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Modal wives and why it is hard to marry well
I define a modal wife (or husband) as a person you would have married (could have married?) had you met them at the right time, unattached, and under normal life conditions. The number of modal wives is typically greater than or equal to the number of real wives, although clever philosophers will recognize possible [sic] counterexamples.
Under one view, you have hundreds or thousands of modal wives, most of whom you never meet. (How many does the average person meet, how soon do you know when you meet one, and how confused would you be if they were all in the same room at once?) Your correct dating strategy is to cast your net very widely, and hope to find and marry one of these people.
Under another view, modal wives are no big deal. Your so-called "modal wives" are no better for you than, say, the best woman you could pick out of a lot of thirty eligibles. The key inputs for a good marriage are attitude and a minimum degree of compatibility, not search and discovery.
If this is true, searching for modal wives, or perhaps even thinking about the concept, can make you worse off. The quest for the perfect mate makes it harder to come to terms with what is otherwise a compatible marriage. Which perhaps is all you are going to get anyway. Marriage is good for you, and don't be too fussy, this is not iTunes. Too much choice, or too much perceived choice, is problematic.
The two views offer directly conflicting advice (TC: My views are closer to the first position, although attitude remains all-important). Yet we may be uncertain which view applies to us and to what extent. You could put all your eggs in one basket and pursue just one strategy, but what a risk if you are wrong. You could act upon some weighted average of the two views; I suspect this is what most people do. But then the two strategies are constantly undercutting each other.
That is one reason why it is hard to marry well.
Addendum: Here is a good post on Deception Island, and do also read the excellent comments thread on this post.
Posted by Tyler Cowen on January 8, 2006 at 06:14 AM in Philosophy | Permalink
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Comments
Speaking as one who has tried both strategies, I strongly suspect that the viability of the second strategy is strongly dependent on whether the person in question adopting the strategy has traits (religious beliefs, intelligence, cultural tastes, dietary preferences, social and political views, sexual attitudes and tastes, physical appearance) close to the societal mean. (And, on another dimension, an extrovert will also have more modal wives than a misanthropist.) A 5'4" Orthodox Jew libertarian or a socialist vegan leather fetishist is going to have fewer modal wives than a moderate Christian with a 110 IQ—and, moreover, the marginal utility of a modal wives for the first two is going to be substantially higher than for the more average gentleman, since the wife selected from a pool of thirty is more likely to be close to his modal wife.
One can adopt a combination of the first and second strategies by using a pool more likely to produce a modal wife: an Orthodox Jew could restrict himself to meeting other Orthodox Jews; a genius economist stays away from the sports bars and instead trolls bookstores and academic events. But the more dimensions along which one's traits are unusual or restrictive, the harder it becomes to adopt even variants of the second strategy without coming across fatal incompatibilities. Woe is the Orthodox Jew who is only attracted to lithe blondes; a politically-active Republican vegan is likely to have trouble as well.
Separately, given the requirement of consent in modern-day marriage, there's a significant difference between "would have married" and "could have married," though "would have married" has its own ambiguities.
Posted by: Ted at Jan 8, 2006 9:05:25 AM
I think this model makes one huge assumption in that it takes the view that the modal wife or husband is strictly determined by a matching process, like a pair of nodes joined to a finite number of other nodes (interests, preferences etc) and that the modal wife is one for whom which you share strictly the same number or greater of nodes (leather fetish, vegan, pro life, whatever).
However, there are certain things that are almost certainly not related to matching and for which there is room for quantitative analysis like money. Or IQ. Is someone with more money strictly better, ceteris paribus vis matching? The same for IQ? Intelligence does not equate to having intellectual interests, so you could have a sports obsessed banker with an IQ of 135 and a prof of game theory at the same level, and one with strictly dominate the other for a dallas mavericks cheerleader even if they look exactly the same.
