I would never run multiple startups, but I think you could do the initial research to see which idea has any real chance of succes by following the method laid out in the book!
Talk them over with someone you trust - never keep ideas only to yourself, that's not a good idea.
Then, do some kind of experiment to validate your idea. Do a very early MVP, a "pretotype" - you might want to take a look at the Design Thinking, there's lot of material, but what you want to know is Pretotyping - https://www.youtube.com/watch?v=t4AqxNekecY
It's tied to the "Fail Fast" mantra :) , and the Lean Startup by Eric Ries, or my favourites, Steve Blank and Alex Osterwalder - see this slideshow:
http://www.slideshare.net/Alex.Osterwalder/successful-entrep...
I'm doing something of the sort - a very early pretotype to have a starting point to talk with my potential customers and discover their REAL needs (aka what they WOULD pay money for :) ). Remember, "no plan survives contact with the enemy".
Picking the one with the most traction is fine. Also picking the one that excites you the most is good. You could pick based on any number of criteria really. But I would still stick to one.