The illusion of justice is more powerful
Lie-detector tests increase the public faith in the justice system, which creates a more stable, law-abiding society.
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The appearance of justice is essential to the justice system’s function. If people feel like wrongdoers will face penalties for their crimes, criminals think twice about offending, and victims do not live in a state of perpetual fear of crime.  Ultimately, the appearance of justice is what keeps crimes low and contributes to the stability of a society, not the actual administration of justice. If people have faith in the system, they do not take matters into their own hands and they do not behave in a lawless manner.
Lie detectors give the public comfort that wrongdoers who lie will not get away with their crimes. Even if the lie detectors are flawed, they offer a sense of trust in the process that increases the public’s faith in the legal system. If the public sees suspected criminals being put behind bars for their wrongdoings through the use of lie detector tests, they are more likely to be reassured that justice has been served. This is beneficial to the creation of a peaceful society and promotes stability. Therefore, lie detectors, even if they are inaccurate and flawed, can promote societal stability and faith in the justice system. As a result, they should be admissible in court.
The goal of the justice system is not to create the “illusion” of justice to deter and placate the public. Its purpose is to actually serve justice by punishing the guilty and protecting the innocent. Anything that does not contribute to these goals has no place in the legal system. Lie detectors have a very real possibility of leading to the punishment of the innocent. Therefore, it has no place in the legal system.
[P1] Lie detectors increase public faith in the justice system. [P2] Increased public faith in the system leads to a more stable, law-abiding population. [P3] Therefore, lie detector tests should be admissible in court.
Rejecting the premises
[Rejecting P3] The role of the justice system is not to administer the illusion of justice to increase public faith. It is to administer "real" justice by punishing wrongdoers and protecting the innocent. Lie detector tests do not help achieve these objectives. Therefore, they should not be admissible in court.