First come first served

Is the natural, normal way of selling tickets: as fast as you can, until there are none left.

But when the demand is very much higher than supply, and everyone knows it, everyone's worried there will be none left, so try to secure tickets as soon as possible. The Principal of Scarcity - "we want what we’re afraid we can’t have" - means that the risk of not being able to get tickets when we do want them turns into an even stronger desire to get tickets in the first place. Everyone hits the websites and phones the second they are open, servers start to melt, and hilarity ensues.

This is especially awkward when the event in question is publicly funded, or for other reasons the limited stock of tickets must be seen to be allocated "fairly"; one's ability to get to the computer and press F5 repeatedly at the crucial moment is not a particularly fair measure on which to allocate tickets.

Dynamically raising ticket prices based on speed of demand might blunt this inital surge, but is still basically FCFS.

Selling tickets at auction can work. I've mostly seen it done for certain charity events, where the point is to show off how rich and generous you are by bidding way over the top for tickets, of course in the name of a good cause. When TicketMaster put a large proportion of its allocation for a some concerts directly on its aftermarket auction site TicketsNow without first offering them to the public at face value, people were understandably upset: a Class Action lawsuit, (recently settled, it appears) was the result. But if the event promoter deliberately chose to auction the tickets in the first place then there would be much less to get cross about.

The other option is the ticket ballot or lottery. Glastonbury Festival's adoption of the ticket ballot has changed the annual scrum of ticket buying panic into a much more orderly affair. Registering in ones own time means the systems are not overloaded, and being able to batch-process the orders also means that the credit card authorisation service, often a bottleneck for large onsales, is no longer a problem: having selected the winning applications from the ballot, the authorisation no longer has to be done in real time.

A brilliant example of how to completely cock this up is the 2012 London Olympics. Because the tickets are divided between all of the different events, each drawn from the ballot separately, the ballot does not diffuse the innate human psychological timebomb that is the principal of scarcity. Rather than putting their name down for only the events they wanted, and waiting patiently for the ballot as with a Glastonbury ticket, many people wanting tickets - or, more accurately, worried that they wouldn't get tickets - applied indiscriminately for everything. I was told an anecdote last night about a couple who applied for £10,000 worth of tickets, and who then got "lucky" (or unlucky) in the ballot, and who now find themselves obliged to attend a large number of Olympic Figure Skating Quarter Finals and the like, tickets with a face value of £5,000, and no opportunity to either resell them or return them to the box office. In this case the natural response of someone trying to maximise their chances of getting a ticket for something worked very much at odds with the process, and I expect the Olympic audience is going to be largely comprised of people who really wanted tickets for something else, aren't very interested in the event, but have shown up because they've had to pay for the tickets anyway and don't want to "waste" the money.

A simple fix would have been to offer Olympic Ticket buyers a list of events in order of preference, and if their number came up, they would get tickets for the top not-sold-out event on their list. That way, they'd be buying a predictable number of tickets rather than a potentially large liability, for events that they actually wanted to see.

An innovative use of the ballot - and one which worked well, though I've not seen it used since - was the Live 8 concert. Wikipedia says:

Although the concerts were free, 66,500 pairs of tickets for the Hyde Park concert were allocated from 13 to 15 June 2005, to winners of a mobile phone text message competition that began on Monday, 6 June 2005. Entry involved sending the answer to a multiple choice question via a text message costing £1.50. Winners were drawn at random from those correctly answering the question. Over two million messages were sent during the competition, raising £3m. Thus entrants had a roughly one-in-28 chance of winning a pair of tickets.

That works out at £45 raised per ticket, quite a reasonable selling price. What's nice about this approach is that
1. You're raising money from all the people interested in tickets, not just the ticket buyers. This is nice because a lot of the costs of provisioning web servers and call centres are proportional to the number of people interested in tickets, and not the number sold. If Madonna decided to play the Barfly, then you'd still get a million people on the website, even though there were only a hundred tickets available.
2. People know what they're buying - a chance at a ticket, not an actual ticket - and can spend exactly as much as they want to.
3. People not prepared to spend a lot still have a chance at a ticket. You could have just sent one text message for the Live 8 tickets, and hoped you got lucky, and if you did you'd get a pair of tickets for a bargain £1.50. So poorer people are not excluded.
4. People prepared to spend a lot can still do so. If you really wanted tickets and you'd spent £45 on text messages, you'd have a pretty good chance of getting in. So richer people can still hand over more of their cash.