901. seguine - April 17, 1999 - 7:57 PM PT
Jayackroyd: "(And if someone can explain when to say "polygyny" and when to say "polygamy", I'd be grateful.)"

As I understand it, polygamy refers to multiple mates of either gender ("gamy" from the same source as "gamete"), whereas "polygyny" refers to multiple female mates ("gyny" from the same source as "gynecology"). Thus, both leks and harems are examples of polygamy, but only harems are examples of polygyny.

Slackjaw: "...why have males not adapted some method for identifying their own offspring?"

It's possible they have. But there's a third party in the equation. Some study I read about in Nature or Science a few years ago found that infants are usually thought to resemble their mothers' husbands.
If this is so, then either human babies have adapted developmentally to resemble their fathers for some period of time after birth, thus signaling to the male provider that the child is legit (and undermining cuckoldry); or humans in general simply believe that most babies resemble the mother's husband (ensuring infant survival against male suspicion).

Is father-resemblance a male strategy, a female strategy, or an infant strategy?

902. jayackroyd - April 18, 1999 - 4:06 AM PT
"...why have males not adapted some method for identifying their own offspring?"

I missed that one. What whirls around in my head when Slackjaw says that is it undermines the broadcast strategy, and the cuckold strategy. (Males don't adapt methods. People do. And half of their ancestors are female.)

It raises an interesting side issue--people don't look much alike, compared to most other mammals. In some cases, like zebras, there's selection pressure to look alike. They're striped not to blend in with shadows (did that idea ever make sense?) but to confuse carnivores as to which is which. And you see more variation among carnivores than among herbivores. But people still show more variation in appearance than other mammals. I've always wondered why this is.

903. resonance - April 18, 1999 - 4:16 AM PT
"They're striped
not to blend in with shadows (did that idea ever
make sense?) but to confuse carnivores as to
which is which."

?

904. jayackroyd - April 18, 1999 - 5:10 AM PT
Carnivores pick out a victim and stalk it. One reason for herding behavior is to make this more difficult. The zebra's stripes combined with their herding behavior make it hard to keep visual track of an individual.

905. resonance - April 18, 1999 - 5:26 AM PT
Sorry, misread. I thought you meant they would confuse the carnivores as to whether or not they were shadow.

906. seguine - April 18, 1999 - 8:10 PM PT
"But people still show more variation in appearance than other mammals. I've always wondered why this is."

More than any mammal but dogs, which vary as much or more than humans. I've always wondered about that too.

(Domestic dogs, of course, are all one species, but I've read that wolves are not identifiably different genetically than dogs, and as we all know they can interbreed without producing sterile offspring. IOW, it's hard to identify a non-behavioral difference between a golden retriever and a wolf.)

Of course, there is this: human physical variation seems smaller in closed communities. People develop racial similarities and strong tribal similarities within races. I'm not sure that, in a community of humans as small or isolated from genetic "interference" as any community of other mammals, there's all that much more physical variation between humans than between other mammals. Maybe apparently high human variation is simply the result of having become repeatedly isolated and reintegrated.

907. seguine - April 18, 1999 - 8:13 PM PT
"(Males don't adapt methods. People do. And half of their ancestors are female.)"

Yeah, but there's no reason males could not adapt differently from females. Obviously, they do.

908. taust1 - April 20, 1999 - 3:25 AM PT
As to why males have not developed methods of recognisisng their own offspring. Would it be worth while. The male dominant strategy is to fertilize as many suitable women as possible a let others bring them up. If one male defected ie recognised own offspring the whole game would end reducing the ability of all males to father offspring. The wonderful thing about evolution is that it is easy to come up with ideas very hard to be scientific and show how they can be falsified.

909. cdm1110 - April 20, 1999 - 6:00 AM PT
I've been a lurker in this thread (and the previous economics thread) for a while, and I have a word of praise and a question for Slackjaw. First, the praise -- as many of you recognize, Slack does a superb job of explaining what are often difficult and technical issues. He's an extraordinary resource on this thread, and anyone who is working through his posts carefully is surely learning a lot. Second, the question: you have said little about the stag hunt/coordination game, which I actually think is at least as powerful as the PD for thinking about real-world problems. Any plans to inlude this?

910. Slackjaw - April 21, 1999 - 12:15 AM PT
cdm,

wow, thanks for the nice comments, and I'm glad to see you delurk.

Yes, per pelle's request, I planned to talk more about collective action, including Stag Hunt as well as k of N contribution games, after we cover subgame perfection, and possibly the infinite PD right after that. The reason is that cooperation in that game is important in understanding collective action (though the importance of that game in particular is overwrought, I agree). But I think many people have the sense that repetition improves matters, or that the infinite setting means collective action isn't really a problem (some may even believe that Axelrod proved this), so I wanted to say something about repetition first.

So, use of the words "stag hunt" reveals some information about you--you have studied game theory before?

911. Slackjaw - April 21, 1999 - 12:16 AM PT
overwrought?

overstated.

912. cdm1110 - April 22, 1999 - 5:03 AM PT
Slackjaw:

I'm an economist, so I've studied game theory, but I'm not a game theorist by any means...

913. jayackroyd - April 23, 1999 - 10:35 AM PT
Message #907

I guess that depends on what you mean by "adapt." If you mean "adapt evolutionarily," I have to say you're missing something. If you mean "adapt a strategy," then, sure.

914. jayackroyd - April 23, 1999 - 10:41 AM PT
Message #906

I thought of dogs, but we've bred that variation into them over tens of thousands of years. Or, at least, since the Egyptions. What's a dog generation? 6 years? If you use the rule of 7x, the answer is 3 years. So say we've been breeding them for 10,000 years. If we say a canine generation is 5 years, we've had 2,000 generations of breeding opportunity. That allows for a lot of modification.

It _is_ interesting that we can get such a variety of shapes and sizes. We've been breeding cats as long, and their variation is remarkably less, mostly coloration.

There are what they call "founder" effects in isolated human populations, like Iceland. The number of initial colonists was small, limiting the available variability.

915. jayackroyd - April 23, 1999 - 10:48 AM PT
Message #908

Agree wholeheartedly with your last remark. This is all just story telling, and is very hard to make falsifiable statements about. So now I'll make one.

I think you're wrong about the dominant male strategy being broadcast always. The dominant male strategy is apparently mixed, with much greater weight given to nurture, with a small investment in broadcast strategies. There simply aren't any human societies where broadcast is used as the dominant male strategy. Whether this is in response to females prefering nurturers or simple greater survivablitity of nurtured kids, it's clear, empirically, that broadcast is not a dominant male strategy for human males. To falsify this, show me a society where broadcast exceeds marriage as a male strategy.

916. seguine - April 23, 1999 - 8:08 PM PT
"I guess that depends on what you mean by "adapt." If you mean "adapt evolutionarily," I have to say you're missing something. If you mean "adapt a strategy," then, sure."

I mean both. Reproductive strategies *are* evolutionary. Besides that, males have obviously adapted physically over time, to various circumstance, in ways females have not; and vice versa. Males and females have adapted, moreover, in the context of one another. Any individual's survival & procreation is not somehow designed to maximize the survival of his species, but simply maximizes the survival potential of his own genes (and whatever survives, of course, is the species).

If your point is that there has to be some sort of rough equity betwen males' and females' strategies in the process of species survival because otherwise there would be no species survival, then that's a reasonable suggestion. But I don't think you can conclude it's universally true without proving first that species success always depends on there being no overall dominance of one gender's genes over the other. Not positive you can do that: the world is a pretty various place. (Ever looked at the mating habits of squid?)

HOWEVER, when it comes to humans, I agree completely with your Message #915. But the point of my response to your original statement, "Males don't adapt methods. People do. And half of their ancestors are female," was that there's no reason I can think of that a female couldn't pass on a genetically determined male reproductive strategy to her male offspring.

917. seguine - April 23, 1999 - 8:15 PM PT
An aside: the gene located on the X chromosome that has been linked in some research to human male homosexuality is passed on maternally. (Apparently, btw, there's some new Canadian research just out that challenges previous studies on the genetic-basis-of-gayness subject, but I don't know anything about it.)

