The mathematics of compromise

Great Debates
41

The morality of compromise is much more nebulous than the math. How does it emotionally “feel” to live in the ‘wrong’ house or work ‘more’ hours than desired? How do the parties approach differences of opinion, of motivation, and of degree of caring about topic X? This last one is probably the most challenging.

Story time:
I had maintained a clean neat house for decades for myself and my chronically ill now deceased first wife. I also cooked substantially every meal we ever ate at home. I’m no slob and I’m no slouch in the kitchen. Many people have complimented me on my homemaking and my cookery.

I’m recently remarried. My new wife believes my cleaning habits are far too slipshod, in fact they’re unsanitary and unsafe. She’d rather I leave a mess untouched for her to clean than to “camouflage” it by cleaning it up to my inadequate standards. I’m not being “weaponized incompetent” to use @MrDibble’s perceptive and pithy phrase. I’m using the same techniques that have stood me in good stead for 40+ years.

So here we are. I straighten a bit, avoid producing a gratuitous mess as I always have, and accept that she’ll re-clean any/everything, rearrange the dishwasher for more optimal cleaning in ways I find unfathomable, and various other incomprehensible things. She’s happy(er) this way and, by accepting this difference (and its implied insult) uncomplainingly, so am I.

Back to the OP:
How do we model this? How well would what I just described work for the other real-world couples represented in this thread? And how are we to map their various responses onto the hypothetical Angie & Brian?

42

I agree, and it’s that nebulous question that I find more interesting. It’s not bad that other folks approach it as a mathematical problem, but I’m curious if that’s how they actually approach such situations in their own lives.

And I think this kind of situation is pretty common, coming up any time partners differ on a cost/benefit decision, where both partners would gain (different but real) benefits from one decision, and both partners would suffer (different but real) costs from the other.

-Angie would rather spend less money and effort and stay home over vacation; Brian would rather spend more money and travel somewhere.
-Angie thinks it’s worth the cost to buy a big TV to watch things; Brian is fine watching things on the small computer monitor.
-Angie is exhausted at the end of the day and is fine with everyone heating up their own dinner and eating on their own; Brian thinks it’s important for the family to prepare and eat a meal together.

and so on.

43

Bolding the next bit only suggests that you think the math is linearly simplistic and of four choices only.

That math does not at all capture how real world relationships and couples negotiations work.

Real world is that the couple needs to do more than just come up with a negotiated solution. They need to understand what their different wants tell them about the differences in their values and goals. That’s a big discussion. Then they can figure out how much each is willing to give in and what they are each willing to give up of their values and goals for the other’s.

44

I agree that’s the far more interesting question. What’s hard is saying something more strategic or meta- about the problem in general.

We can say that the fewer such differences there are, the easier a time the couple will have. IOW, marry someone with similar likes and dislikes.

We can say that the more the couple is similar in their ability to compromise, to give-and-take, the less conflict there will be. Two doormats will have a more placid life than two my-way-or-highway types. Even given the two couples are similar on the agree/disagree level of my first desiderata. One of each are especially unlikely to be stably happy long term.

I could probably think about it some more and come up with 2 or maybe 3 other Big Issues, or Dimensions, of “couples compromise science”. After that IMO the “science” falls apart and it’s all anecdote.

45

That’s not at all the case, but whatever, this is a boring pedantic side discussion which I’ll happily let go.

46

Math, using different utility curves trying to optimize several different objectives, is not a tool that couples use, calculating solutions; it describes what actually happens.

Angie and Brian may be an incompatible couple. He values their spending quality not exhausted time together, a quality vacation, shared meals, and she values a bigger house with a bigger tv over spending more quality time and experiences with him.

Ideal is that they recognize that these are not isolated negotiated compromises but part of a big picture. They have to understand what each item actually means to the other before they can decide how much of their respective values and goals they are able to give up on for the other, and what they each really need to get from each other.

That will rarely result in a tv half the size of what she wants so they’ve each gone outside their comfort zone. It may be that there are certain nights of the week that are for sure we eat together nights and others not.

47

The reality of practically anything will be more nebulous than the math.

The question is whether a precise language has the potential to describe some slice of the situation accurately. That is the case here.

I didn’t write my own first post in regular hyu-mon language (because that’s literally what the title requests), but every statement was fully in keeping with both the letter and spirit of the thread.