As fas as selection goes I think the problem that many smart good looking women who have relatively vanilla interests end up focussing very heavily on the cash/intellect side of things and spread a far net. The problem is that their quarry (smart successful good looking men) have less time decay in their value on the marriage market. Hence they get screwed around and you end up with sex and the city. For this group, the marginal strategic analysis ends up with a bad dynamic result.
Posted by: Alex at Jan 8, 2006 9:47:41 AM
I think Tyler's model is dynamic enough to take into account income and intellect; it merely assumes that there exists a set of women who meet the criteria
f(w-sub-1, w-sub-2, ..., w-sub-n) > W
and that the search costs for finding a member of that set may be high enough that it is better to satisfice at a level X beneath W, because (NPV(W)-NPV(X)) < (NPV of cost of finding W - NPV cost of finding X). Nothing stops income or intelligence from being in that function.
Alex does raise a different issue, which is whether the search cost is positive at all for some people. Smart successful good-looking libertine men have little incentive to satisfice below a relatively high W to the extent they derive utility from new sexual conquests. A religious person who objects to premarital sex, on the other hand, would derive additional utility from marriage the average Sex-in-the-City denizen doesn't, and we would thus expect to see what we actually observe, which is shorter search times and younger marriages amongst this population. Of course, this is also consistent with my theory that such a person is likely to have a larger set of modal wives to work with, and that satisficing involves smaller costs than for the idiosyncratic; I suspect all three factors come into play.
Posted by: Ted at Jan 8, 2006 10:14:55 AM
I am married to one of my modal wives. She is very happy about my application of revealed preference; I married her when other (she claims, modal) wives were available. Perhaps we should call such winners of close contests "supermodals."
The existence of supermodals implies that, although we might think of the class of modal spouses as clearly better to the class of non-modal spouses, they are not actually equivalent to one another; it is still possible to make ordinal rankings that show strict preferences within the modal set.
Some of my friends insist that knowing that you've deliberately satisficed, by incorporating search costs into your decision and pulling the trigger on a non-modal, can gnaw on a man's soul, and seriously inhibit the achievement of the level of happiness expected from terminating the search. These friends are both unmarried and unhappy.
I continue to believe that the cardinality of the modal-wife set is much greater than 1, and that modal encounters persist (all too rarely) for the duration of one's life. There is an indescribable feeling of euphoria which comes when finding another member of the modal set, even after 15 years of marriage.
Posted by: ModalHubby at Jan 8, 2006 10:49:11 AM
This brings up the so-called Sultan's dowry problem... Assuming you do meet a likely prospective spouse under the right conditions, do you marry him/her immediately, or wait and keep searching, and if so how long? The longer you delay, the greater the chance you will meet someone else whom you like even more, but at the risk of losing your current prospect.
I believe the mathematical answer is to estimate how many prospective spouses you will meet in your life, and then choose the first one better than the first 37% of them. I wonder if anyone has actually done this!
Also, if you assume there is a strong ranking between modal spouses (and not just a binary yes-or-no evaluation) then it seems essential to meet as many of them as possible. I bet the increasing use of on-line dating sites and ease of travel in modern society are leading to more well-matched marriages.
Personally I estimate there are around 50,000 modal wives out there for me.
Posted by: CaptainEO at Jan 8, 2006 12:18:51 PM
You are all ignoring the problem of self-awareness or the fact that information about what your modal spousal characteristics are changes over time. This gives some advantage to waiting. But, assuming the desirability of children, men gain more by waiting -- maturity, income, experience --, while women past 30 lose enormously by waiting. This complicates the problem as many women are most marriageable early, while men are often more marriageable late. Both also do not have equivalent costs in adjusting to failed first efforts.
Posted by: nn at Jan 8, 2006 12:31:24 PM
Wait -- Why do women past 30 lose enormously by waiting?
This from a 27-year-old who doesn't consider her happy single life as "waiting" --
Posted by: green LA girl at Jan 8, 2006 1:27:38 PM
Isn't the difference between the two views one of degree? It seems to me that the second view is the same as the first one, except that it assumes that modal wives are more common.