918. resonance - April 23, 1999 - 10:48 PM PT
I think it's reasonable to assume that our DNA prepares us for certain patterns of behavior, and these patterns are either stunted or expressed depending upon how successful they are in our society. It's a given that we have some predisposition to react to specific stimuli in certain specific ways. The often cited examples are very simple, like pain reaction and blinking -- but there are more complex, abstract reactions that are equally automatic, like the body's reaction to being startled, or the recognition of some danger in the environment. And there are very complex, abstract reactions that humans share among themselves, which arise from very ambiguous data (such as the human tendency to recognize 'faces' in the swirling pattern of wood grain or in the oddly shaped stones of a mountainside) People do react differently to things which have 'faces'.

If we are wired to detect 'face' stimuli and react differently to whatever possesses a 'face', then I don't see why we can't be wired to detect and pay attention to other stimuli (like specific traits, overt or subtle) and react differently to the people that exhibit these traits. The complexity would be about the same

Which means that in the absence of those detectable traits, we would maintain some optimal mating strategy, and in the presence of those traits, utilize some other mating strategy. The genes expressed in the mind are usually fairly polygenic as far as we can determine (i.e. one gene's expression affects several traits). Which means it is possible that certain obvious traits may be linked to other, less obvious traits, like mating traits in societies where mating is fairly controlled (i.e. our own).

If this is indeed the case, then we can propose that mating strategies may be highly modal (which does away with a lot of the problems we encounter when trying to explain the separate roots of polygamous and monogamous behaviors).

919. jayackroyd - April 24, 1999 - 9:03 AM PT
Seguine--

"But the point of my response to your original statement, "Males don't adapt methods. People do. And half of their ancestors are female," was that there's no reason I can think of that a female couldn't pass on a genetically determined male reproductive strategy to her male offspring."

Well, that was my point.

"If your point is that there has to be some sort of rough equity betwen males' and females' strategies in the process of species survival because otherwise there would be no species survival, then that's a reasonable suggestion."

No, that's not. I don't really know what you mean by "equity." There is evidence of conflict--that the sexes are engaged in an arms war, where females shoot for a different allocation of energy committed to pregnancy than males do, for example. But the genes for the arms race may or may not be sex-linked--dads can pass genes to daughters that increase their likelihood of surviving pregnancy, and moms can pass to their sons genes that lead to rapid fetal development.

920. jayackroyd - April 24, 1999 - 9:19 AM PT
Message #916

I find this post hard to follow. On face recognition, we have a substantial chunk of brain mapped to the task of recognizing faces.

"Which means that in the absence of those detectable traits, we would maintain some optimal mating strategy, and in the presence of those traits, utilize some other mating strategy. "

You seem to be saying that phenotypes may arise depending on how people are wired. Well, yeah, but isn't that kinda obvious? I believe the reason we see differences across societies in mating behavior is due to resource availability. Survivability of offspring that make large demands on parental resources after birth.

I thought this issue might be modeled as a two player game. But we could look at it as two decision problems under uncertainty. See next post.

921. jayackroyd - April 24, 1999 - 9:39 AM PT
Consider the decision problem that both sexes face:

Maximize (P(reproductive success of offspring)). That depends on the probability of offspring surviving to reproductive age, expected number of offspring, expected number of offspring's offspring.

The trouble is that the parameters that affect the probabilities are different for men and for women. Women have these elements in their decision problem:

Desirability of mate (i.e. likelihood of highly productive offspring)(DesM)
Risk of death through childbirth (DCB)
Risk of raising the child solo (NoDad)
Risk of death of infant or self by cuckolded nurturer (Murder)

Male decision problem is different:

Desirability of mate (DesM)
Risk of cuckoldry (Cuck)
Risk of mom raising child solo (remember, we're hunter/gatherers, so dad can't nurse) (NoDad)

As NoDad goes down, broadcast strategies look better for both genders. Moms can go after alpha males without fearing offspring not surviving, and alphas can broadcast away. Of course, that's gonna create selection pressure for sexual dimorphism, as alphas battle for the rights to impregnate many, and females practice sexual selection on the likelihood of offspring winning said battles.

922. jayackroyd - April 24, 1999 - 10:03 AM PT
So, to start with, it seems pretty likely that the male nurturer role must have been quite important. Diamond talks at some length about the period of support required by a weaned human infant, and how it makes people distinct from all other mammals. Resource availability must have imposed a meaningful constraint given the infant support requirements.

Now look what hidden ovulation does.

It allows moms to choose higher on desirability index, while lowering the risks of Murder and NoDad. For dads, Cuck goes up, but NoDad goes down. And it means that they too can try to go higher on the desirability index, hoping to create a cuckold.

It seems like a mixed strategy dominates--men nurture, but still mess around when they can with women who are also messing around. You can tell stories of how this might happen. You've got the Mrs. Robinson scenario of young men and older women. You've got the hunk scenario of women hooking up with males very high on the desirability index.

923. seguine - April 24, 1999 - 4:07 PM PT
"No, that's not. I don't really know what you mean by "equity." "

Yes, it is, because I mean efficacy equity. But never mind--I think we're probably making the same point but talking past one another.

"As NoDad goes down, broadcast strategies look better for both genders."

Yes.

"[Concealed ovulation] allows moms to choose higher on desirability index, while lowering the risks of Murder and NoDad. For dads, Cuck goes up, but NoDad goes down. And it means that they too can try to go higher on the desirability index, hoping to create a cuckold."

The problem is that a male strategy can develop whereby extremely possessive males react to the female advntage in concealed ovulation by restraining the females and murdering children that don't resemble themselves. Limitations on female size & strength, whether due primarily to limits on female physical resources that must be used for childbearing or due to male sexual selection (it's odd that female manageability is rarely included in a list of desireability factors wrt male choice), give a physical power advantage to males. Unless you can measure just how effective concealed ovulation might be in countering male *paranoia* over cheating, and unless you can prove that males can't really identify their own offspring (I suspect the incidence of non-ID might be lower than you imply) it's hard to say for sure that HidOv contributes a whole lot to decreasing NoDad or Murder. But I bet you CAN say that HidOv contributes substantially to intensity of male control of females, & that this is a successful male strategy when resources are not abundant, particularly for non-alphas.

924. resonance - April 24, 1999 - 5:08 PM PT
""Which means that in the absence of those detectable traits, we would maintain some optimal mating strategy, and in the presence of those traits, utilize some other mating strategy. "

You seem to be saying that phenotypes may arise depending on how people are wired. Well, yeah, but isn't that kinda obvious? I believe the
reason we see differences across societies in
mating behavior is due to resource availability."

Um, maybe I edited too sharply. Obviously, phenotypes arise from genes, but that's neither here not there -- it is at best a given in my statement.

I am saying that one person -- say, a female -- will display a certain phenotype and that another person -- a male -- will choose a mating strategy based upon the absence or presence of certain phenotypical traits. I am not ignoring the fact that we obviously choose mating strategies based upon the *non*-inheritable characteristics of a potential mate or the environmental conditions as well, because these must heavily influence the process of selecting any successful mating strategy. I'm just saying that some of the alternation in mating strategies (i.e. from monogamous to polygamous) may arise from genetic tendencies of recognizing certain patterns of behavior in potential mates which in turn are influenced by that potential mate's genetic tendencies.

If this is true, then it would account for a lot of the differentiation in mating strategies practiced not only within a society, but at different times by the same organism.

925. resonance - April 24, 1999 - 5:12 PM PT
As far as resource demands dictating mating behavior, I'm at a loss. Look at the 'wealth moment' in Western society as compared to the 'family size moment'.

926. seguine - April 24, 1999 - 9:50 PM PT
BTW, this item in the list of female decision problems gave me pause:

"Risk of death through childbirth"

It finally occurred to me why. The risk is not insubstantial. From a female offspring-maximization standpoint, that's odd, isn't it? I've seen it posited that maternal risk of death is related to cranial size of infants, which is what allows for greater human intellectual development relative to other animals. But I don't think I buy that, since something like 2 in ten births of otherwise *normal* pregnancies require medical intervention to save the life of mother or child, and as far as I know that figure doesn't take into account stuff like gestational diabetes, preeclampsia, stroke, etc. IOW, cranial size isn't all of the risk by any means. Then there's the matter of male size being a function of competition with other males. But that shouldn't necessarily bear on the relationship between male and female size: females might prefer big males, but males of any size should prefer big, robust females unlikely to die in childbirth. But that's not the case: females almost universally prefer males larger than themselves (with high-status females snagging the biggest and tallest males), and males almost universally prefer smaller women. Male size could be a proxy for provider competence. But what good, in terms of reproductive success, is a small woman with a 20% chance of bleeding to death the first time she gives birth?

