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Why is sharing the rating with students so critical? I can see why people would be curious, but I'm not sure why it matters so much?

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Because students don't know how much a company wants them, and so cannot set their ranking with that knowledge in mind. For example, Apple could rank a student a 9 and Microsoft a 2, but to the student it looks like their level of interest is the same. The student could personally prefer Microsoft, but have a low chance of getting matched, whereas if they knew Apple was closer to a sure-shot of having a job, they might be more risk-averse and rank Apple as their most desired over Microsoft.

I still don't see how on average it's worse for students. It might be worse for student A who would have applied to MS knowing a higher chance of getting in, but that's then probably worse for student B who genuinely wants to work at MS and doesn't get the slot that A took.

Isn't it better if everyone expresses their true preferences and then we do the best matching we can on that basis, rather than having students attempt to game the system in response to company ratings? Your description makes the system sound close to optimal to me.

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