Help with algorithm to allocate record albums

This may be a bit of an unusual request. I hope I posted it in the right section. If not, please feel free to move it.

While cleaning out an attic, I found a box of old vinyl records albums. Since I do not have a turntable and I figured hardly anyone else did, I was about to throw them away. Before I did, I posted a message on our neighborhood newsgroup. I was blown away by the response. I got at least 15 responses from people offering to take them and begging me not to throw them in the trash.

So, as a neighborhood service, I volunteered to collect any old albums anyone else may have lying around and then distribute them to those who do. Again, I was not prepared for the response. I now have close to 700 albums containing almost 1,000 records. And there are a couple of neighbors who are still going through their garages and attics looking for old albums. I spent a good portion of the last 2-3 weeks entering them into a database that I set up.

With this many albums and takers, it is not practical or safe to put them all out on the patio and invite people over to look through them. My plan now is to generate a form listing all of the albums and let each taker put a priority number next to the ones they want. They would put a "1" next to their 1st choices, a "2" next to their 2nd choices, and so on.

Now I need al algorithm to analyze the priority numbers from all of the takers and allocate the albums as fairly as possible.

I have what I think is a workable start, but I could use some help getting it right. Here's what I have so far:

Allow each taker to put priority numbers on as many albums as they want. They can choose any number of 1s, 2s, 3s, and so on. They can choose just a few albums or hundreds. One person could make 10 albums priority 1, 5 priority 2, and 50 priority 3. Another could mark 100 albums 1 and no others. Still another could make 5 1s, 5 2s, 5 3s, 5 4s, 5 5s, and so on.

First, allocate all of the albums that have only 1 taker, regardless of the priority number. Since only 1 person wants those albums, let them have them. I have one reservation about this as I will explain below.

For the rest that have more than one taker, come up with a way to assign a dynamic "value" to the collection of albums allocated to each taker so far. Each time they get another album, add to their collection value. I am thinking of assigning a value to each priority number, like "10" for a 1, "9" for a 2, "8" for a 3 and so on. If a taker has acquired 2 albums that they rated #1, 3 rated #2, and 1 rated #3, their collection value would be 2x10 + 3x9 + 1x8 = 20 + 27 + 8 = 55.

Use this value in comparison to the values of the other takers who want that album to calculate a weighted probability that they would get the next album they want. Suppose 4 takers want the same album and they have collection values of 55, 50, 35, & 10. One algorithm would be to calculate the % each is of the total (row 6), invert that (row 7), and normalize that to sum to 1 (row 8). Then allocate that album to A with probability 21%, B with 22%, C with 26% and D with 31%.



These parameters need some tweaking. I think Taker D with a collection value of only 10 ought to get more of an edge over Taker A with a collection value of 55 than 31% vs 21% . So either I need to assign a greater difference in values or adjust these percentages. One way to do that, is to raise them to some power, then re-normalize.

If we raise them to the 1.5 power, we get this:



Now D has an edge of 34% v 19% over A, which seems more fair.
I would apply this in a loop starting with the albums with the highest priority ratings.

My reservation about allocating the albums only 1 person wants is that it would increase their collection value. That may be OK, but it seems not quite fair to penalize them for taking albums that no one else wanted. One solution would be to not count those albums in the collection value. Another would be to count them at a discount.

If anyone has any better ideas, I would love to hear them.

Thanks

 

this question is not for us here, it's more for github
I found this link with code example
https://github.com/iris-edu/dataselect/blob/master/src/dataselect.c

and it says
"Allocate record staging buffer */. if (stagelengthstr)."

 

Why is that? It's a math problem. I am looking for a formula or formulas to fairly allocate the record albums. I was hoping that someone with expertise in probability or statistics might find this problem interesting enough to devote a little time to it.

Are you some kind of moderator who gets to decide what it and is not appropriate here?

Well, GitHub may be a good place to ask this question, but your example has nothing to do with my problem. The "records" I am talking about are not records in a database. They are vinyl records.