Perhaps risk of maternal death is a function of male choice: selecting smaller, less robust females ensures mating compliance. If one mate dies bearing children, another mate can be acquired. Meanwhile, no other male can sire children with her: she's either pregnant, nursing, or dead. And given the risk of pregnancy which does NOT include murder by a cuckolded spouse, she's better off not adding the cost of a broadcast strategy to her plate.

927. resonance - April 24, 1999 - 11:31 PM PT
I don't know about the 2 in 10 figure , especially limited to 'normal' pregnancies-- it seems a little high to me.

Choosing a mate that will not survive childbirth may in some way help one's breeding strategy by preventing other males from breeding with her, but I really doubt that can be in any way a viable breeding strategy overall. Children born of that strategy would be much less likely to survive, given the higher odds that their mother would be dead, I think -- especially if you're considering some form of broadcast strategy on the part of the male.

As far as death in child birth being a limit on breeding strategies:

Were I to hazard a guess on this matter I would guess that multiple birth strategies aren't so much affected by the risk of death in childbirth as you're implying, in the same way that humans tend to inherit diseases which strike in old age -- the birthing and a lot of the raising usually tend to be done when death strikes for most of the offspring.

Besides, you can't just look at a woman's size in terms of surviving childbirth. For example, smaller women require less energy to maintain than larger, more 'robust' women, which means that a tribe can support more of them. This is a place where jay's argument on limiting resources really comes into play, but then we're talking about problems of classical population genetics, and not necessarily the ev psych stuff we're talking about now. And there's the standard arguments made about how smaller women are more easily physically dominated and ordered around and suchlike by their beastly larger stronger male mates, which means that there's even more mating going on or whatever. Males don't have to do dishes or something and can spend more time procreating around the block, I don't know. Maybe you can argue that in evolutionary psychological terms the definition of a perfect 10 is five 2s, but that doesn't seem to be the way it works in observable reality.

928. resonance - April 25, 1999 - 12:11 AM PT
If I ever have a band, I'm going to have to call them 'The Broadcast Strategy.' And the first album will be called 'Robust'. There's just something faintly ridiculous about all this terminology, it brings to mind a 'Lit' video.

929. seguine - April 25, 1999 - 9:14 AM PT
"...the birthing and a lot of the raising usually tend to be done when death strikes for most of the offspring."

What is that, the Lazarus strategy?

I have to confess, I don't understand what you're saying here at all.

But as for the 20% figure, it sure isn't out of line with my own anecdotal experience. Quite frankly, maybe 30% or more of the women I know who've had children, including myself, should thank their lucky stars for advanced medical technologies. From what I can tell, and from what I've read about rates of maternal and infant survival before the modern era, any woman today who opts for "natural" childirth in a setting more than a couple hundred yards away from a hospital equipped with all the most recent gadgets and best-educated personnel is either indigent or crazy.

930. seguine - April 25, 1999 - 9:15 AM PT
"Besides, you can't just look at a woman's size in terms of surviving childbirth. For example, smaller women require less energy to maintain than larger, more 'robust' women, which means that a tribe can support more of them."

That's not necessarily true at all. Bigger women are perfectly capable of having lower metabolic rates than smaller women. I think it's probably true for most of the women I know: the smaller of us burn fuel less efficiently over all. I'm a apt example: I'm average height (5'5"), but smaller-boned & smaller-muscled than average. My weight ranges around now, but was distinctly low when I was young. I never diet, I'm not overweight, and in fact, the subject of how much food I can consume for lunch has sometimes become the object of hilarity among co-workers. But I know plenty of women who are taller and bigger-boned than I am, who require a lot fewer calories than I do to maintain an average weight. All in all, I'm more costly than they are in terms of food resources.

But anyway, the issue isn't absolute female size (which is really what you're talking about when you bring up resource consumption) but relative female size. Females range quite a lot in size. What's constant is our puniness relative to our mates.

931. jayackroyd - April 25, 1999 - 3:26 PM PT
"If this is true, then it would account for a lot of the differentiation in mating strategies practiced not only within a society, but at different times by the same organism."

I've only got a minute today, but have meant to make a variation on this point. I think males may well mix their strategy over time. Young, virile but low status males may broadcast, and nurture when they get older. Women with old high status husbands may cooperate in this strategy, creating cuckolds.

932. resonance - April 25, 1999 - 5:14 PM PT
"What is that, the Lazarus strategy?
I have to confess, I don't understand what you're saying here at all. "

Oh, it isn't hard. If you have a child every three years and you're say 10% likely to die during childbirth assuming some minimal assistance or knowledge, then on average ar least one of your children will be near maturity, perhaps two or three, before you die.

"That's not necessarily true at all. Bigger women are perfectly capable of having lower metabolic
rates than smaller women. I think it's probably
true for most of the women I know: the smaller
of us burn fuel less efficiently over all."

This is irrelevant. Smaller women, because they have a higher muscle to fat ratio, may indeed have a higher metabolism than someone of the same mass with a higher fat to muscle ratio. Yet we aren't talking about caloric efficiency or metabolic rates in this matter -- we're talking about the necessary caloric intake per body, and for smaller women it tends to be a smaller number. Small women overall will require less calories than big women overall, even if larger women require less calories per kilo of bodyweight. And we're not concerned with the biomass of females in a breeding population, we're talking about the number of viable breeding partners. If you pass on genes which due to a smaller dictated body size allow three, instead of two, of your offspring to survive a famine within the tribe, then your genes are half again as likely to proliferate.

933. resonance - April 25, 1999 - 5:17 PM PT
"But anyway, the issue isn't absolute female size
(which is really what you're talking about when
you bring up resource consumption) but
relative female size. "

I disagree. The constraints of resource consumption are going to play at least as large a role, if not larger, than the purported need for women to be smaller than men for ev psych purposes. You can't divorce one from the other in explaining why women are small or 'robust'.

934. seguine - April 26, 1999 - 6:20 AM PT
"we're talking about the necessary caloric intake per body, and for smaller women it tends to be a smaller number. "

Oh, really? Perhaps you can cite some statistics that support that assertion. I can offer only anecdote, but I wouldn't make such a presumption on certainty as you have here.

"The constraints of resource consumption are going to play at least as large a role, if not larger, than the purported need for women to be smaller than men for ev psych purposes."

Fine, then you'll have to explain why the constraints of resource consumption don't favor women being larger than men. Females, after all, need the extra resources to bear progeny. Or why constraints on resources favor females being larger than males in some species and not others. (For that mater, if it were evolutionarily advantageous, men might simply have developed more efficient metabolisms than women. Who the hell knows?)

As JayAckroyd pointed out earlier, we're short on verifiable information and this stuff tends to come down to Just So Stories.

935. seguine - April 26, 1999 - 6:28 AM PT
"Oh, it isn't hard. If you have a child every three years and you're say 10% likely to die during childbirth assuming some minimal assistance or knowledge, then on average ar least one of your children will be near maturity, perhaps two or three, before you die."

Oh, it's pretty hard after all. Because you're assuming, wrongly, that the risk/incidence of maternal death is the same for first, second, third, and subsequent births; or that the risk *only* increases with age. In fact, first births are often quite problematic.

936. seguine - April 26, 1999 - 6:33 AM PT
"I think males may well mix their strategy over time. Young, virile but low status males may broadcast, and nurture when they get older. Women with old high status husbands may cooperate in this strategy, creating cuckolds."

I think it's a certainty that males mix their strategy over time.

BTW, the existence of prostitution virtually everywhere suggests a need for broacasters to be acommodated without cuckolding other males.

937. resonance - April 26, 1999 - 6:38 AM PT
"Oh, really? Perhaps you can cite some statistics
that support that assertion."

