I don’t think Cruz gets to pick his VP in a contested convention.
http://www.freerepublic.com/focus/f-news/3416435/posts
Reince: Even VP Nomination Could Be Contested
Weekly Standard ^ | April 1, 2016 | Jim Swift
On Greta last night, RNC chairman Reince Priebus suggested to Fox News viewers that even the vice presidential nomination could be contested at the GOP convention in Cleveland later this year.
GRETA: The convention. Tell us for planning purposes. If it is a “open/brokered/contested” convention, will it last longer than we expect?
PRIEBUS: No.
GRETA: It’s gonna just be those days?
PRIEBUS. That’s right.
GRETA: You think it’s gonna be put to bed?
PRIEBUS: We will put whatever systems in place, we will have meetings however long we need to have them... In order to make sure that we not only have a nominee both for president, and remember, there’s a separate vote for vice president... as well that no one’s talking about that. But there’s another vote for vice president... And then on Wednesday and Thursday we’re gonna have a program. And there’s going to be a convention, with, uh, obviously, our nominee to be concluded on Thursday night.”
What if the intentions are to run as a Third Party?
Interesting thought—it does take his biggest bargaining chip out of his back pocket, if you will.