What's the fairest system for allocating items amongst a group?

September 13, 2014 7:15 AM

I have a task to do at work in the next few days that I would appreciate some advice on... I have a limited number of items (eg 6 of this one, 3 of that one etc) to share amongst a group of people. They have each given me a list of their preferences (1st, 2nd and 3rd preferences). What's the fairest system I can use to make sure that as many of them as possible are as happy as possible with what they receive?

Looking at their preferences, there's a couple of items that a LOT of them want, so most won't get their 1st preference for that thing. That's what makes it tricky!

I've had a first attempt at sharing the things out but I'm wondering if there's any better ways I could do it.

posted by monster max to Grab Bag (9 answers total)

You could try sorting everyone into piles based on their first choice. If there's a certain pile where there are, for example, 3 items available and 3 people who want it, then you can set the pile aside because it's all set. Then let's say you have a pile with more items than people. Let's call this pile A. You could then go to the pile B where there are more people than items, and pull any people who have Pile A as their second choice. To make it a bit fairer, when distributing people to their second choice, you can shuffle around and pull randomly.

Another alternative is just to do it lottery style. You could either do this as an open lottery where people pull numbers and then make their choice that way, or you could make it a closed lottery, where you randomly assign each person a number, then give them their first, second, or third choice depending on availability.
posted by litera scripta manet at 7:43 AM on September 13, 2014

It seems to me that no matter how you do it you will have a few people who are stoked and a lot more who are bummed, so rather than focus on the pickers I would focus on randomizing the pickee.

Assign each item a random number and then have people choose numbers out of a hat. You get what you get. Afterwards people can trade if they want.

It sounds like you're looking for a system where people won't be disappointed and there won't be resentment so eliminating individual choice might be the way to go.

Can you elaborate on what's at stake?
posted by Room 641-A at 8:19 AM on September 13, 2014 [1 favorite]

I'd do a random pick, like Room 641-A suggests. You could have everyone pick a number (or draw cards from a deck) and take turn choosing until the items are gone. People's disappointment then is with the random draw, not you.

You could do this yourself, since you have a list of people's preferences, by assigning them random numbers and then going around, giving each person their highest-ranked item still available on each rotation.
posted by not that girl at 8:38 AM on September 13, 2014 [2 favorites]

How nerdy is the group?

Fair division procedures.
posted by BrashTech at 9:15 AM on September 13, 2014 [2 favorites]

Well, you could draw up a big grid where X represents the financial axis, and Y represents the emotional axis, and let participants drag items around on the grid . . .

Ok, not serious, though I'd be tempted to give Stephenson this nod if I were in your shoes.

You could give everyone a certain amount of virtual currency and auction things off. Or you could let people use real currency, and then divide the auction proceeds evenly among all players. I think an auction would be fair, but people aren't used to them and many probably wouldn't feel one was fair.

Lottery for first pick will feel fair to most people.
posted by mattu at 9:21 AM on September 13, 2014

It sounds like your items are very unequal in value, because there are a few that everyone wants. If so, there will be dissatisfaction if people just take turns choosing. (If you're dividing one iPad and five jars of pennies among three people, the person who gets the iPad shouldn't have another chance to pick.) You could use your knowledge of people's preferences to assemble "gift baskets" that you think are more reasonably equal in value and a multiple of the number of people. (One iPad, three jars of pennies, and two jars of pennies.) Then let people take turns choosing those, and trade afterwards if desired.

For the purposes of this answer, assume jars of pennies are indivisible. And valuable.
posted by drdanger at 9:22 AM on September 13, 2014

Give everyone an equal amount of points and then hold an auction? Start with auctioning off the most desired item first and then work down.

If multiple people all start by betting the maximum points on the same item(s), choose the winner at random (roll a die or draw lots or whatever). The winner gets the item but has 0 points left to bid on anything else and the losers still have their points left to bid on other things.
posted by Jacqueline at 10:01 AM on September 13, 2014

Google the Method of Markers and they can make the selections themselves.
posted by wittgenstein at 3:54 PM on September 13, 2014

Common here is to pick names out of a hat, first name, first choice amongst the items. Sedona picks from the rest, etc.
posted by Iteki at 8:49 AM on September 14, 2014