Who else could have been selected as Warren G. Harding's VP, aside from Calvin Coolidge?
The convention was a mess, and the other contenders all hated each other and/or were despised by the party leadership -- so none of them could plausibly get the nod. Harding himself wanted Irvine Lenroot (who, as a progressive, would balance the ticket) and the party leadership agreed. Lenroot himself didn't actually want the job, but was nominated anyway. At that point, the party bosses all buggered off (not wanting to incur another night of hotel costs!), and a delegate nominated Coolidge on his own initiative. The assembled delegates loved the idea, and Coolidge was nominated.
It's been suggested that Lenroot wanted his name withdrawn, but the facts don't support that. A vote on his nomination was scheduled, and had Coolidge not been suggested, Lenroot would've gotten the nod. The only thing required is for Harding and party bosses to stay around for a few more hours and suffer the extra hotel expenditures.