Doubling Down
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One interesting phenomenon is the tendency of people to double down on beliefs. For those not familiar with doubling down, this occurs when a person is confronted with evidence against a beloved belief and her belief, far from being weakened by the evidence, is strengthened.
One rather plausible explanation of doubling down rests on Leon Festinger’s classic theory of cognitive dissonance. Roughly put, when a person has a belief that is threatened by evidence, she has two main choices. The first is to adjust her belief in accord with the evidence. If the evidence is plausible and strongly supports the logical inference that the belief is not true, then the rational thing to do is reject the old belief. If the evidence is not plausible or does not strongly support the logical inference that the belief is untrue, then it is rational to stick with the threatened belief on the grounds that the threat is not much of a threat.
As might be suspected, the assessment of what is plausible evidence can be problematic. In general terms, assessing evidence involves considering how it matches one’s own observations, one’s background information about the matter, and credible sources. This assessment can merely push the matter back: the evidence for the evidence will also need to be assessed, which serves to fuel some classic skeptical arguments about the impossibility of knowledge. The idea is that every belief must be assessed and this would lead to an infinite regress, thus making knowing whether a belief is true or not impossible. Naturally, retreating into skepticism will not help when a person is responding to evidence against a beloved belief (unless the beloved belief is a skeptical one)—the person wants her beloved belief to be true. As such, someone defending a beloved belief needs to accept that there is some evidence for the belief—even if the evidence is faith or some sort of revelation.
In terms of assessing the reasoning, the matter is entirely objective if it is deductive logic. Deductive logic is such that if an argument is doing what it is supposed to do (be valid), then if the premises are true, then the conclusion must be true. Deductive arguments can be assessed by such things as truth tables, Venn diagrams and proofs, thus the reasoning is objectively good or bad. Inductive reasoning is a different matter. While the premises of an inductive argument are supposed to support the conclusion, inductive arguments are such that true premises only make (at best) the conclusion likely to be true. Unlike deductive arguments, inductive arguments vary greatly in strength and while there are standards of assessment, reasonable people can disagree about the strength of an inductive argument. People can also embrace skepticism here, specifically the problem of induction: even when an inductive argument has all true premises and the reasoning is as good as inductive reasoning gets, the conclusion could still be false. The obvious problem with trying to defend a beloved belief with the problem of induction is that it also cuts against the beloved belief—while any inductive argument against the belief could have a false conclusion, so could any inductive argument for it. As such, a person who wants to hold to a beloved belief in a way that is justified would seem to need to accept argumentation. Naturally, a person can embrace other ways of justifying beliefs—the challenge is showing that these ways should be accepted. This would seem, ironically, to require argumentation.
A second option is to reject the evidence without undergoing the process of honestly assessing the evidence and rationally considering the logic of the arguments. If a belief is very important to a person, perhaps even central to her identity, then the cost of giving up the belief would be very high. If the person thinks (or just feels) that the evidence and reasoning cannot be engaged fairly without risking the belief, then the person can simply reject the evidence and reasoning using various techniques of self-deception and bad logic (fallacies are commonly employed in this task).
This rejection costs less psychologically than engaging the evidence and reasoning, but is often not free. Since the person probably has some awareness of the self-deception, it needs to be psychologically “justified” and this seems to result in the person strengthening her commitment to the belief. People seem to have all sorts of interesting cognitive biases that help out here, such as confirmation bias and other forms of motivated reasoning. These can be rather hard to defend against, since they derange the very mechanisms that are needed to avoid them.
One interesting way people “defend” their beliefs is by regarding the evidence and opposing argument as an unjust attack, which strengthens her resolve in the face of perceived hostility. After all, people fight harder when they believe they are under attack. Some people even infer that they must be right because they are being criticized. As they see it, if they were not right, people would not be trying to show that they are in error. This is rather problematic reasoning—as shown by the fact that people do not infer that they are in error just because people are supporting them.
People also, as John Locke argued in his work on enthusiasm, consider how strongly they feel about a belief as evidence for its truth. When people are challenged, they typically feel angry and this strong emotion makes them feel even more strongly. Hence, when they “check” on the truth of the belief using the measure of feeling, they feel even stronger that it is true. However, how they feel about it (as Locke argued) is no indication of its truth. Or falsity.
As a closing point, one intriguing rhetorical tactic is to accuse a person who disagrees with one of doubling down. This accusation, after all, comes with the insinuation that the person is in error and is thus irrationally holding to a false belief. The reasonable defense is to show that evidence and arguments are being used in support of the belief. The unreasonable counter is to employ the very tactics of doubling down and refuse to accept such a response. That said, it is worth considering that one person’s double down is often another person’s considered belief. Or, as it might be put, I support my beliefs with logic. My opponents double down.
A Philosopher's Blog 
I’ve never heard the term “double down” used this way.
People who deny reality and cling to false beliefs are usually said to be “in denial”. Such as when a doctor tells a mother her child is dying and she refuses to believe the doctor. Believing instead her child will recover.
To say someone is “doubling down” usually means they’re going to make twice the effort they were making previously. Such as “Obama is doubling down on gun control” meaning: “Obama isn’t giving up his effort to better control guns. He’s going to try even harder now”.
I guess the way you’re using the term it can mean both “denial” and “doubling down”… meaning people in denial become shrill, angry, name-callers (e.g., “anti-______”, “extremist!”,”conspiracy theorist!” “nutter!”, “truther!”, “denier!”), and will even go so far as to pass laws against those who disagree with them…
Examples:
“People who believe in Anthropogenic Climate Change are doubling down in the face of evidence presented by their critics.”
“People who believe in The Holocaust™ are doubling down in the face of evidence presented by their critics.”
“People who believe in Dark Matter are doubling down in the face of evidence presented by their critics.”
AJ
In the examples that you give I think it’s largely a case of 1/propaganda that has inculcated these beliefs for various agendas and 2/ fear of thinking for oneself and standing out(this is understandable as the propagandists are very skillful and throw in a lot of emotion in the first two at least).
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