Well, off the cuff I can tell you that there are three figures which go into the generic calculation of someone's basal metabolic rate. The first two are the height and the body weight of the subject, each multiplied by some factor. And the third is the age. I think I've seen different figures, but for women the generic calculation for someone's BMR something like 700 calories + 4 point something x weight in pounds, + 4 point something x height in inches, minus some factor times age in years. So, even allowing for the differences arising from percentage of muscle and so on, there you are.

"Fine, then you'll have to explain why the
constraints of resource consumption don't favor
women being larger than men. Females, after all,
need the extra resources to bear progeny."

Why would they want to be smaller? Precisely because they do have to nourish progeny. Remember, the limiting factor here isn't times of plenty -- in which both a small and a large mother can maintain enough body fat to keep up their energy reserves and provide for the fetus (and then nurse it) -- but a time of famine. In that time the smaller mother will require a smaller proportion of her total caloric intake to sustain herself than her larger companions -- and therefore a higher percentage of her caloric intake will go to the fetus or the infant.

938. resonance - April 26, 1999 - 6:44 AM PT
"Oh, it's pretty hard after all. Because you're
assuming, wrongly, that the risk/incidence of
maternal death is the same for first, second,
third, and subsequent births; or that the risk
*only* increases with age. In fact, first births are
often quite problematic."

And? Even if you raise the bar for the first birth, you're still looking at a phenomenon where the death rate has to get pretty high before limiting the number of births becomes a necessity for ensuring gene dispersion. No one is saying that birthing mortality doesn't cut into the chance that a gene will be passed on -- obviously, if the gene is for something like very narrow hips, there may be a problem. But that's immaterial. I think you still have to have some extremely high rate of mortality before you start cutting into the overall survivability of a multiple birthing strategy.

939. jayackroyd - April 26, 1999 - 8:36 AM PT
"BTW, the existence of prostitution virtually everywhere suggests a need for broacasters to be acommodated without cuckolding other males."

Did small packs of hunter/gatherers have prostitutes? Certainly in the semi-nomadic people I spent a year with, there was no room in the society for prostitution. There was a rumor that one older guy's nephew was helping out with the older guy's new, young wife, but that's in our cuckolding realm.

The urge to broadcast is apparently widespread, and not fully met without direct exchange of resource for sexual services among sedentary agriculturalists. That doesn't mean that prostitution and broadcast evolved together.

940. resonance - April 26, 1999 - 4:23 PM PT
"The urge to broadcast is apparently widespread,
and not fully met without direct exchange of
resource for sexual services among sedentary
agriculturalists. That doesn't mean that
prostitution and broadcast evolved together."

There's probably some merit in arguing that prostitution is partially tolerated as a sexual release valve, but broadcast strategy? The way I understand it, most johns have one steady whore they go to, and a whore isn't exactly a good bet for parenting either. I think we may be rushing a little bit here.

941. seguine - April 26, 1999 - 9:03 PM PT
"The urge to broadcast is apparently widespread, and not fully met without direct exchange of resource for sexual services among sedentary agriculturalists. That doesn't mean that prostitution and broadcast evolved together."

Of course not. (Although we'll never know for sure.) But what difference does that make? Any latent (or mildly conserved) trait can become more pronounced under favorable circumstances--such as the development of agriculture, complex societies, and disposable capital. My point is simply that in calculations of the effectiveness of one reproductive stratagem over another it's inadvisable to overlook little details like the prevalence of sexual arrangements that probably serve to maintain broadcaster genes in a population without the broadcaster (male or female) having to run the risks of cuckoldry.

942. seguine - April 26, 1999 - 9:24 PM PT
"for women the generic calculation for someone's BMR something like 700 calories + 4 point something x weight in pounds, + 4 point something x height in inches, minus some factor times age in years. So, even allowing for the differences arising from percentage of muscle and so on, there you are."

Resonance. This doesn't address your contention, it is a calculation of the number of calories an individual must consume to maintain the weight he or she is already at. If she's 60" tall and fat, you could come up with an identical BMR for someone who's 70" tall and lean. Plus, the differences in average size, and in fat-to-muscle ratios betwen females of different ethnicites (i.e., whose phenotypes emerged in varying circumstances more and less resource abundant) suggest that there's nothing absolute about female size relative to infant survival, but that female *metabolism* may vary as needed. Again, that doesn't explain the preference of both sexes for males being larger than females.

943. resonance - April 26, 1999 - 9:53 PM PT
What? My point was about how smaller-massed women require fewer calories than larger massed calories even if they require more calories per unit of body mass. How can you say that the BMR data doesn't bear on that?

"If
she's 60" tall and fat, you could come up with an
identical BMR for someone who's 70" tall and
lean."

Yes, the whole point earlier was about size overall when we were bandying the term 'robust' about.

"Plus, the differences in average size, and in
fat-to-muscle ratios betwen females of different
ethnicites (i.e., whose phenotypes emerged in
varying circumstances more and less resource
abundant) suggest that there's nothing absolute
about female size relative to infant survival, but
that female *metabolism* may vary as needed."

Well, you were the one who brought size into the discussion of breeding strategy WRT birth mortality and linked weaker, smaller women with death in childbirth as some kind of male strategy. All I did was make the obvious conclusion -- selecting mothers that are more likely to die just means you are cutting into the survivability of the offspring due to lack of nurturing.

944. resonance - April 26, 1999 - 9:54 PM PT
Anyway, I would disagree and say that the tendencies in female size *do* have some effect on infant mortality, but that they have varying benefits and penalties (at least in the original environment) which work to cancel any penalty inherent in their size. But I think that's not really a point which needs a whole lot of attention, either.

"Again, that doesn't explain the preference of
both sexes for males being larger than females."

I think it certainly bears on the subject. There are lots of standard, resource-based arguments for why women would select larger men and men would select smaller women, and if these preferences lead to an increase in survivability they would be selected for. No one knows why a woman would start preferring larger men, and it's irrelevant. If by so doing she increases the chance that her offspring will survive, then her trait will be selected for. I am not dismissing the manner in which size differential might be selected for via other criteria -- just making the obvious case for resource criteria.

945. seguine - April 26, 1999 - 10:01 PM PT
"In that time the smaller mother will require a smaller proportion of her total caloric intake to sustain herself than her larger companions -- and therefore a higher percentage of her caloric intake will go to the fetus or the infant."

Again, the point is the relative size of females to males, not the size of females generally, which varies *considerably* more than the size of full-term babies of any ethnicity at birth. And the size of babies is not correlated with the size of the mother (hence some of the problems of childbirth alluded to earlier).

Note that nature does not provide that, because of resource limitations, male size decreases. But why shouldn't it? After all, a small male with an efficient metabolism should be able to provide for his mate and offspring better than a big, greedy feeder: scarce resources could be diverted from themselves to their big mates, who could thereby accommodate big, healthy babies.

I know, you'll say that males competed w/each other for mates, thus size is advantageous in battle and a proxy for fitnes in sexual selection. But there must be a reason that something other than size(agility? intelligence?) could not operate as a stonger proxy for fitness. I say it's simply that sexual selection is not altogether a female phenomenon (although it's often represented that way). Coercion and control of females could easily be a male strategy facilitated by greater relative size. Moreover, coercion and control of females is widely observed and probably couldn't occur in the absence of greater male size.

946. seguine - April 26, 1999 - 10:24 PM PT
"No one is saying that birthing mortality doesn't cut into the chance that a gene will be passed on -- obviously, if the gene is for something like very narrow hips, there may be a problem. But that's immaterial. I think you still have to have some extremely high rate of mortality before you start cutting into the overall survivability of a multiple birthing strategy."

Tribe A is full of females with big bones, wide hips, and the women are all 5'10" tall. Tribe B is full of small women withy narrow hips who could stand to eat more. The latter die in first childbirth at a rate of 1 in 250 women, while the big girls die in first childbirth at a rate of only 1 in 500 women. If there are 1000 women in each tribe, and 4 offspring on avg for each woman, and all become pregnant, then assuming that the first child of all maternal mortalities also died, one would expect Tribe A to produce 8 more children per generation than tribe B. That's .8% more progeny, and .4% more females. All things being equal, an exponential increase in fertility of Tribe A over Tribe B should be expected over time. The big girls ought to prevail.

