Cognitive dissonance is a concept in social psychology. It is the discomfort felt by a person who holds conflicting ideas, beliefs or values  at the same time. In this state, people may feel surprise, dread, guilt, anger, or embarrassment. Reacting to this unpleasant state, people have a motivational drive to reduce dissonance. Leon Festinger's theory of cognitive dissonance was developed to predict and explain how people reacted to this situation.

Cognitive dissonance theory says that people have a bias to seek consonance between their expectations and reality. According to Festinger, people engage in a process he termed "dissonance reduction". This can be got in one of three ways: 
lowering the importance of one of the discordant factors, 
adding consonant elements, or 
changing one of the dissonant factors. This bias sheds light on otherwise puzzling, irrational, and even destructive behavior.

People in dissonance may change their feelings, thoughts or memories so they are less in conflict. However, often they do not, and instead set out to manipulate the social scene around them so that their embarrassment is less. For example, they may try to explain away the dissonance with a wider theory or they may intensify their efforts at persuasion and publicity so that others join them in their beliefs.

Case study 
Festinger's book When Prophecy Fails is the story of how a cult leader reacted when her prophecy of doom failed.

Festinger and his associates read an interesting item in their local newspaper: "Prophecy from planet Clarion call to city: flee that flood". The prophecy came from Dorothy Martin (1900–1992), a Chicago housewife who experimented with automatic writing. She had previously been involved with L. Ron Hubbard's Dianetics movement, and her cult incorporated ideas from what was to become Scientology.

The group of believers had taken steps which showed their commitment to the belief. They had left jobs, college, and spouses, and had given away money and possessions. They prepared for their departure on a flying saucer, which was to rescue the group of true believers. She claimed to have received a message from a fictional planet named Clarion. These messages revealed that the world would end in a great flood before dawn on December 21, 1954.

After the failure of the prediction, Dorothy Martin left Chicago after being threatened with arrest and involuntary commitment. She later founded the Association of Sananda and Sanat Kumara. Under the name 'Sister Thedra', she continued to practice channeling and to participate in contactee groups until her death in 1992. The Association is active to this day.

Sequence of events 
Festinger and his colleagues infiltrated Martin's group and reported the following sequence of events:
Before December 20. The group shuns publicity. Interviews are given only grudgingly. Access to her house is only for those who can convince the group that they are true believers. The group evolves a belief system—provided by the automatic writing from the planet Clarion—to explain the details of the cataclysm, the reason for its occurrence, and the manner in which the group would be saved from the disaster.
December 20. The group expects a visitor from outer space to call upon them at midnight and to escort them to a waiting spacecraft. As instructed, the group goes to great lengths to remove all metallic items from their persons. As midnight approaches, zippers, bra straps, and other objects are discarded. The group waits.
12:05 A.M., December 21. No visitor. Someone in the group notices that another clock in the room shows 11:55. The group agrees that it is not yet midnight.
12:10 A.M. The second clock strikes midnight. Still no visitor. The group sits in stunned silence. The cataclysm itself is no more than seven hours away.
4:00 A.M. The group has been sitting in stunned silence. A few attempts at finding explanations have failed. One member begins to cry.
4:45 A.M. Another message by automatic writing is sent to Martin. It states, in effect, that the God of Earth has decided to spare the planet from destruction. The cataclysm has been called off: "The little group, sitting all night long, had spread so much light that God had saved the world from destruction".
Afternoon, December 21. Newspapers are called; interviews are sought. In a reversal of its previous distaste for publicity, the group begins an urgent campaign to spread its message to as broad an audience as possible.

The experiences supported the idea that the group did have a bias to seek consonance between their expectations and reality. In fact, events had proved conclusively the falsehood of their ideas, but the group rearranged their explanations to give themselves the least psychological pain.

References 

Psychology