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Intuitively, I'd think that cognitive dissonance (CD) is one explanation of confirmation bias (CB), since if it's the case that most people believe "I am right about most things", then admitting one is wrong about something is dissonant with that. Searching "cognitive dissonance confirmation bias" I found a ton of (almost all non-academic) places asserting something similar, but no concrete evidence linking the two. Moreover, I don't see anything about CD here or in any of the various other places I've read about CB.

Is there any research that identifies a connection between the two and tests it?

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Related studies you might find interesting.

Confirmation bias in sequential information search after preliminary decisions: An expansion of dissonance theoretical research on selective exposure to information.

The authors provide evidence that the increase in confirmation bias under sequential presentation is caused by heightened commitment due to the participants' increased focusing on their decision

Confirmation bias: A ubiquitous phenomenon in many guises.

Confirmation bias, as the term is typically used in the psychological literature, connotes the seeking or interpreting of evidence in ways that are partial to existing beliefs, expectations, or a hypothesis in hand.

Google Scholar has many more too, but you'll probably have to filter a bit.

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If you look at the definitions, you realise that you don't need the research for explaining the relationship between the two.

Cognitive dissonance is the direct (emotional, if you will) result of holding two opposing beliefs at the same time:

In the field of psychology, cognitive dissonance is the mental discomfort (psychological stress) experienced by a person who simultaneously holds two or more contradictory beliefs, ideas, or values.

Confirmation bias is the attempt to "twitch" information opposing to your beliefs so as to not generate a conflict in your cognition, so that it doesn't generate the discomfort that we just defined as cognitive dissonance:

the tendency to search for, interpret, favor, and recall information in a way that confirms one's preexisting beliefs or hypotheses.

To say that confirmation bias's use is to avoid cognitive dissonance is something that derives from the definition of both.We do indeed avoid holding two opposing beliefs at the same time to avoid the psychological distress caused by it. No need to scientifically prove that. Furthermore, saying that cognitive dissonance is one explanation for Cognitive Bias seems to be an understatement of the above.

Easiest simile is, if you define the symbol "1" as representing one item of anything and the symbol "0" as representing no item at all, you do not have to prove that you can represent adding one item to nothing by the symbol "1". It's a working convention you simply accept.

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  • $\begingroup$ I'm not sure it follows from the definitions as directly as you suggest. Take the "interpret/favor" part of CB, where someone believes X and then comes across evidence against X. CD simply says that the person does not like holding these contradictory pieces of information in their mind, and will want to resolve things one way or another. It does not predict that the person will tend to resolve their beliefs in favor of X instead of against X. But CB is the precise phenomenon that they will tend to favor X more than is rational. $\endgroup$ – Genghis Kahneman yesterday

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