947. resonance - April 26, 1999 - 10:52 PM PT
Until the famine comes. And famine, not times of plenty, are when the biggest genetic changes in the tribe occur. I'm not looking for a senseless argument, Seguine, but you're missing something very important here. When the famine comes, the tribe with smaller women will be able to support many more breeding pairs than the tribe full of Amazons. More of their children will therefore survive. This is overly simplified, but so is every thing we've been talking about here. You can't just look at male dominance as the reason small women would be selected -- resources play a big role, too.

948. resonance - April 26, 1999 - 10:55 PM PT
BTW, I know anecdotal evidence doesn't much matter here but I'd just like to add that I'm very tall and I prefer women closer to my height, which is just one small reason but a reason nonetheless why I'm dubious about the whole 'big strong man dominating little woman' thesis of the disparity between size of men and women. And it's not as though we don't have several other reasonable theses about why men are bigger to work with as it is.

949. resonance - April 26, 1999 - 11:06 PM PT
For example, one of the arguments commonly made is that if the woman is much smaller than the man, the woman will be perforce be more complaisant to the man's urges, which makes it more likely that the man would monopolize the woman.

But a smaller woman would be less likely to successfully fend off, say, the advances of another male. Which means that she would have a higher chance of having her progeny killed by her vengeful thug mate, in addition to being less of the sure monopoly that we are proposing makes her such an attractive mate in the first place.

So we can see two real reasons why breeding strategies would work against smaller women -- and therefore we must look harder for reasons outside of breeding strategy why there might be pressure for women to be smaller than their men. Because, after all, women *are* on average smaller than men -- something has to be driving this disparity.

What's more -- if there were, say, pressures for women to become smaller then why is it that we don't see women *getting* smaller as we progress through the history of humanity? If smaller women are going to be selected by men more often so that they can dominate them, then you'd expect the average size of women (correcting for environment and nutrition) to *drop* from this pressure when all else is equal (i.e. no famines or sudden environmental pressures). Yet we don't see anything like that, unless I'm much mistaken. So, clearly, there have to be other factors at work, here.

950. seguine - April 27, 1999 - 7:26 AM PT
"You can't just look at male dominance as the reason small women would be selected -- resources play a big role, too."

I'm not *just* looking at male dominance. But I am looking at it, and I'm not making any aprioristic assumptions about whether resources *must* play the larger role in the disparity in size between men and women.

It seems quite odd to me that discussions of human evolution or ev psych rarely take into account the possibility of male dominance of females as a mating strategy. Instead we hear about slightly less charged topics like cuckoldry and broadcasting and male aggression toward other males, with rape ignored and wife beating consigned to the sidelines of cuckoldry's consequences for female broadcasters.

Again, your deferring to resources as the primary explanation of female size difference RELATIVE TO MALES fails to take into acount the other variable limiting female diminution, which is the optimal size babies need to be at birth in order to survive. Furthermore, there's no obvious reason nature could not accommodate a change other than female size that would guard against starvation in times of famine. I've mentioned two: more efficient female metabolism among big, robust females; and smaller males. Other species do manifest such adaptations; why not humans? One possible answer is: male mating strategies.

"I'd just like to add that I'm very tall and I prefer women closer to my height"

Closer to, but not taller than. Am I correct?

951. seguine - April 27, 1999 - 7:27 AM PT
"But a smaller woman would be less likely to successfully fend off, say, the advances of another male."

No kidding. But the other male would have to contend with his victim's mate. That's a risk that should constrain the occurrence of rape, just as long as complex social structures remain in place. (Note that women are raped everywhere in wartime, where dominance structures betwen males have broken down or are in flux.) Why do you think it's in women's INTERESTS to submit to male domination? Because it also affords them protection. (I refer you to the situation in Jordan.)

"why is it that we don't see women *getting* smaller as we progress through the history of humanity?"

First, everyone is getting bigger in countries with ample resources. Second, males and females in industrialized nations are getting closer in size. I don't know if that's a function of females getting bigger faster or males getting bigger more slowly, but there's no way to know for certain whether the changes have to do more with resource availability or cultural developments that may accompany the transition to increasingly complex societies. What's more, the fact that such changes can be seen over a relatively short period of time suggest that things like relative size may be influenced rather easily. You can't look at human phenotypes in non-relative terms and make presumptions about the ancient ancestral environment; otherwise, we'd see a lot less human variability than we do. If resources were the primary or only constraint on female size, then all women everywhere would be a certain avg size relative to the size of *babies*. Not men.

952. resonance - April 27, 1999 - 1:34 PM PT
"Again, your deferring to resources as the primary explanation of female size difference RELATIVE TO MALES fails to take into acount the other variable limiting female diminution, which is the optimal size babies need to be at birth in order to survive. "

If you said this the first time someplace, I definitely missed it.

"Furthermore, there's no obvious reason nature could not accommodate a change other than female size that would guard against starvation in times of famine."

?

Nature doesn't just pop out advantageous mutations on demand. I might as well argue that 'there's no obvious reason nature could not accomodate a change other than the ability to build an airplane that would provide humans with the ability to travel long distances in a short time'.

To put this in another light:

Any economizing change in metabolism would be of benefit to both sexes and would rapidly spread throughout both, and become the baseline. And even if it were to somehow be limited only to women, still, we are talking about an even playing field -- the advantage would be so beneficial that it would dominate the gene pool in a handful of generations. And so we are back to square one -- means of finding a competitive edge in the contest to pass on the most genes.

"I've mentioned two: more efficient female metabolism among big, robust females; and smaller males."

More efficient metabolism is absolutely, inherently meaningless to this matter. The only thing which matters is the total amount of calories needed to support life *and* support a fetus. It doesn't matter at all whether a large woman who requires 1900 calories a day uses them more efficiently than a smaller woman who requires 1600 calories a day and uses them relatively inefficiently. When there are only 1800 calories a day available, the smaller woman will survive. The larger one will not.

953. resonance - April 27, 1999 - 1:35 PM PT
If carrying a fetus doubles the caloric requirements (for the sake of argument) then if someone can provide 3600 calories a day for a pregnant female to subside on, the smaller woman will be able to survive *and* allow her fetus to develop normally, and the larger one will not.

I have absolutely no idea whatsoever where the 'smaller males' thing has relevance, or even what you specifically mean by it.

"I'd just like to add that I'm very tall and I prefer women closer to my height"
Closer to, but not taller than. Am I correct?"

(laughing) I don't know any women taller than me. If my perfect woman walked in the door 6'10", though, she'd still be my perfect woman. I'm actually tired of dating shorter women, it hurts my neck after a while.

"No kidding. But the other male would have to contend with his victim's mate."

This is irrelevant. We're not talking about the success of rape as a mating strategy, we're talking about the success of smaller women as organisms. And if their success is dependent upon the ability of men to dominate them or some such, then their own vulnerability works against them because it makes them less likely to bear and nurture viable offspring. 'So,' you say, 'men must be causing it, not women!' To me, that's circular and excessively post hoc. (I know, most of Ev psych is circular and excessively post hoc, but still this strikes me as a bit egregious). And the easy assertion is that men don't like this notion because, well, it makes them look bad. But that doesn't change the fact that there's all sorts of things wrong with the notion in the first place.

I should think that male domination (which of course can be seen in the real world and is a real phenomenon) would be a case of culture adapting to the body, not so much body adapting to the culture.

954. resonance - April 27, 1999 - 1:35 PM PT
There are any number of good reasons why the size of women should be selected toward larger by breeding preference and kept smaller by constraints of resources. The obvious one that you mention is the fact that larger stronger women will be more likely to survive childbirth. Larger women will be better able to fend off attackers and rapists, larger women will be more likely to give big men larger male children, etc. etc. etc.

Men who are the same size as women are almost always stronger, because men have a higher muscle to fat ratio, and the heightened aggression of men makes them more prone toward perfecting violent skills. So why wouldn't the tendency be toward picking partners who are as close to your size as possible -- ones you can still dominate but who give the best offspring and are the most likely to remain to nurture them -- if dominance is a critical component to ev psych? You see, there's all sorts of problems with the assertion, and we have to look elsewhere for at least the bulk of the reason why women are smaller than men.

And, really -- men who have some kind of genetic predisposition (if such exists) to like *larger* women will tend to be weeded out of the population over time, simply because they will have a much smaller range of potential mates available to them than someone who likes smaller women.