Posted by: Brandon Berg at Jan 8, 2006 1:38:27 PM
Actually, I personally don't thnk that is anything such as a modal wife !!
The cardinality of the modal-wife is mathmatically equal to only 1. That is , all
aspects compatablity at every attribute being met to be that persons choice is limited to only one.
But Ted also proposed a good value proposition. Still need to wrap my head around his alogrithims that he outlined.
Posted by: /pd at Jan 8, 2006 1:44:04 PM
PD proposes a hypothetical spouse who has traits that stochastically dominate all other candidates. Perhaps it's possible that the wealthiest woman in the world is also the most beautiful and intellectually and emotionally (and geographically!) compatible (and add: the best lover, cook, baker, co-parent, financial planner, editor, critic, housekeeper...) for some lucky man, but for the overwhelming majority of us, the best we can hope for is someone who is Pareto-optimal in her qualities, is northeast of a particular n-dimensional utility curve, and feels the same way about us.
That's not to say that there isn't a woman out there who would have cardinality value of 1 for any given man, or that woman wouldn't be several standard deviations better than other women in the modal set.
Brandon, I think, makes a good point, that the different views are one of degree, ranging from the "soulmate" viewpoint (the modal set = 1, and there is a huge drop-off in utility between #1 and #2), the slightly more cynical Cowen-modal viewpoint (the modal set = some small number n), and the satisficer who rejects the concept of a modal set on the grounds that the benefits of marriage outweigh the benefits of an idealized marriage. The satisficer who comes to the conclusion sincerely that he has a large modal set is simultaneously adopting both of Tyler's stated strategies, and may well be happier in his marriage than one who adopts either strategy #1 or #2 self-consciously, simply for having lower expectations. But it's a fundamentally risk-averse/low-return strategy--though one that may well have an evolutionary advantage to the incomplete extent that marriage is a prerequisite for for childbearing.
I don't think this is quite akin to the "Sultan's dowry" problem, unless one assumes the modal set is 1, as it is in the classic version of that problem.
NN adds the factor of desirability into the equation, and the model is flawed to the extent we fail to consider the reciprocal search problem and the possibility of unrequited love.
While M-sub-Ted is the set of women who Ted's modal wives, N-sub-Ted is the set of women who view Ted as a modal husband. And one also has to consider the issue of SW, the fluctuating set of single (searching?) women. While it's emotionally healthier for Ted if membership in N-sub-Ted is a prerequisite for membership in M-sub-Ted, regardless, the set F of feasible modal matches at any given time is the intersection of M, N, and SW.
As one ages, the set F grows and shrinks, as one's personal traits (inter alia, experience, wealth, and physical attractiveness) change. This can be expressed in terms of search cost. One can theorize that, to the extent social factors of desireability weigh attractiveness higher for women than for men and wealth higher for men than for women, men's desireability would depreciate more slowly over time, reducing their search costs. An 18-year-old male probably has negative search cost, both from the utility of searching and because the expected value of potential mates will be higher years down the road as his desireability increases. A 36-year-old woman who wishes a marriage to bear children, however, has a much higher search cost. (Confounding factor: the increasingly reduced cost of single motherhood (cf. Lori Gottlieb's "The XY Files" in the September 2005 Atlantic Monthly) creates another option for women, thus reducing their search costs, and thus reducing the benefits of a strategy of satisficing.) While John Derbyshire's infamous claim that women's peak attractiveness is shy of 20 is certainly an exaggeration for most men, a 37-year-old single male does not face the same fear of depreciation that a 37-year-old female does.
We can make the model even more sophisticated by adding nn's observation that one's f-function changes over time, though the second derivative is almost certainly negative: what one wants as a 18-year-old is likely much different than what one wants as a 28-year-old, but the latter probably doesn't differ that much from what one wants as a 38-year-old. Of course, one's partner's traits change over time, as well, and one hopes that one chooses wisely such that one has not put undue weight on the impermanent traits of one's partner.
