Cognitive biases
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Original Question
What cognitive bias is it when a voter votes for a candidate and therefore is now biased in favor of that candidate just because they voted for them? The voter made a judgment, and they assume that they have good judgment, and so they have to avoid admitting that their candidate was the wrong choice in the face of evidence suggesting they were a poor choice because that would go against their belief that they have good judgment? Its easier for the voter to ignore and deny this reality to maintain their own self image and not doing so.
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Answers
6As I understand the question, this could be an example of confirmation bias or a case of Dunning-Kruger where a person's deluded overestimation of their skillset obscures the reality of their actual skillset. Or, as comedian John Cleese describes it: Someone is just too stupid to know how stupid they are.
I agree with Jordan Pine that the feeling that person feels is cognitive dissonance. But since the choice of changing their opinion has also a personal effect on their self-esteem, I would say it is a case of Self-Serving bias
Another bias, which I don't know however, if it is indeed the case in question, but is worth being mentioned, is the Partisanship (and consequently Partisan-based Cognitive Dissonance) which leads people to reject evidence that's inconsistent with the party line or discredits party leaders.
Federalist Papers #9 and #10 best answer this question but only to an American political Philosopher.
In addition to Choice Supportive Bias as Dr Bo mentioned, I also thought of conservatism. The person may insufficiently adjust their support for the candidate in question upon receiving evidence of their ineffectiveness as a leader.
The ancient Greeks not only introduced philosophy to humanity but also logic and paradoxes as well.
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This sounds very close to cognitive dissonance. With CD, the setup you described causes the person such mental discomfort when confronted with evidence their decision may have been wrong, they become irrational or even “hallucinate” things happened that didn’t happen.