"First, everyone is getting bigger in countries with ample resources. "

Which just supports the notion that famine is what places pressure on breeding women to be small! It's an easy connection -- the social structure doesn't necessarily become more egalitarian when resources change, so you can't point to some cultural emancipation of women as the primary reason they get larger in countries where the resources are more extensive. This is Ockham's razor through and through.

955. resonance - April 27, 1999 - 1:36 PM PT
"If resources were the primary or only constraint on female size, then all women everywhere would be a certain avg size relative to the size of *babies*. Not men."

Whyever so? Resources are not evenly distributed. To reverse this statement, if dominance were the primary or only constraint on female size -- or, indeed, if it were a critical or important constraint on female size -- then we would see a much smaller variation in female size relative to men. But we don't.

956. jayackroyd - April 27, 1999 - 1:47 PM PT
Message #947

Hunter/gatherers don't experience famine. They're population density isn't high enough. Infant elderly and child mortality might bump up in a year where resources are relatively scarce, but people are very opportunistic feeders.

957. resonance - April 27, 1999 - 1:54 PM PT
A period where their resources are sufficiently constrained that people who require less resources are selected for, then. (IOW famine, but that's just my opinion).

958. jayackroyd - April 27, 1999 - 1:59 PM PT
"I've mentioned two: more efficient female metabolism among big, robust females; and smaller males. Other species do manifest such adaptations; why not humans? "

Dimorphism with the female larger than the males is not as common. Raptors come to mind.

IAC, the issue is not selection for size, it's selection for size differential. Diamond says that size differential maps directly to harem size. Female control seems likely to part of it. Watch impala males herd their harem is an example of mating behavior that is designed around males controlling females. (Impala males are territorial, females are not. Impalas retain reproductive control by keeping females in their territory.)

But there's no reason to focus on people when you're talking about dimorphism. Dimorphism is common.

And I can't remember the story that explains why raptors are dimorphic, with the female being larger, or I'd offer it here.

959. jayackroyd - April 28, 1999 - 11:24 AM PT
BTW, this discussion of dimorphism in the small, where men are said to prefer smaller women is backwards, isn't it? If you're using the standard sexual selection scenario, it's the female doing the selecting. And that is how it works, anyway, isn't it? Men are suitors and wooers, women are choosers.

That's borne out, anecdotally, by my reading of the personals pages. You never see a guy specifying a desire for a short woman, even if the guy is short. But it's not at all uncommon to see "SWF, 5'10", fit and peppy, seeks soulmate, at least 6'."

960. seguine - April 28, 1999 - 12:21 PM PT
Gentlemen, while a number of responses to your objections (and corrections of Res's assertions) are itching to fly off my fingertips, I'm painfully short of time. If I get back to this discussion it won't be for a while. Apologies.

961. seguine - April 28, 1999 - 12:32 PM PT
But this I can't reisist: "If you're using the standard sexual selection scenario, it's the female doing the selecting."

But I am *not* using the standard sexual selection scenario. I think it's plainly inadequate.

"And that is how it works, anyway, isn't it? Men are suitors and wooers, women are choosers."

This, of course, is why women never decorate themselves.

It's obvious to most women, if someone would only consult us, that males do indeed exercise choice, and women do a vast amount of wooing and suiting. People are not bower birds.

962. jayackroyd - April 28, 1999 - 12:40 PM PT
Message #957

But that's not gonna exert selection pressure on the adult females you were asserting would be pressured. Keep in mind that fossil evidence hunter/gatherer societies show a higher average level of health than sedentary agriculturalists. They tend to be taller, and show less evidence of youthful malnutrition. People can and do eat an enormous variety of food. It's hard to starve out a hunter/gatherer. But you decide to try to increase the carry capacity of an area through cultivating only a few crops, your population will grow to that carrying capacity. Then crop failure means famine.


See The Third Chimpanzee pages 185-187.

"The average height of hunter-gatherers in (Greece and Turkey) toward the end of the Ice Age was a generous 5 feet ten inches for men, five feet six inches for women. With the adoption of agriculture, height crashed reaching by 4000 BC a low value of only five feet three for men, five feet one for women."

963. jayackroyd - April 28, 1999 - 12:48 PM PT
Message #961

"People are not bower birds."

True. But people are also not free from purely biological pressures.

Do you disagree that women tend to prefer men to be taller than they are? I honestly think this is more common, in this society, than men who prefer women who are shorter. I'll pick up the Voice today, and give you a height reference count.

On decoration, and women wooing and so forth I take your point. Howsoever, it's a stealthy kind of wooing, wouldn't you say?

964. jayackroyd - April 28, 1999 - 12:48 PM PT
Message #961

"People are not bower birds."

True. But people are also not free from purely biological pressures.

Do you disagree that women tend to prefer men to be taller than they are? I honestly think this is more common, in this society, than men who prefer women who are shorter. I'll pick up the Voice today, and give you a height reference count.

On decoration, and women wooing and so forth I take your point. Howsoever, it's a stealthy kind of wooing, wouldn't you say?

965. Slackjaw - April 30, 1999 - 1:20 PM PT
Team,

not sure who is still reading this thread, but I have not given up on it. I have some game theory of my own to do, so that one day I can be paid to sit around and contemplate game theory.

966. uzmakk - May 4, 1999 - 3:16 PM PT
Lurk.

967. dexceus - May 6, 1999 - 9:25 AM PT
I've just recently wondered into the Fray and found this wonderful thread. After reading through all the posts I just have to make a coulle of comments.
First, I've absolultey loved Slackjaw's thread on Game Theory. I'm an undergrad Psychology student and ran into Game Theory last year while reading about Evolutionary Psychology (the books were _The Selfish Gene_ by Richard Dawkins and _The Moral Animal_ by Robert Wright) THey breifly touched on the subject and it facinated me. Unfortunatley I haven't had the time or money to persue it on my own. You managed to make it understandable and interesting to someone who isn't all the mathmaticly inclined.
Second, on the ongoing thread about why men would perfer smaller woman, your missing something big here. Remeber that small size is a sign of youth which normaly can be equated with fitness to breed. Males will almost always choose youth over all other 'postive' traits, while females will almost always choose resources (or ability to aquire resources) over anything else.

Dexceus

968. jayackroyd - May 6, 1999 - 2:00 PM PT
"small size is a sign of youth"

only if the female is not mature.

969. ChristinO - May 6, 1999 - 2:18 PM PT
Short in stature and wide of hip means more easily physically subdued, cheaper to feed but still fit for childbearing.

970. jayackroyd - May 6, 1999 - 2:21 PM PT
But the claim above is not that short women are more attractive--and I don't think you'll find any evidence for that.

The claim is that men prefer shorter women to taller women.

It's my claim that women prefer men who are taller than they are more than men prefer women who are shorter than they are. I did do my Voice personals study, and it does bear this out. I'll post the numbers tomorrow.

971. MsIvoryTower - May 6, 1999 - 2:25 PM PT
I think men have a preference for young women, and don't much care whether they're short, tall or medium.

On the other hand, I think women have a decided preference for men who are taller than they are, not necessarily the tallest man, but definitely taller than they are.

972. ChristinO - May 6, 1999 - 2:31 PM PT
Jay,

Pardon if I'm being dense, but are you saying men prefer short women because they're less attractive than tall women?

If short women are preferred then they are more attractive regardless of how one feels about Cindy Crawford. Preference decides attractiveness.


MsiT,
Essentially I think it's a protective v "macho" thing. A woman wants a man who is physically larger because he makes her feel protected. A man wants a woman who is smaller because she makes him feel strong.

973. ChristinO - May 6, 1999 - 2:33 PM PT
Okay, mine is the last name in too many threads at this point so I'm off to the chuck-wagon.

See you in a bit.

974. dexceus - May 6, 1999 - 4:06 PM PT
"small size is a sign of youth"

"only if the female is not mature."

Short women are often mistaken for being much younger then they are, evne if they are mature. My mother is pretty short, when I was in elemetnary school my friends thought she was my older sister who was in high school. She was 33 at the time. So a shorter stature can 'trick' a male into beleiving that the female is younger and therefore more able to bear children.