Posted by: Ted at Jan 8, 2006 3:23:48 PM
For these purposes I believe in intelligent design, or psychological engineering. I don't expect that it's any easier to find a modal wife than to find a perfect unoccupied home. If you want something done right, you have to do it yourself. I know that everyone else says that Pygmallion is a bad idea, but they just don't know what they are talking about. OTOH, most people probably should build their own home either. If you aren't able to figure out how to make something work well, you probably should leave it to experts or to chance.
Posted by: michael e vassar at Jan 8, 2006 3:37:33 PM
"There is an indescribable feeling of euphoria which comes when finding another member of the modal set"
I really, really know what you're talking about. :)
"Wait -- Why do women past 30 lose enormously by waiting?"
Well, if you want to have children, you lose fertile years in which you could have them. Even if you don't want to have children, you still become less attractive to most men (and thus have fewer options) as you age, since men are of course generally more attracted to women at the peak of their fertility than older, less fertile women.
Posted by: Jacqueline at Jan 8, 2006 3:48:27 PM
Too much thinking, try this:
ARTIST: Lovin' Spoonful
TITLE: Did You Ever Have to Make Up Your Mind
Did you ever have to make up your mind
Pick up on one and leave the other behind
It's not often easy and not often kind
Did you ever have to make up your mind
Did you ever have to finally decide
Say yes to one and let the other one ride
There's so many changes and tears you must hide
Did you ever have to finally decide
Sometimes there's one with big blue eyes, cute as a bunny
With hair down to here, and plenty of money
And just when you think she's that one in the world
You heart gets stolen by some mousey little girl
And then you know you'd better make up your mind...
Sometimes you really dig a girl the moment you kiss her
And then you get distracted by her older sister
When in walks her father and takes you a line
And says, "You better go home, son, and make up your mind"
And then you bet you'd better finally decide...
Posted by: Robert Schwartz at Jan 8, 2006 4:45:58 PM
This discussion has so far ignored the big danger of the "modal spouse" theory -- self-deception. Self-deception both in evaluating potential spouses and in evaluating your own prospects has a long and destructive history which may still be better understood by poets than by quantitative scholars. Some examples:
1. Grass-is-greener syndrome -- some men always wants the woman one can't have, so that once the woman agrees to marry, her desirability drops. A guaranteed recipe for unhappiness.
2. He-won't-do-it-to-me syndrome -- affects many women who have affairs with married men under the belief that either he will leave his wife for the mistress, or, if they marry, that he won't cheat or leave again.
3. Swimsuit Issue syndrome -- I'd never have to work again if I had a dollar for every overweight, immature 30-ish or 40-ish male sports fan I've met who seriously expects to marry a thin, superhot blonde woman, and then wonders why he has trouble finding marriage-worthy dates.
Even if the modal theory were true for the perfectly rational economics blog reader, I would argue that for the majority of the people in the world, the modal theory is a damaging idea that encourages problems 1,2, and 3 above, as well as other self-deceptions. The world as a whole would be better off if more people accepted Tyler's second option -- picking the best of 30 eligibles.
I find the suggestion above that the second theory is fine for 110-IQ Christians and not for 130-IQ intellectuals to be especially pernicious. Sorry, you 130-IQ people, you are just not that special. If you have a 130 IQ, unless you intentionally choose a boring career among non-college-graduates in a small town, your IQ will not be remarkable or impressive in your social circle. Thinking otherwise is --guess what-- self-deception.
I blame Plato for all of this. Plato, of course, was the first big promoter of the Modal theory, although he defined it as one ideal soul mate per person. Worst of all, he made it very clear that no one on earth could find absolute, pure ideal Truth, just its shadows, but he didn't make it clear that finding a perfect soul mate is even harder than finding perfect Truth.
