Math and parenting

May 6, 2013 9:10 PM

Division of labor in child care: A game-theoretic approach The analysis shows that it is difficult to achieve the equilibrium of equal sharing of child care, even when this is the preference of the parents. This leads to a discussion of alterations and meta-strategies for couples who want to share care equally. Gender differences between parents are also modeled, including the impact these have on outcomes and equilibria.Full text PDF
posted by bq (14 comments total)

I don't know basically anything about game theory, but this seemed to be an important paragraph to me. This is talking about when both "players" are in a "stuck" situation. A "cats game" of sorts:

For the father to create change, he has to raise his total number of hours, reducing his own payoff until there is a surplus of care. These barriers seem qualitatively different. To cross her barrier, the mother is required to do something that directly risks her status as a good mother [...]. The father, however, crosses his barrier by doing something that causes him personal inconvenience rather than public shame, and his status as a good father is at risk only if the additional care impacts his ability to be a good provider.

posted by fontophilic at 5:52 AM on May 7, 2013

I really wanted to read this paper. I find that I don't know nearly enough math to follow it. Can someone who understands it better explain it in English rather than algebra?
posted by bardophile at 7:14 AM on May 7, 2013

Somehow this person managed to create a parenting "game" in which sleep is not a substantial and separate goal. I wonder if the author has ever met a parent or child.
posted by carmen at 7:42 AM on May 7, 2013 [2 favorites]

That was fascinating. Thanks!
posted by jaguar at 7:50 AM on May 7, 2013

For bardophile:

Gist of the math part is that the experimenters have set up a situation as follows:

Two working parents, Mother and Father have a child that requires 3 hours of care every day.

The parents agree that providing less than 3 hours of care is no good.
The parents both believe that at least 1 hour of care is required to create a bond with their child.
The parents both want some time to themselves.
The parents both want an even division of labour, but not as much as they want the above 3 things.
The parents allocate their time in half-hour blocks.

So just looking at those rules the parents can spend 0.5, 1, 1.5, 2, 2.5, or 3 hours on child care each, but their total has to equal 3 hours to make sure the child is fully cared for (and doesn't burn the house down or something).

Since they both want to spend at least an hour with the kid, the best time allocations are Father: 1 hour, Mother 2 hours; Father 2 hours, Mother 1 hour; or Father 1.5 hours Mother 1.5 hours.

The experimenters add, that since the parents both also value personal time, the Optimal situation is 1.5/1.5, however the 1/2, 2/1 split also works.

They finally argue that the best situation for Father is him doing 1 hour and Mother doing 2 hours, because it satisfies his bonding needs and maximizes his free time. And the best situation for Mother is the reverse.

They then go on to say that because mothers tend to be allocated more time off work when a baby is born, and because of breastfeeding being something a mother does, many couples start out with the F1/M2 split, even if they say then want the 1.5/1.5 split.

And since the 1/2 split works they stick with it even though it isn't optimal. The experimenters point out that within the confines of the game only parents who manage to start with the 1.5/1.5 split will end up there. Any other division of labour leads to a 1/2 or 2/1 split.

I don't agree with fontophilic's interpretation of the quoted paragraph. They aren't really stuck. It is that the Father in the 1/2 split actually has a better situation for himself than if he upped his childcare contribution. So he doesn't do it because it is worse for him.
The Mother in this case doesn't simply lower her contribution because it would result in a lack of childcare, which essentially is so bad that it can't be allowed.
Mind you, the experimenters also included a rule that the parents can't change their hours at the same time, so there has to be a surplus or deficit for at least one round to change from the 1/2 splits.
posted by keeo at 7:59 AM on May 7, 2013 [12 favorites]

keeo: You are my hero! Thank you so much for that clear summary!
posted by bardophile at 9:07 AM on May 7, 2013

Mind you, the experimenters also included a rule that the parents can't change their hours at the same time, so there has to be a surplus or deficit for at least one round to change from the 1/2 splits.

But that's an artificial rule that doesn't reflect the reality of most parents, isn't it? Why would you set up that kind of rule if you want to explain real human behaviour?
posted by bardophile at 9:09 AM on May 7, 2013

Keeo: Great summary, thank you.
Bardophile: I may be misunderstanding, but I think the rule isn't actually that far off from real human behavior, since in reality I think it's far more common for circumstances to affect the amount of time a parent spends with a child (sickness, busy time at work, travel, etc.) and for the parents to then shift allocations to compensate, than for both parents to decide in advance to change things.
posted by chickenmagazine at 9:14 AM on May 7, 2013

Exactly, so unless a surplus or deficit is created (which neither has an incentive to do) they stay at their current levels of contribution. Stuck.