975. Slackjaw - May 7, 1999 - 12:04 AM PT
dexceus: thanks for your kind words about this thread. I regret that I haven't had time to push along in this thread lately.

But, here are some fun facts.

Strange but true: The current issue of Slate actually contains not one but TWO articles related to fundamental work on game theory, and more particularly, mechanism design theory. I am referring to the new Explainer on Dutch auction IPOs, and Steve Landsburg's new Everyday Economics.

In fact, these are special cases of the two very research topics that led to the Nobel Prize winning research of William Vickrey (on auctions) and James Mirrlees (on taxation), recognized by the Royal Swedish Academy of Sciences in 1996.

Interestingly, when the 1996 Economics Nobel was awarded for this work, some people cited it as an example of the irrelevance of the prize and the science of economics in general. What was all this cockamamie theoretical work, and who gave a damn? I will just note that within the last year, Slate has published at least 4 articles containing practical insights derived *directly* from mechanism design and the theory of auctions.

One thing in the Explainer that confused me was the assertion that the Dutch auction leads to more revenue in theory. Vickrey won the Nobel in part for showing that this isn't true. He proved the astonishing fact that 1st price sealed bid, 2nd price, English (traditional) and Dutch auctions yield EXACTLY the same expected revenue! In fact, you can read about it in The 1996 Nobel Press Release (do a search on Dutch Auctions, or read the whole document if you're interested). So I don't understand why Explainer claimed otherwise. I'm waiting for a reply.

976. Slackjaw - May 7, 1999 - 12:06 AM PT
Of course, I thought that perhaps the difference is that Vickrey's revenue equivalence result is for an auction for one good. The IPO is an auction for several goods (multidimensional). Of course, this could not have led to Explainer's assertion about the theoretical properties of the multidimensional Dutch auction, because we don't really know them yet! (A student here is working multidimensional auctions, and my advisor wrote a thesis on them some years ago, but it is just such a hard problem that not much is known.)

Do read the whole Nobel press release if mechanism design/implementation theory is interesting to you. There is a lot of material and it can keep you busy for a while.

I should say, there are MANY, MANY (infinitely many, in fact) different types of Auctions, most of which don't have names. The Revenue Equivalence Theorem holds for a much wider class than was originally recognized by Vickrey in his research.

This stuff all falls under the rubric of Bayesian game theory, or games of incomplete information, which is maybe two topics away in my grand outline.

977. Slackjaw - May 7, 1999 - 12:20 AM PT
speaking of Bayesian game theory, when we get there we ought to have a digression on Bayesian statistics, which is a special case of Bayesian game theory. It is really cool how it totally thrashes the classical statistics everyone learned as an undergraduate.

There is one example of a classical hypothesis test that is at the .95 level of confidence, but one application of Bayes' Theorem shows that the HALF of all rejections of the null hypothesis are wrong! (.95 level of confidence means that if the null hypothesis is true, the test should recommend its rejection in no more than 5% of observed samples.)

I will dig it up; it's totally fascinating.

978. uzmakk - May 7, 1999 - 10:50 AM PT
Mechanism design? Sounds great slackjaw. Your thread requires real work, real consideration, and I don't have time for it. My sister is a statistics type. I am going to print out large sections of your thread and show them to her this weekend and we will chat about them, and I will be smarter the next time I communicate with you. Just to let you know that I appreciate your thread.

979. jayackroyd - May 7, 1999 - 11:14 AM PT
"Pardon if I'm being dense, but are you saying men prefer short women because they're less attractive than tall women?

If short women are preferred then they are more attractive regardless of how one feels about Cindy Crawford. Preference decides attractiveness."

I'm saying men tend to care about height difference less than women do, that women tend to prefer to be with a man who is taller than she is, and that's where dimorphism in the small comes from. That's consistent with the standard sexual selection story, where females select male traits.

My informal personals study did bear this out. I left the damn Voice at home again, but something like 9 out of 92 women looking for men specified height greater than the advertisers, while 4 out of 107 men looking for women specified height shorter than the advertiser. One (I can't remember which gender) specified the opposite way.

One thing I noticed in going through the ads is that men tend to specify their height more often than women, while women tend to specify their weight. In both cases, when they do specify, the men are 5'10" or more, and the women are under 150 lbs. I didn't do a count on those, so the claim may just be observer bias.

980. Slackjaw - May 7, 1999 - 11:20 AM PT
thanks Ooze.

Explainer told me that ordinary IPOs aren't auctions at all; to his credit this really is clear from the column.

981. ChristinO - May 7, 1999 - 1:09 PM PT
Jay,

Oh, okay, I get it.

I've also noticed the height/weight division along gender lines. According to the personal ads there seems to be no greater crime than for a man to be short or for a woman to be fat. Another thing I've noticed, though, is that men specify weight requirements more often than women specify height requirements. I would suppose that to mean that most women just assume that most men will be taller than them anyway but that most men assume that the majority of women who respond to personal ads will be fatter than they desire.

982. RustlerPike - May 9, 1999 - 4:50 AM PT

ChrisO:

I e-mail you, I ICQ you - no answer. What's a guy gotta do to get a reply from you?

983. ChristinO - May 10, 1999 - 11:25 AM PT
I'll send to you. I don't know what's up. It's good to see you!

984. dexceus - May 10, 1999 - 12:37 PM PT
Slackjaw,
Just curious, do you plan on going into any other games besides Prisoner's Dillema? It's the only one that I'm really familliar with and would love to hear about some of the other ones. Thanks.

985. Slackjaw - May 10, 1999 - 2:27 PM PT
yeah Dex...have you seen the previous stuff on legal regimes and oligopoly? That's pretty different from PD. I will round up the posts if you haven't seen it.

I do feel compelled to talk about PD though, even though it is overworked, because there seem to be many misconceptions about it. But, as for collective action, stag hunt and chicken are also interesting.

For the next topic, dynamic games and subgame perfection, I plan examples based on fairly canonical games--centipede, chain store paradox, ultimatum, dictator...but also repeated PD. Just to show what happens.

986. Slackjaw - May 10, 1999 - 2:28 PM PT
I will also talk about some experimental evidence from behavioral game theory, stuff you should find interesting.

987. dexceus - May 11, 1999 - 7:27 AM PT
Slackjaw,
Yes, I did read that and have found it very interesting. I was mainly refering to some of the games that you had mentioned in passing , but had not gone into. I very much look forward to your continued posts. They have been really good and highly educational. ONe of these days I'm going to go back through here and print out all of your posts so I'll have a reference.

988. Slackjaw - May 12, 1999 - 6:15 PM PT
here is an interesting little game to puzzle over, called the beauty contest. I actually posted this in the fray last summer, but now that we have gone through the mechanics of Nash equilibrium and dominant strategies, it's illustrative to go through it again.

It's like this: you and a group of people of size n are each to name a number between 0 and 100. The person who names a number closest to 2/3 of the AVERAGE number named wins a desirable prize. The rest get nothing. What number should you name?

Hint: proceed by iterated deletion of dominated strategies. Ask yourself, what numbers could NEVER win this game? Then eliminate them. Then analyze the remaining game, with those numbers eliminated, in exactly the same fashion.

It's called the beauty contest because of its similarity to an English newspaper game noted by John Maynard Keynes (that's pronounces "CANES," by the way). Evidently some newspaper would publish a list of faces, and the charge was to pick the one most commonly identified as the most beautiful. Keynes himself compared this to picking stocks: you don't want the ones that will do best, but the ones that common sentiment thinks will do best, or maybe the ones that common sentiment thinks that common sentiment thinks will do best, or...

989. Slackjaw - May 12, 1999 - 6:17 PM PT
this is a great game to study experimentally, because the answer one gives says something about his or her thought process, and how it compares to the game theoretic benchmark.

990. AuNaturel - May 12, 1999 - 6:47 PM PT
The word for what men prefer in a woman is "neotany", that is where the adult still retains the features of the immature. Turned up nose, hairlessness, reduced musculature. This preference probably came about because of an instictive feeling in males that big hairy muscular critters were competition. So females took advantage of not looking like a threat or competition.

Females compete and select just as much as males, just using a different strategy. The woman wants to mate with the highest status male(s) not only because that will produce the fittest offspring but because she wants the long term material and social advantages he can provide. She makes herself as desirable as she can to catch his eye and keep his attention long enough for a pair bond to form.