A corollary to my argument above, BTW, is that no matter which theory you believe in, if you want to find a good spouse, you are better off spending your time and money on self improvement (lose the gut! read real books! cultivate your garden!) than on mate-searching.
Posted by: Voltaire at Jan 8, 2006 8:28:33 PM
The assumption underlying this entire discussion is that economists can use such terms as search costs, satisficing and modal set in a discussion and still get a decent sample of phone numbers from said prospective mates.
So this disussion is more on the macro side of sexonomics. On the micro side, you still have to use game/IO theory to get phone numbers.
When people meet for the first time, they go through a routine: what do you do, where are you from, are you here with friends, how old are you, etc. The key would be product differentiation. As a potential mate, you would have to first assess your own value on the market and work with that. Then you have to demonstrate that value (use salesmanship)in a social situation and then differentiate yourself from the other dozen guys a girl has talked to that night. Differentiation would probably be key when it comes to getting phone numbers from which to expand your pool of modal spouses.
Does anyone remember the scene in a Beautiful Mind where John Nash and his buddies score with the ladies and he supposedly comes up with the idea for Nash Equilibria?
Posted by: Aaron at Jan 8, 2006 8:33:12 PM
Also, I think there is a trick in Tyler's phrasing. Selecting the best from a pool of 30 "eligibles" depends on how you define eligibles -- are all single women eligible, or do you start with a pool of 30 vegan, Republican, Orthodox Jews, if that is what you require of a potential mate? Depending on how you define eligibles, the difference between eligible and modal may disappear.
IMHO, it is easier, not harder, for people with unusual preferences to find mates, at least in the Internet age. Competition is much fiercer for emotionally stable, wealthy, super attractive, super thin people in your perfect age range than it is for vegan Republicans. If you are equally happy with a vegan Republican and with a mainstream supermodel, you are probably going to end up happy with a vegan Republican.
Posted by: Voltaire at Jan 8, 2006 8:57:36 PM
"The assumption underlying this entire discussion is that economists can use such terms as search costs, satisficing and modal set in a discussion and still get a decent sample of phone numbers from said prospective mates."
I believe in assigning value to things.
Hey, my personal ultramodal dropped me an e-mail to call my comments a "thing of beauty." If my girlfriend didn't appreciate these things, I'd just be satisficing.
"Sorry, you 130-IQ people, you are just not that special."
I'm thinking more of the 140-150 IQ people. If intelligence has a bell-curve distribution, and intellectual compatibility requires a mate's intelligence to be within a range of +/- n standard deviations from one's own, then the person who's three or four standard deviations from the mean has a much smaller pool than the person who's near the mean. You can perhaps disagree with the premises (if n is large enough, the effect disappears), but the math is inexorable.
"no matter which theory you believe in, if you want to find a good spouse, you are better off spending your time and money on self improvement (lose the gut! read real books! cultivate your garden!) than on mate-searching"
That's not inconsistent with my model, which acknowledges the importance of the intersection of the modal sets. Too, self-improvement has its own utility benefits outside of mate-searching. There comes a point where additional marginal time in mate-searching outweighs additional marginal time in self-improvement, however.
"IMHO, it is easier, not harder, for people with unusual preferences to find mates, at least in the Internet age."
I agree 100%, but that just increases the expected value of the small-modal-set strategy and the opportunity cost of satisficing.
"This discussion has so far ignored the big danger of the "modal spouse" theory -- self-deception."
Self-deception is one of many rationalizations for paternalistic policies that reduce utility. At the end of the day, it's extraordinarily more likely that I know what's better for me than anyone else will, even to the extent I deceive myself into confusing my potential mate's youthful complexion and callipygian figure with traits that will actually bring me more utility, such as her appreciation for and willingness to engage in abstract discussions of how different legal regimes for divorce and marriage interrelate with utility and dynamic modal sets. Otherwise, there'd be more than a fringe market for professional matchmakers, and the matchmakers would be more willing to disclose success rates and offer a pricing structure that wasn't so heavily weighted on non-negotiable up-front non-refundable payments.
