This discussion is fascinating, anthropologically speaking. Some observations:
* Many commenters seem to be holding to this weird idea that if you don't believe God will smite you, you will not be able to behave responsibly, give your word in a trustworthy manner, etc. If there's not a supernatural enforcer then there are no consequences to lying/breaking your oath. Interestingly, it looks to me that even atheists are endorsing this false idea here!
* An understanding of symbolism and its nuances is also lacking. Perhaps this isn't a surprise, as Enlightenment thinking and literalist Protestant thought have largely erased cultural understanding of symbolism. Thus we have confusion in two ways: many folks swear on the Bible out of convention or lack of critical thought, rather than belief, but will rationalize if pressed, and then folks who are very thoughtful may choose the Bible (looking "normal") or something else (looking "different"). The document chosen, if there is a conscious choice made, symbolizes something about their approach to the ceremony and the position. It is not necessarily a magical choice. (A magical approach takes symbolism a step further and imbues the symbolic object with supernatural power. Contrary to popular belief, this is not a universal approach vis a vis the Bible. Remember that the Christian church and Christian faith and practice existed before the Bible was written, easy to forget in a "sola scriptura" cultural milieu!)
* Amusingly, some really Bible-believing folks will not swear, on a Bible or on anything else, due to Matthew 5:34-37. This intellectual consistency is lost of course when we reduce swearing on the Bible to either convention or magic.
Human rituals cannot be usefully be interpreted as legal acts or as declarations of intellectual belief in a set of propositions. They are symbols. The intellectual incoherency of commonly swearing on a book that says not to swear alone ought to tip you off. I sympathize, folks! I grew up quite literal-minded and so have had quite a struggle coming to terms with the Protestantism I grew up with. Learning the intellectual history of thought and religion and understanding the ways different cultures engage with the divine/supernatural/morality has been very helpful -- and some of that learning must be experiential. Taking part in physical rituals taps into a very different part of the human experience than reading philosophy.