What's the fairest way to divvy up multiple options amongst a group?May 6, 2016 2:51 PM   Subscribe

My wife is starting a year of medical school rotations. There are 6 possible schedules for the year, and her group of 6 students must decide amongst themselves who gets which schedule. What's the fairest way to decide? It's completely up to the students, and everyone is friendly and open to discussion.

Each schedule is the same set of departments you're rotating through, just in a different order. Everyone will have slightly different preferences depending on when vacations fall, the desire to go through the department you're most interested in at the optimal time, etc. But there is one choice out of the six that is at the bottom of EVERYONE'S list (because it doesn't line up well with important tests).
posted by mshrike to Education (15 answers total) 1 user marked this as a favorite

Everyone put \$100 each into a "kitty"

Use the Rent Calculator here, with 6 people, 6 rooms, and \$600 to determine which "room" (schedule) is worth the most to whom.

In the end, everyone gets \$100-[calculated rent] out of the kitty.
posted by sparklemotion at 2:58 PM on May 6, 2016 [2 favorites]

Have everyone rank the schedules 1-6 in order of preference, with the option to put multiples at any other rank than #1 ( ie you could rank 3 different options and as your second choice a if they are equivalent). See if that solves anything - you might have less of a conflict than you think. The fact that there is one bad rotation complicates this - is there anything else you can barter (guaranteed first choice for something else that will be a conflict?)
posted by fermezporte at 3:03 PM on May 6, 2016 [2 favorites]

If you try sparklemotion's idea (which is neat--thank you for the link!), just make sure that you use Monopoly money, not real money. We recently had a scandal in which a student (essentially) paid someone \$1,000 for a desirable rotation pathway trade.
posted by 8603 at 3:05 PM on May 6, 2016 [1 favorite]

The Monopoly money has to be backed by something, otherwise there's no "skin" in the game and everyone would just bid the max on everything.

The math doesn't work out with a straight \$100-[rent] though, I'm trying to figure out something that would.
posted by sparklemotion at 3:08 PM on May 6, 2016

I would say a draft. Six rounds of six picks each. Then snake the rounds. For example, if you pick 1st in round 1, you pick last in round 2, first in round 3, last in round 4, 1st in round 5 and last in round 6. This will guarantee that the person with the best choice also gets the worst choice at the end. Then, since there are six of you, I would put the numbers 1 through 6 on separate papers in a hat and draw for draft order. You could also roll two dice and set the draft order based on highest to lowest totals or something like that. I would also allow, once the draft order is established, for trading your picks. There are 36 picks, as long as each person has 6 picks, they can trade order if there is a willing trade partner.
posted by AugustWest at 3:17 PM on May 6, 2016 [1 favorite]

If they're simply 6 people choosing from 6 options, then just go with random chance. Draw a name, let them pick a schedule. Lather, rinse, repeat.

Let people trade after the draw if they personally want to -- someone who draws early might be basically fine with the option chosen by someone who drew late, and the person who drew late might vastly prefer the schedule picked earlier, so they might be willing to make the trade amongst themselves. But that's for them to work out.

Someone is going to get screwed into taking the shift no one wants, but that's going to happen regardless. There's no way to avoid it, no matter how fair you make the process.
posted by jacquilynne at 3:23 PM on May 6, 2016 [5 favorites]

The math doesn't work out with a straight \$100-[rent] though, I'm trying to figure out something that would.
If you're going to use the rent calculator, it needs to be \$200-[rent], and one or more people might end up having to pitch in a little extra to make the person who ends up with the suckiest schedule whole.

But, it looks like Spliddit is a tool that will try to produce envy-free outcomes based on each person's relative preferences. Specifically, the "goods" calculator with 6 people and the 6 schedules as the "goods" should may work. Ethical concerns aside, you might actually add on \$100 as a "divisible" 7th good, to add that extra bit of incentive.
posted by sparklemotion at 3:34 PM on May 6, 2016 [2 favorites]

If everyone doesn't want #6, then ranking isn't going to solve anything. Draw straws, let people horse trade amongst themselves if they want.
posted by feckless fecal fear mongering at 3:42 PM on May 6, 2016 [3 favorites]

I agree with "everyone list their preferences in order and see how it shakes out". And then probably draw straws for the admittedly crap choice.
posted by Sara C. at 4:21 PM on May 6, 2016

\$100 isn't enough - I don't know what everyone's budgets are, but I'd damn sure pay out a cool grand if it meant I had a good schedule FOR THE YEAR.

That's \$85 a month. Less than some people's phone bills.
posted by a halcyon day at 6:59 PM on May 6, 2016

fermezporte's idea about allowing multiples on any rank could solve it immediately. It might not, but still, I'd try one round of that before going to something with more of a punitive short straw.
posted by Miko at 7:56 PM on May 6, 2016

The fairest way? Everyone takes equal turns at every shift for an equal amount of time through the entire period. Rotations at quarters; rotating too much is even more hell on sleeping patterns, but rotating shifts fairly is a must.

It's also beneficial for everyone on the team to have deep experience that may differ between the different shifts.

Free market swapping is a potential blowoff and preference appeasal, but it can be gamed.
posted by porpoise at 3:12 AM on May 7, 2016

\$100 isn't enough - I don't know what everyone's budgets are, but I'd damn sure pay out a cool grand if it meant I had a good schedule FOR THE YEAR.

As would I, which is one of the problems of using an artificial market system like this to "fairly distribute" things. Unless you're all starting out on a level playing field financially, you're going to have your classmates who are already financially advantaged buying the best schedule unless you bring it down to an amount that is "trivial" for everyone... and then the whole system doesn't work so well.

It's a better system for dividing rooms because you're all already agreeing to an approximate rent, and then negotiating who gets what on a recurring cost. I wouldn't use it for this.
posted by deludingmyself at 7:51 AM on May 7, 2016 [1 favorite]

Is there anything else you can bring into the equation? e.g. whoever has the worst rotation is compensated by first pick of workspace, or teacher, or whatever.
posted by danohu at 7:57 AM on May 7, 2016 [1 favorite]

They ended up randomly assigning the slot that nobody wanted, then working through the rest by listing out preferences and talking through it. Thanks for the suggestions everyone!
posted by mshrike at 9:24 PM on May 7, 2016 [2 favorites]

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