But the OP saw the term “positive externality” and concluded that there would be nothing of relevance in what followed. That’s an understandable mistake when the terminology might as well be written in Martian. It’s the natural result of pragmatic non-familiarity with an esoteric subject.

But this shit is solid, yo.



In this case – if we take what’s written in the OP seriously – then there is a clear possibility for the couple to arrange their household in a way that makes both of them happier.

This “theorem”, aha, actually holds quite generally. Comparative advantage is highly relevant even at the household level… especially if each person trusts the other.



This part is hardly nebulous at all.

If you had the opportunity to put another 10 hours a week in order to afford a place you’d prefer to live in, and were excited about the opportunity to make the transfer – and the other person was not at all opposed – then that is a clear improvement in situation. There is gain and no harm. The positive externality is a twist that makes it easier in a healthy household for the other party to reciprocate, and result in an even more desirable outcome for both members of the household.

That’s as clear as these things ever get.

You can always add complications. Maybe the promotion at work is more stressful than expected. Maybe the new house has annoying quirks in the living that were not apparent in the seeing. Maybe trust in the relationship itself breaks down. Maybe one person gets hit by a bus. There aren’t any certainties in life.

Nevertheless.

It remains generally solid that the person who wants something more should be the one who puts in most of the effort to get it. Or in the case of costs, it makes sense for the person for the lower cost to do the task. When our boy was born, who was the one who woke up every night (for more than a year!) to feed him? It was, quite naturally, the one who found it much easier to fall back asleep after the disruption.

Burdens like these are balanced in other ways. Each partner pulls the weight they can carry more easily, for the general benefit of both.



In most cases, I wouldn’t expect to see exactly equal hours on any single task from a happy and trusting couple.

Quite the opposite.

Hours worked is more observable than personal preference. If two people are carefully balancing observable effort to precisely match, then that’s often (not always, but often) because there are deeper questions of underlying motivation, and the balance in observable effort is how suspicion is allayed. That’s the sort of behavior you’d expect from college roommates, not life partners.

(There is mathematics for this, too.)

Efforts will tend to be asymmetrical in high-trust environments because talents and preferences are asymmetrical. In a relationship that is working, this will be because the other person is picking up slack along different dimensions… and both people feel that the burden carried in one place is fairly matched with the burden somewhere else.

But that’s not even what the OP (as plausibly interpreted) is about. The OP is straight win-win with asymmetrical efforts,

48

I disagree here with that otherwise excellent post, depending on what the other issues are.

Angie working extreme hours, six ten hour days a week, is not only a cost borne by her. It taxes their time together. She is exhausted and stressed most of the time, not wanting to have the dinner together he wants but to snarf something down and go to sleep, maybe falling asleep watching a show on that big tv. She is not available to equally participate in the other work of the relationship, available to connect with him in many meaningful ways.

Calculations have to include unintended consequences that are reasonably predictable.

49

I’m no economist. But I can (or could have 40 years ago while still in college :slight_smile: ) certainly describe the OP’s whole scenario in linear programming terms. This is a straightforward optimization problem, given suitable weightings that are at least in principle discoverable, etc. We don’t even need to assume a bunch of spherical cows as long as the preference space isn’t too pathological (or subject to continuous revision, a problem seen with certain emotional disorders).

And as you quite perceptively say, in more trusting couples we’d expect to see a more asymmetric division on any one topic. I’ll add that “more insightful” helps too. Members of couples who don’t understand themselves very well have a much harder time being a good partner, which makes the couple a messier proposition.

I’m all for a mathy solution. So’s my math prof / retired engineer & clean-obsessed wife.

But as @DSeid says just above, this house size/work hours problem is not solved in isolation. It’s part of solving lots of other problems and is an iterated game to boot. It’s not necessarily “prisoner’s dilemma”, but it may well contain elements that have trouble settling to a Nash equilibrium that’s actually acceptable to both. For our model to deliver a “good” solution to this problem pretty well require that it incorporate a lot of other problems, tradeoffs, and solutions. Which implies a lot of other preference functions. Tall order practically.

The OP seemed to want to talk of other things. So I tried to accommodate him. Not out of humoring him in his silly wants, but because that way too may be a) interesting to yak about, and b) enlightening to some of us.

