The air is loud with denunciations of the way in which tickets for next year’s London Olympics are being allocated.

There are 6.6 million tickets and, in the first round, applications were received from 1.8 million people seeking a total of 20 million tickets. A ballot was conducted to determine how the tickets were allocated. Is this the fairest way to make the distribution? Those who got none think not.

Rich Harris, blogging on the viewpoint site of Centre for Market and Public Organisation at Bristol University, makes the case that it was unfair because wealthier people could apply for more tickets that they really wanted, secure in the knowledge that if they actually got them they could afford to pay for them.

Later they will have the chance to sell them back at face value, but in the interim are out of pocket, perhaps by thousands of pounds. Essentially they were taking a bet without knowing the odds. Poorer people lacked the resources to play that game. They applied for only what they could afford and in many cases got nothing. He believes a quota on the number of tickets you could apply for would have levelled the playing field.

That may be true, but the overriding objective of the organisers is to sell all the tickets. By bundling them up in the way they did, they encouraged people to apply for less attractive events to better their chances of getting something. Let’s suppose they had set a quota of four tickets per applicant. Everybody would have gone for the most popular events – the opening ceremony, and athletics, for example – which would have been hopelessly oversubscribed, while less popular events would have had tickets unsold. It would have reduced cash-flow and might have cast a pall over some events. So even if a quota system would have been fairer, I’m not convinced it would have met the organisers’ objectives.

Some – most eloquently, Martin Samuel in the Daily Mail - believe that a “first come, first served” system would have been better. “It can’t be that difficult, selling tickets” he argued. “Here’s what you do. 1. Count how many seats you have in your arena. 2. Decide on a pricing system based on proximity to the action and public interest in the event. 3. Hand tickets over in return for money. 4. That’s it.” 

Not quite. He is overlooking, or ignoring, the experience of the 2008 Beijing Olympics, when a first-come first served approach was tried for the second round of ticket sales. On October 30 2007 a total of 1.85 million tickets went on sale through a ticketing website, a hotline and 1,000 designated bank branches. The website had 20 million hits in three hours, the call centre 3.8 million calls, and queues formed at the bank branches. The system couldn’t cope, and just 43,000 tickets were sold out of the 1.85 million on offer. The Beijing organisers then reverted to a ballot.

Imagine Mr Samuel’s reaction had a similar catastrophe befallen the London Olympics. He’d be begging for the fairness of a ballot and berating the organisers for their naivety in believing first come, first served, would work.

Those who failed in the ballot will have priority when unsold tickets are made available on a first come, first served system at the end of the month. Since there were nearly a million disappointed applicants, that could be tricky. We could easily see a repeat of the Beijing fiasco and fresh complaints of unfairness.

Would there have been a better system than the ballot for the first round? The principal objections were that it favoured those with deep pockets, and forced those lucky in the ballot to give the London organising committee an interest-free loan which was greater in value than the number of tickets they were allocated.

Various websites have been pondering the issue, with the best discussion I could find on the geeksaresexy site.  One possible solution mooted there would have been a true lottery in which applicants buy tickets for a token sum, say £1, in a lottery which is then drawn, with the winner entitled to buy tickets for the Games. Applicants would not be out of pocket and if a limit was set on the number of lottery tickets anybody could buy, the rich would not be favoured over the poor.

A sophisticated version of this, suggested by Brandon Pisani, would have tickets for all events divided into blocks. The blocks might include a mixture of seat prices (high, medium, and low) or there might be blocks limited to a single price band. Those whose lottery numbers came up would have a week to buy their tickets; unsold tickets could be sold off first come first served, or added to a second lottery round.

It’s complicated, as he admits. But people wouldn’t be giving the organisers an interest-free loan, and it would be equitable as between the rich and the poor. It’s not clear to me, however, how efficiently this system would ensure that seats were sold. Most applicants want more than one ticket. So does getting a single winning lottery ticket entitle you to buy as many seats for that event as you want, subject to a limit of, say, four?

On that assumption, there could be a lot of unsold tickets if the average purchase turned out to be only two seats. The organisers would have the difficult task of guessing how many seats the lottery winners would buy, in order not to leave some disappointed, or, on the other hand, of having too many seats left unsold. Explaining this system would also be a challenge; many people seem baffled by the much simpler system that was actually used.

The alternative, of allowing applicants to buy as many lottery tickets as they wanted seats, wouldn’t work. Everybody bar the naive would go for the maximum allowed, say 10, to increase their chances of getting a winning ticket. The actual chances of winning would be unchanged, and most winners would in any event have only one winning ticket. So they’d have to go to the Games alone, or sell the ticket back.

Anybody got a better idea? There must be some mathematicians or statisticians - or, more likely, economists - out there who have studied allocation problems.

The method chosen by the London organisers is essentially a well-disguised way of using price to help achieve the allocation, without actually admitting it. Markets are very good at allocation, if not always fair. But I suspect there’s no alternative.  

What really grates with me is using a quasi-market method to allocate tickets, and then refusing to allow an after-market that would re-allocate unwanted tickets to those who really wanted them. “Touting” is strictly forbidden, as if it’s an offence to sell something you own for what it’s worth to somebody else. But that’s another issue.