![David Molnar [Update:, PhD]](https://www.srcf.ucam.org/~dm516/wp-content/themes/twentyeleven/images/headers/chessboard.jpg)
The way of allocating tickets to formal dinners is flawed at St Edmund’s. Currently, hoarding tickets is the self-reinforcing rational behaviour. A minimal proposed change in ticket allocation can align public and private interests at no additional cost.
Currently, tickets are sold online weeks in advance, but payment is only required after the tickets have been used. Unneeded tickets may be returned up to a few days before the evening without ever having to pay. In consequence, newly released tickets run out almost instantly, because everyone blocks as many tickets as they can. Those who do not spend their nights hunting for freshly released tickets are left with the waiting list. In the days before the dinner a lot of tickets are returned, and so many find out only at last minute that they have a dinner booking, severely constraining their ability to plan or to invite guests.
I would like to show that (a) there can be a cost-neutral cancellation fee, which (b) reduces overbooking without punishing genuine need for cancelling.
Cost neutrality (a) means that a fee levied from those returning tickets does not increase their average cost of dining compared to today, as long as they do not cancel more often than the college average. This only requires that all levied cancellation fees are fully used to subsidise ticket costs for everyone at the next dinner. The fee then may be any amount, even 100% ticket price.
The total cost of formal dining is the same both with and without cancellation fee if (number of formal halls) * (received subsidy per ticket) = (number of cancelled bookings) * (cancellation fee): \(\)
$$n*f+0*c = n(f-s) +p*c$$
$$n*f = n*f-n*s+p*c$$
$$0 = p*c-n*s$$
$$n*s = p*c$$
n: total number of formal halls while member of the college,
c: total number of bookings cancelled,
p: cancellation fee,
f: full price per of ticket without subsidy
s: subsidy per ticket, paid for by cancellation fees
The ticket price subsidy each time depends on how many tickets were cancelled the last time. The expected subsidy per ticket is s=<c/n> * p, with <c/n> the average rate of cancellations. The number of diners is always the same, as halls are always fully booked.
Combining the two
$$n*<c/n>*p = p*c$$
$$<c/n>=c/n$$
shows that if the personal cancellation rate equals the average cancellation rate, then total dinner costs will be the same with or without cancellation fee, proving (a). It also follows that frequent cancelling is punished, reliability is rewarded. It takes $$(< c/n >)^{-1}$$ dinners to get one cancellation fee back through subsidies.
Such a regime does not necessarily mean that hoarding will end, as required for (b). If everyone hoards to the same extent, then their total costs will not change, as was a requirement for (a). This however would require cooperation between everyone to overbook the same number of tickets, and then pay up. The rational behaviour is now to book and cancel only when necessary, if one doesn’t want to subsidise everyone else’s dinners out of one’s own pocket. The average cancellation rate will therefore decrease until everyone only cancels when it is worth the fee.
The friendliness of the system is preserved. A limited number of cancellations remains overall free. Those who really need the flexibility of holding seats and cancel can do so for a price, thus satisfying (b).
Under the current regime it requires cooperation or enforcement to stop rational actors to enter a race to the bottom. Under the proposed regime it requires an all-involving conspiracy to enter a race to the bottom. The invisible hand works for free.
As a final note this system must equally apply for everyone to work, also for fellows and their pre-reserved seats, and for the CR. This will encourage everyone to allocate only as many seats as will likely be needed. Set up this way there will be no cost, and for that a huge benefit for everyone.