Rashi (Sh’mos 28:15 and 28:30) gives us two reasons why the Choshen, the breastplate worn by the Kohain Gadol, is called the “Choshen Mishpat.” One of the reasons, based on the Talmud (Z’vachim 88b and Arachin 16a) and the Midrash (Vayikrah Rabbah 10:6; see also Y’rushalmi Yoma 7:3), is that just as the offerings brought in the Mishkan (and in the Temple) atoned for various sins, the Bigday K’hunah (priestly garments) also atoned for certain sins, with the Choshen atoning for perverted justice (“mishpat”). The Kli Yakar provides numerous parallels between the Choshen Mishpat and improperly conducted court cases, including it being one of only two garments that are described as “work requiring thought,” something obviously required if judges are to come to the most appropriate decision.
Even though there are parallels between the two, and the very name “Choshen Mishpat” (and the Torah describing Aharon “carrying” the “mishpat” of the Children of Israel) indicates that this garment impacts “judgments,” these connections don’t tell us why or how the Choshen atones for improper decisions, only that it does. With some garments, such as the pants covering the part of the body involved in adultery, the connection is clear. Is the decision-making process being thought of as coming from the heart enough to warrant the Kohain Gadol wearing the Choshen on his heart being an atonement for bad judicial decisions?
The other reason given by Rashi for it being called the “Choshen Mishpat” is based on its ability to facilitate a definitive answer (when the right kind of question is asked, using the appropriate process). It is therefore possible that the contrast of only G-d being able to provide a definitive answer with human beings, who are prone to both error and stretching the truth, is what brings about this atonement. Since the only Being to always be right, and always be completely truthful, is G-d, atonement must be available for the inevitable mistakes made by (and through) human judges.
Another possibility is based on the consequences of misapplied justice (whether the misapplication is done inadvertently, as implied by Rashi’s wording on 28:15 or done purposely, as implied by his wording on 28:30, or a combination, such as appointing unworthy judges who are not qualified to render decisions, even if their decisions were not purposely wrong). Although there could be a miscarriage of justice in both capital cases and monetary disputes, since we are told (Bamidbar 35:33) that there shall be no atonement for improperly spilled blood, it is unlikely that the miscarriage of justice the Choshen atones for is a court that wrongfully (or mistakenly) put someone to death, or let someone who should have been executed go scot free. True, the context there is different, but the concept is similar; there is no “substitute atonement” for spilled blood (or not avenging it). Besides, there is a strong preference (if not mandate) for the courts to avoid executing anyone (see Makos 7a). Therefore, the atonement of the Choshen is likely limited to a court decision that requires a monetary payment when there shouldn’t be one, or not requiring payment or compensation where there should be.
Imagine the following scenario: Two business partners, with multiple shared bank accounts, come before a court, with one partner saying that a check was deposited into the wrong account and the other insisting it was deposited in the right account. Both partners have equal access to both accounts, and the money from each account is shared equally by the partners. (Let’s put aside why they have multiple accounts.) Assuming the case isn’t thrown out based on its ridiculousness, there can be no “miscarriage of justice” in this situation, because the money belongs to both partners no matter which account it’s deposited into. Would a person be upset at himself for putting the change from a purchase in his left pocket instead of his right pocket (assuming neither has a hole in it and he didn’t encounter any pick-pockets)? The only way there could be a “miscarriage of justice” in a monetary case is if money that belongs, or should belong, to one party is in someone else’s possession instead!
Since the basis for the concept of a financial “miscarriage of justice” to even exist is that there are two distinct parties involved, it is only when the parties see themselves as “distinct” that such a miscarriage can come into play. Although there are, unfortunately, too many cases of siblings fighting over their inheritance, it is certainly possible for children of the same parents to consider themselves as one “unit,” as interested in the financial well-being of their siblings as they are of their own. In such cases, one sibling would never bring another sibling to court over financial matters. By extension, the same can be said of extended family, and of a shared community. Very often, when two members of a community are unsure of something of a financial matter, the involved parties will agree that the money in question should be donated to a community charity. What if each of the two parties had so much “Ahavas Yisroel” that it didn’t bother them if the other one had money that rightfully belonged to him? Could the concept of a “miscarriage of justice” apply there?
The Choshen Mishpat had twelve precious stones embedded in it, each with the name of one of the twelve Tribes engraved on it. When the Kohain Gadol wore it, he “carried the judgment of the Children of Israel” (28:30), all as one unit. And if they were really one unit, not twelve separate units, or 600,000 separate units, it really didn’t matter which “pocket” the money ended up in; once they are considered one unit, there couldn’t be a “miscarriage of justice.” Therefore, since the Choshen Mishpat symbolically brought the nation together into one unit, it was able to atone for any (perceived) miscarriage of justice.