We were discussing the idea that everyone who applies by the January deadline has an equal chance of receiving an offer if they meet the criteria. ExCwmbranDweller was saying that feels counter-intuitive, because if you have a bag of 500 sweets and you give out lots of them at the beginning, you'll be less generous as time goes on and you worry about running out.
I gave this reply:
I think it's more like a sweet shop with a climbing wall outside. Every year they hold an event where those children who have a sweet voucher and climb high enough on the wall can have a sweet. The children practise climbing at school, and all have a certificate saying how high they can usually climb.
The owners recorded how many children got to which heights last year (and the year before etc). They only have about 500 sweets but they know from experience they can offer sweet vouchers to 1000 children, because 50% of the children always decline and decide they want a sweet from a different shop. Based on the heights the children reached in previous years, the owners attach a horizontal bar to the climbing wall that approximately the right number of children will reach. Everyone can see how high this is.
The sweet shop announces that the children can come and show their certificates and ask for a sweet voucher.
The children arrive in dribs and drabs over the course of several weeks. The owners decide to offer a sweet voucher to any child whose certificate states they can climb to within 2 metres of the bar. The last child to come gets the same treatment as the first child to come, to make it fair, even if this means handing out extra sweet vouchers.
If the owners hand out over 500 sweet vouchers, they don't worry too much. A few of the children might decide to give their sweet voucher back, and several won't be able to climb as high as they thought. If the owners hand out a lot more than 500 sweet vouchers, they might make a note to set the bar a little higher next year.
When the children eventually climb the wall, the owners find that significantly fewer than 500 children actually reach the bar, so the owners decide that any child with a sweet voucher who reached within 1 metre of the bar can claim their sweet.
Even then, there are still a few sweets left over, so the owners then offer up the remaining sweets to any other child (without a voucher) who also reached within 1 metre of the bar, in a first come, first served system.