Well, I think it's very hard to accept the fact that human decisions can be arbitrary, especially when it comes to the judgement of something that you worked very hard to create. It's along the same lines as calling someone's child ugly. Even if it's a random person, that remark will still sting, you will wonder if everyone else feels the same way.
If you really wanted to avoid the emotional consequences of this decision, you could make it completely random. It would be not only stress-relieving but an act of humility given the truth: that you will never be able to predict the success of these companies.
You have a peice of information they do not: you know that it's nothing personal. But if you tell a reject that it isn't personal there are two scenarios that are most prominent in their minds: that you tell the truth, or you're trying to make them feel better while there is something subtle wrong about themselves that they can't find. The latter option has much more weight put on it because the consequences are more dire. If they have two options with equal probabilities, as far as they know, but with one result being far more devastating than the other, it would be stupid to neglect this possibility, because what if it's true? If this was tribal warfare this could mean life or death, people aren't just going to believe your words.