"The Academy News" - the MTA student newspaper - asked me to answer the following question:
"I know my friend cheated on a test. What should I do?"
The Gemara (Bava Metzia 83b) relates that R' Elazar the son of R' Shimon, was authorized by the government to arrest thieves. The Gemara then records that R' Yehoshua ben Korchah criticized him, writing to him: “Vinegar son of wine!” [I.e., the bad son of a good father (Rashi). R' Elazar's father was the great R' Shimon bar Yochai.] How long will you hand over the people of our God to their execution!?”
R' Elazar the son of R' Shimon wrote back to R’ Yehoshua ben Korchah: “I am ridding the vineyard of its thorns!” [I.e., I am ridding the Jewish people of its evildoers. The metaphor of a vineyard is based on a verse in Isaiah (5:7): For the vineyard of Hashem of Hosts is the house of Israel.]
To this, R' Yehoshua ben Korchah, in turn, responded: “Let the Master of the vineyard come and get rid of His thorns Himself.” [I.e., God can deal with the wicked without your assistance.]
Of course, the penalty here (death) was out of proportion to the crime (theft). Rashba and Rivash both state in their responsa (3:393 and 251, respectively) that R' Elazar the son of R' Shimon's actions were an example of the extraordinary powers a leading rabbi may exercise under extraordinary circumstances. If crime is so rampant that it threatens to cause a breakdown in society, the leading rabbis and courts are empowered to use all means necessary to repair the breach (see also Shulchan Aruch, Choshen Mishpat 2). This is true all the more so when they are authorized to take such measures by the secular government. R' Elazar the son of R' Shimon held that thievery of his generation was in such a category and he thus was permitted or even obliged to turn over these Jewish thieves to their deaths at the hand of the government (cf. Ritva). On the other hand, R' Yehoshua ben Korchah presumably disputed the necessity of applying these extraordinary powers (see Shulchan Aruch, Choshen Mishpat 388:9; see also Teshuvos Mishneh Halachos 9:380). Thus he condemned R' Elazar the son of R' Shimon's efforts to have these thieves killed.]
It would thus seem that a student should not take into his own hands the responsibility of alerting the “authorities” to the cheating of another student. The case may be made, however, that under certain circumstances a student may reveal to a rebbe or teacher that another student has cheated, if he does so for the purpose of the cheating student’s benefit — viz., so that the rebbe or teacher will demonstrate to him the error of his ways and help him to develop proper integrity and character (see Chafetz Chaim, Be’er Mayim Chaim 10:34).