I at least enjoyed your clear explanation of viewing this as a positive externality case. And your little relationship joke. :slight_smile:

50

FWIW my WAG is that normal couple preference space is subject to continuous revision. Neither individual nor the relationship itself is static, changing as a result of every individual solution made. It isn’t just an iterative “game”, it’s one in which the preference spaces constantly change as a result of each turn, one in which part of the utility is seeing your partner happy, and which, in less well functioning relationships resentment over senses of unfairness or not being cared about enough or valued sufficiently or appreciated enough are often unarticulated.

We don’t just each bring baggage, we create new baggage of our own every day together.

51

True. And ordinary enough that each of us has probably experienced that.

I was more referring to dealing with the nutsos whose mood disorders, BPD, whatever, essentially drive them to change their demands for the purpose of keeping their hapless partner off balance.

52

Bumping to return to this, reflecting on the comments made by @Hellestal on how real world couples (and others in high trust relationships) most commonly end up with multiple very asymmetrical solutions to these sorts of problems.

@Left_Hand_of_Dorkness, your stated preferred solution was that “they share both the sacrifice and the benefit equally” …. Is that how you actually approach such situations in your own life?

53

I won’t die on the hill of the word “equally”, because in the real world that’s not something that can be or should be measured, but a word like “significantly” or “fairly” would work for me. For the rest of it, absolutely.

54

Well “fairly” is an “obviously correct, and boring and cowardly” position. “Significantly” not much better! :grinning:

The devil is in what is fair and what is significant.

For me @Hellestal’s insight is very significant. Long term relationships usually don’t bother with equal, or fair, or even significant. We each do what we are capable of, putting most to what comes relatively easier to us compared to them, sacrificing what we feel capable of sacrificing for the perceived needs and wants of the other. Over time probably it ends up as near equal, fair by definition in a functional partnership, and always significant, but individual choices are not considered in that way for most of us at all. It’s a long term deal. When I can and you need I do and visa versa. We don’t aim for balanced or keep tabs on effort. Even iterative game theory need not apply.

I am sure there is math that describes that!

55

Yes. Remarkably like “From each according to their ability. To each according to their need.”

Experience shows us this works a lot better in a committed couple than it does in a society of strangers, but the point is the same. This maximizes collective benefit and minimizes collective cost. In whatever concrete or nebulous units one uses to measure “benefit” and “cost”.

56

A good application for Fuzzy Logic.

FL boils down to a center of gravity calculation. Set up a balance like a see saw. A long board with a fulcrum in the middle. You are dealing with dissimilar, emotional issues so each issue is given a shape representing it’s presence, a size representing it’s mass, and a position on the board representing it’s importance. Something common to all issues is a rectangle the length half of the board. Something small but very important is perhaps a circle near the far end of the board. By adjusting size, shape and position of disparate issues on both sides of the board a balance (compromise) can be reached.

Actually cutting out membership functions in the size and shape that expresses your emotion may be half the battle. Membership functions could take the form of animals like mouse elephant etc. Of course the same issue may be the same shape but a different size and position on each side of the board.

Fuzzy Logic yields a vague result from imprecise data.

57

Oh yeah you can do the same thing in Excel with numbers. Each of you has a matrix. The columns are issues and there are 3 rows A,B,C. Row A is the size of the issue 0-10. Row B is the importance of the issue 1-10. Row C is A * B. (Sum of row C} / (Sum of row A) = D.

When your D values are equal you have equilibrium. Not as much fun as cut outs.

58

Interestingly, as annoyed as I got a couple of months ago with the mathematical approaches folks offered, this approach makes a lot of sense to me. I’m not sure if I just wasn’t understanding the math that others were offering (full disclosure: I have a high schooler’s background in math and no more), or if I just disagree with their particulars, or if I’m just in a better mood today.

In any case, thanks for this explanation; it seems really reasonable to me!

59

In a memorable math lesson in High School the chapter that covered this topic used a historical scientist’s attempt (1890’s-1910’s?) at finding the cheapest and yet most nutritional meal one could eat daily. So like, 3 carrots, 1 lb of cabbage and 3 potatoes or something will not only give you all of the necessary nutrients, but that is the cheapest bulk material you’d need to purchase to fulfil those requirements.

I have looked for the study over the years and have found many similar, but never the guy I remember reading about in High School.

60

Was it the Stigler diet problem?