Connecting With Strangers on LinkedIn?

Do you connect with everyone on LinkedIn who invites you to connect with them? No. I hope to feel like I have a responsibility to protect the people in my network, again, and takers. If somebody is a peer stranger, it's hard for me to make those judgments. And so what I've been doing lately is I've actually been looking at, first of all, do we have a common connection; then secondly, have they given the good explanation for why they want to connect?