Mechanism Design for the Holidays

In today’s Ask Amy column, a reader asks Amy how she should deal with her two feuding sisters on Thanksgiving, given that neither wants to be in the other’s presence:

DEAR AMY: A family dispute has erupted, and I'm not sure how to fix it for the holidays. My little sister and my older sister had a blowout in June and have not spoken since. My mother was dragged into this, which caused the older sister to scream at my mother.

The little sister, whose boyfriend is an ex-con with two children, lost her job and moved back home for a while. She treated the house, and my mother, disrespectfully during that time.

My mother has decided that she is not having Thanksgiving for anyone, and I don't think she should. Therefore, I opted to invite everyone to my house.

However, the little sister won't come if the older one is here and vice versa. My father is angry with both of them over how they treated my mother, and he won't come if either of my sisters comes. I don't think either sister is aware of how angry our parents are.

My question is this: How do I phrase the invite to my sisters? Do I tell them to make peace or not come? This will alienate the older sister even more, and we miss her kids.

Should I inform them of how upset my parents are?

Is it even my place to fix this family issue?

Please help me figure this out. - Middle Sister

Amy is understandably pessimistic about MS’s odds of resolving the issue, but nevertheless, she urges MS to invite everyone and encourage them to bury the hatchet.

I would urge greater attention to the game theoretic aspects of the problem. The question is how to get as many civil family members as possible to attend Thanksgiving dinner. Setting aside the angry father for the moment, the two sisters present a variant of the classic coordination game. If both attend, they will likely fight or snub each other, creating an awkward situation for everyone. If neither attends, Middle Sister is deprived the company of either sister. So the trick is to get one to attend and the other to stay away. Middle Sister might consider sending both her sisters an email as follows:

You two are mad at each other, and I don’t want family members fighting at my Thanksgiving dinner. In order not to play favorites, I will be flipping a coin (in the presence of another neutral party) to decide which of you will be invited.

Dad, who is angry with both feuding daughters for being mean to Mom, complicates matters. A more complex mechanism is called for; here’s what I recommend:

You two are mad at each other, and Mom & Dad are mad at you. I don’t want family members fighting with each other at my Thanksgiving dinner. So here’s how it’s going to work:

(a) If neither of you apologizes to Mom and Dad, then neither of you is invited to Thanksgiving dinner. This is true whether you reconcile with each other or not.

(b) If only one of you apologizes to Mom and Dad, only the apologizer is invited. This is also true whether you reconcile with each other not.

(c) If you fail to reconcile with each other, but both of you apologize to Mom and Dad, then I will be flipping a coin (in front of another neutral party) to decide which of you gets invited.

(d) If you reconcile with each other, and both of you apologize to Mom and Dad, then both of you are invited to Thanksgiving dinner.

In case (a), only M&D will come. In cases (b) and (c), M&D plus one sister will attend. In case (d), the best-case scenario, everyone makes up and attends. In every case, you’ve maximized the number of civil attendees subject to their willingness to make amends. In addition, this mechanism gives each sister an incentive to apologize to M&D, since doing so increases her likelihood of attending Thanksgiving (without having to deal with anyone with whom she hasn’t yet reconciled). And it also gives the sisters an incentive to reconcile with each other, since otherwise they each stand a chance of being excluded.

One problem with the mechanism is that it doesn’t account for the utility of seeing the nieces and nephews. More generally, it implicitly assigns a fixed and equal weight to Mom, Dad, Big Sis, and Little Sis, while assigning no weight to anyone else. The mechanism could be tweaked to account for these problems – for instance, by weighting the coin flip toward the sister with the nicer kids, or by uninviting M&D in the case where the sisters reconcile with each other but neither apologizes to M&D. But these alterations could compromise Middle Sister’s appearance of neutrality, so I recommend going with the unaltered mechanism.