Clay, you ignorant slut.  You have preferential attachment backassward.

What would drive the distribution pattern into a power-law isn't Joi's ego.  You can't scale or clone Joi.  Preferential attachment is when a new participant enters a network they have incentives to connect with those most connected. 

LinkedIn, however, is not a frictionless network.  You have to know someone to join, you have to know someone's email address to initiate a connection, they have to confirm it, and if you don't know them you have to go through a referral.  These transaction costs foster trust, but they are also barriers to preferential attachment.  Joi's preference for connectivity will also max out because there is a cost to connectivity, providing referrals, which does have positive externalities, but maxes out with his available time.

So I'll take that bet.  If I win, we will dine at New Bamboo and I'll run up a tab of Singha.  And if I lose, not only will I buy you a pansy-ass vegetarian meal at Blue Ribbon, I'll throw in as many Pabst Blue Ribbon as you can muster.