What is fair?

The Boston Red Sox routinely sell out of tickets. Demand far outstrips supply. To me, this suggests that their prices are not high enough. My brother says this is not fair; tickets should be given to those who want them the most. I disagree with this assumption, but let's agree with him for a second. So how do we allocate tickets most fairly?

• Give them out randomly. This may seem fair, but not according to our definition above. Tickets are most definitely not given to those who want them most. If there is an aftermarket for tickets, it will only increase demand as people try to get tickets just to resell them.
  
• Make people stand in line. Those who really want the tickets will sacrifice their time. The problem is that some people can sacrifice their time more easily. Surely a banker waiting in line is making more of a sacrifice than an unemployed high school student; there is nothing really unfair about this. Plus there is a huge productivity loss here; all those people in line could have done productive work.
• Auction them to the highest bidders. Those who really want the tickets will pay for them, making sacrifices as needed. The problem, my brother will argue, is that $100 is worth less to Bill Gates than to a plumber. (The marginal utility of additional income surely decreases.) I think such arguments essentially boil down to "it's unfair that the rich have so much more", but I'm having trouble articulating this.
  
• Auction them, charging more to those with higher incomes. Thus we attempt to charge the same utility for each ticket. It's intriguing, like the progressive fines in some Scandinavian countries, but it has some logical difficulties. The Boston Red Sox now becomes more like the IRS. And obviously progressive prices can't be like this, or there's less incentive for people to earn money, which usually benefits to society.
  

So none of the approaches is perfectly fair, but auctioning the tickets is at least efficient. Contrast the auction with random selection by imagining two people bidding for a single ticket. Bill is willing to pay up to $100 per ticket while Theresa will only pay $50. Say you instead chose the recipient randomly and Theresa just happened to be picked. Assuming there's an aftermarket, Bill will buy the ticket for $100 from Theresa. (Theresa will agree to the sale, because she'd rather have $100 than the ticket.) So the final outcome is like the auction, except $50 has been arbitrarily transferred from the Red Sox to Theresa.

Now let's reconsider our original assumption that fairness is an ideal goal. I really want a Porsche 911 GT2. In fact, it's possible that I want one more than Bill Gates, who's willing to pay much more. Does that mean that the dealership should sell one to whoever wants it the most, regardless of cost? Of course not.

I think that auctioning is the best approach, but it might have negative PR for the ball club that could eventually hurt profits. Perhaps a better approach is to auction half the tickets and hold the other for people waiting in line.

Of course these same principles apply wherever demand outstrips supply. I think of opening nights at movie theaters in particular. Why not sell those tickets at a premium?