and consumer behavior, might even be explained by conscientiousness/openness as a hidden, confounding variable from a deeper level than these surface behaviors.