The author goes on to describe a situation where in a mother overestimates the amount of hours of childcare needed (4) and the father underestimates (2). The father may feel he is doing 50% of the work at 1 hours, and the mother feels she is doing 75% of the work at 3 hours. There are very few ways to reach equilibrium from that state.
posted by fontophilic at 10:04 AM on May 7, 2013 [1 favorite]

bardophile, the whole thing is artificial. It doesn't take into account the effects of any of the larger social structures in which the family are enmeshed (such as income earning, availability of third-party child care, flexibility of work hours). It makes a number of assumptions that simplify the model to make it more mathematically workable, but that disconnect it from the situations that it attempts to model. For instance, it also doesn't account for the utility of having a "manager," someone who schedules doctors appointments and makes final decisions about all of the myriad things that must be done for child care. These are part of the sociological/anthropological/feminist explanations of the continuing gap. The game theory aspect is certainly interesting, but it can only at best be a starting point if one is interested in close analysis of real life.
posted by carmen at 10:44 AM on May 7, 2013

It seems to me that there's an assumption that the couple isn't really talking about the issue. This strikes me as bizarre. I understand that it's simplified in order to facilitate mathematical modeling, but I don't understand why you would simplify things to the point that they don't fit reality.

If a couple has egalitarian goals, surely they are likely to discuss the degree to which they are succeeding in meeting those egalitarian goals?

I guess I just don't find this a convincing explanation of the behaviour that they are trying to explain.
posted by bardophile at 12:24 PM on May 7, 2013

Actually, I don't find the assumption that the couple isn't discussing the hours each is putting in as unrealistic--or maybe more accurately, I think the assumption that discussions won't or don't necessarily lead to shifting workloads is not unreasonably strong.

My partner and I both have egalitarian values with respect to housework; he agrees that it is right and fair that he should be doing half of it. Nonetheless, I'd estimate that I do about 80% and he does 20%. He has good intentions but when there's too many things he wants or feels he needs to do--work full-time, go on his morning run, talk to his parents once a week, etc etc--it's invariably the cleaning and cooking that doesn't make the cut. We can, and have, talked about it endlessly but short of me micromanaging his schedule and making chore lists for him--which is totally unpleasant in its own right--my choices become "don't do his share of the cleaning / cooking and live in a way that makes me crazy (dirty house) and poor (takeout every night)" or "just do it myself." Note that this stylized choice is also the one facing the hypothetical mother in this model--do less than the bare minimum needed and hope the father steps up, or do more than her fair share.

My sense is that this sort of conflict is really common, maybe even more common than conflicts about money, particularly among couples in my age group (early to mid 30s). I don't know too many guys who will publicly say that they think their wife should do the majority of cooking and cleaning despite both people working full-time, and yet in the vast majority of my friends' relationships, there's a noticeable pattern where the woman is taking on more than her fair share of the homemaking and general life-running and the guy has more time available to pursue hobbies or socializing. It's a frustrating dynamic that doesn't appear to be particularly helped by talking (or fighting) about it; I think it's totally realistic that someone can believe in an egalitarian split of household labor yet let their other desires (for hobbies, for time with friends, for relaxing in front of the TV rather than cleaning the toilet at 9pm) overrule their intellectual commitment to equality. Same way as I can believe in fair pay and not exploiting third-world labor and yet still continue shopping at Banana Republic and GAP because my desire for affordable, work-appropriate clothes that can be relatively easily obtained outstrips my intellectual commitment to whatever else.

Anyway. I found this an extremely interesting article, particularly the conclusions about the effect of the "starting point" and the implications that has about how important it is for Dad to take paternity leave after mom goes back to work if you want to end up at a more equal spot in the long-term.
posted by iminurmefi at 12:54 PM on May 7, 2013 [11 favorites]

I thought the article was interesting, but ultimately odd because it is strange to me to apply formulas to things that will never really have numbers. I found the general premise to be sound, and I agree with iminurmefi. I wish the article went into more detail on the "Dad thinks baby needs 2 hours of care, Mom thinks 4" concept - I think this is twofold: women are held to a much higher standard for childcare; and also, women often "invisibly" perform chores before they hit a level that would attract the male partner's notice. I think the invisible factor plays into the part where change in their model doesn't happen simultaneously. For example, if Mom stops doing her 1/2 hour of laundry every day, it might take a week before laundry reaches a crisis level and Dad has to spend 5 hours straight doing all of it (or more likely, Mom and Dad now do 2 1/2 hours each).
posted by fermezporte at 1:35 PM on May 7, 2013

iminurmefi, that makes sense to me, thank you.
posted by bardophile at 2:09 PM on May 7, 2013 [1 favorite]