But you make a strong case for having a preference for having a preference for the "satisficing" strategy. Those with larger modal sets are more likely to be happy with their mates (and for longer periods of time) than those with smaller modal sets.
Thought experiment: Would Tyler be happier if he derived great pleasure from dining at Taco Bell than he is with his smaller modal set of preferred Mexican cuisine?
Posted by: Ted at Jan 8, 2006 9:41:51 PM
"Swimsuit Issue syndrome -- I'd never have to work again if I had a dollar for every overweight, immature 30-ish or 40-ish male sports fan I've met who seriously expects to marry a thin, superhot blonde woman, and then wonders why he has trouble finding marriage-worthy dates."
It works both ways. There is no shortage of decidely B-list women who consider themselves ultra-hot and won't give the time of day to any man who isn't super Alpha, let alone one who who displays even the _slightest_ touch of nerdiness.
Posted by: Peter at Jan 8, 2006 9:46:38 PM
NB that "having a preference for having a preference for" in the 9:41 comment was meant as "having a meta-preference" and was not a typo. There were times at my life when I had a preference for having a preference for satisficing; alas (or fortunately, as the case may be), I did not actually have a preference for satisficing, and regularly failed in attempting to exercise that strategy, sometimes multiple times with the same person.
Posted by: Ted at Jan 8, 2006 9:56:08 PM
"As fas as selection goes I think the problem that many smart good looking women who have relatively vanilla interests end up focussing very heavily on the cash/intellect side of things"
this would be an interesting question to consider as well
Posted by: yoyo at Jan 8, 2006 10:34:39 PM
Modelling of modal marriages must include opportunity costs of search vs. opportunity costs of marriage. Divorce must be accounted for, and that factor is missing in the cursory analysis. Lastly, the existence of multiple modal partners is a multioptima solution problem. Hence, a new economic model of polygamy may be drawn. Ph.D. proposals, anyone?
Posted by: chsw at Jan 8, 2006 10:37:14 PM
Voltair writes, “IMHO, it is easier, not harder, for people with unusual preferences to find mates, at least in the Internet age. Competition is much fiercer for emotionally stable, wealthy, super attractive, super thin people in your perfect age range than it is for vegan Republicans. If you are equally happy with a vegan Republican and with a mainstream supermodel, you are probably going to end up happy with a vegan Republican.”
Somewhere on agoraphilia (which for a while saw a string of economic analyses of romantic endeavors) Glen Whitman considers the effect of niche interests on one’s pool of prospective mates. It’s not clear that finding a good mate is easier or more difficult for weird people. When you’re weird, the supply of people like you isn’t the only thing that contracts; the demand for them does too.
Posted by: Jeff Brown at Jan 9, 2006 1:51:58 AM
"The assumption underlying this entire discussion is that economists can use such terms as search costs, satisficing and modal set in a discussion and still get a decent sample of phone numbers from said prospective mates.""
Think of it as part of your search strategy. A woman who reacts negatively to the economic way of thinking may not be the right mate for an economist.
Posted by: David Friedman at Jan 9, 2006 3:23:07 AM
A woman hopes that the man would change after the wedding. He wouldn't.
A man hopes that the woman wouldn't change after the wedding. She would.
Posted by: Pavel at Jan 9, 2006 5:38:03 AM
Voltaire also wrote: “… if I had a dollar for every overweight, immature 30-ish or 40-ish male sports fan I've met who seriously expects to marry a thin, superhot blonde woman, and then wonders why he has trouble finding marriage-worthy dates.”
I wonder whether there might be some evolutionary advantage conferred to a species some of whose members price themselves out of the mating game.
Posted by: Jeff Brown at Jan 9, 2006 6:10:04 AM