Of course this leads to many suitors losing out. She casts a wide net, draws in many fish and throws most of them back. The more attractive she is, the higher percentage of high status males she wil draw in.

High status males don't need to pick and choose. They have as much sex as they want with as many females as they can. They have to decide which available feamale(s) to pair bond with, if any.

Lower status females can have an incredible sex life with higher status males (if they chose) but usually get stuck pair bonding with a lower status male.

The Lowest status males take sloppy seconds and leftovers, if that.

991. Slackjaw - May 12, 1999 - 11:14 PM PT
by the way, I should have mentioned re. the beauty contest that if two people mention the same number, they flip a coin for the prize.

so, here's the solution (from the game theoretic point of view, anyway) to the beauty contest: 0. Indeed, this prediction is even more fundamental than one based on Nash equilibrium, in the sense that this is simply the result of iterated deletion of dominated strategies. 0 is thus not only the unique Nash equilibrium--we also say it is the unique rationalizable outcome. Rationalizability is much more closely connected to basic notions of economic rationality, and it is intimately connected to deletion of dominated strategies.

Specifically, one can tell straight away that no number greater than 66.666... could ever win this game; for if it did, the average pick would have to be greater than 100, which is not allowed. But of course everyone should know that--it doesn't require us to believe in Nash equilibrium or anything. But then the game is really only over numbers from 0 to 66.666..., and the largest possible pick in this game is (of course) 66.666..., so 2/3 of the average could NEVER be greater than 44.444444666..., so all choices should in turn be less than this. If you repeat this over and over, you eventually converge to zero as the unique choice for everyone.

And of course it's also a Nash equilibrium: suppose everyone else chose zero. Could you do better than choosing zero yourself? No, of course not. If you all choose zero, the average is 0, and 2/3 of 0 is still 0. Then you personally get 1/n chance at the prize (n is the number of people). If you choose a greater number, you have no chance at the prize. That's worse than what you get by choosing zero.

992. Slackjaw - May 14, 1999 - 6:04 PM PT
so, how do real people play the beauty contest?

Nobody really knows. But we know quite a bit about how undergraduates and CEOs play. Rough averages for various groups:

UCLA undegraduates: avg. guess of about 41
Pooled average, all undergrads: about 33
U. of Pennsylvania undergraduates: about 28
CEOs at a Wharton experiment: about 26
Caltech undergraduates: about 10

These are for novices, who've never seen this game or very much game theory before. These are also estimates for early rounds of experimental sessions. Typically, after a dozen or so rounds, almost all groups learn to play the Nash equilibrium, and averages converge to 0.

993. Slackjaw - May 14, 1999 - 6:11 PM PT
I should say, last summer in the Fray, with over 25 participants (who submitted answers to me privately), the average guess in beauty contest was about 19.

994. Slackjaw - May 15, 1999 - 4:54 PM PT
so the next natural theoretical topic in game theory is dynamic games of complete information. Remember, by "complete information," I simply mean that everyone's goals are common knowledge--there is no uncertainty about utility functions. By "dynamic game" I simply mean that the moves take place over time, rather than simultaneously as in the static games of complete information that have been covered up to this point.

Again the predictions about the outcome of a game will be based on the notion of equilibrium. We will come to see that different types of games require slightly different equilibrium notions however, and that these equilibrium notions are related in a natural way.

For dynamic games of complete information (for which I will here on out use the non-standard abbreviation "dgci"), the natural equilibrium concept is what's called a refinement of Nash equilibrium. The refinement is called "subgame perfection," leading to "subgame perfect Nash equilibrium."

It was proposed by a German economist named Reinhard Selten in 1975. It is important enough, and started a big enough literature, that Selten shared the 1994 Nobel Prize in Economics with John Nash (and another guy we'll get to later).

Basically, every subgame perfect Nash equilbrium (SPNE) is a regular old Nash equilibrium, but the converse is not true: there are Nash equilibria that are not subgame perfect. Basically, the reason is that there is a close correspondence between a dynamic game and a static game: every dynamic game has exactly one static representation, but a given static game could have come from any of several different dynamic games.

995. Slackjaw - May 15, 1999 - 4:57 PM PT
This is a little subtle and took me a while to understand when I first studied game theory. But think (once again) of the static prisoner's dilemma. It looks like this when represented as a static game (this is called the "normal" or "strategic" form):

..__d___c__
d|1,1..|4,0....|
.|____|____|
c|0,4..|3,3....|
.|____|____|

It's hard to represent in the fray, but interpret the table like this: first, ignore all periods. They are place holders. d refers to defect, c to cooperate. The d and c that are on the vertical are player 1's strategies, those on the horizontal are player 2's. The numbers in the table are payoffs--the first number is player 1's payoff from a given strategy combination; the second number is player 2's. For example, if (d,c) is played, or player 1 defects and player 2 cooperates, then player 1 gets 4 and player 2 gets 0.

There are several possible dynamic versions of the PD, that would each be represented in the normal form exactly above. For example, in the dynamic game (represented in "extensive form"), player 1 may move first, or player 2 may move first. Both of these extensive form could be represented as a static game, with the normal form above.

The reason is that a strategy in the normal form of a game is to be interpreted simply as a complete plan of action for the whole game, a choice from the set of things you can do whenever it's your turn to do something. Imagine the PD where player 1 moves first, but strategies and payoffs are as usual. It's true, player 1 moves before player 2, but we can still represent this extensive form with the normal form above: player 2 knows all the things player 1 can do, and knows what happens if she chooses any of her possible responses, so she should be able to tell before the game even starts what she will do in any possible contingency.

996. Slackjaw - May 15, 1999 - 4:58 PM PT
It's as if she writes down her planned action in each possible contingency, hands it in an envelope to a referee, and lets the referee actually execute the action for her. Note that this assumes a certain amount of committment: she can say, "when it's my turn, I want to take action X." The issue of credibly committment is why SPNE differs from Nash equilibrium--some Nash equilibria involve incredible committments; SPNE don't, by the nature of their construction.

So what the hell is a subame? It's any piece of a larger dynamic game (extensive form game) that can be interpreted as a game in itself. For example, suppose in the dynamic PD here, player 1 chooses C. Then player 2 can either choose C or D, but starting at this point where player 2 must so choose, we simply have a (1 person) game. This is a subgame. A subgame can start at any decision point in an extensive form game but must go all the way to the end of the game.

SPNE simply says that a Nash equilibrium of the whole game is unreasonable if it's not a Nash equilibrium in EVERY subgame. Remember, a Nash equilibrium is simply a combination of strategy choices such that each player is maximizing his utility by choosing his part of said strategy combination, *given* the choices of all the other players.

It may seem startling that not all Nash equilibria have this property, but they don't. A great example comes from a game called the Ultimatum game. It works like this: there are 2 players, and player 1 is given a pile of money. In the game's first move, she can propose any division of the pile she likes between herself and player 2. In the second move, player 2 can either accept or reject the offer. If 2 accepts, the players get the shares 1 proposed. If 2 rejects, neither player gets anything.

(cont.)

997. Slackjaw - May 15, 1999 - 4:59 PM PT
What possible divisions of the pie can be Nash equilibria? A moment's reflection will show that, assuming more money is always better than less, ALL of them are! For suppose player 2's strategy is "reject any offer less than the whole pie minus $.01." If player 1 offers 2 any less than this, 2's strategy dictates that the offer be rejected. But then both players get nothing, and 1 prefers a penny to nothing. So, given this strategy for 2, the best 1 can do is offer the whole pie minus a penny.

OTOH, if player 1 is going to offer 2 the whole pie minus 1 cent, then clearly the strategy for 2 of "reject anything less than the whole pie minus 1 cent" maximizes 2's share of the pie, and hence, by assumption, his utility.

In short, given the other strategy, each player maximizes utility by choosing as specified above.

This outcome may seem quite incredible--1 seems to have a lot of "bargaining power," but only gets a penny. What is wrong with this?

It is predicated on an implicit threat by 2 that 2 might not want to carry out if he ever had to. For example, suppose that 1 deviated from the above strategy, and instead offered 2 the whole pie minus 2 cents. 2's strategy dictates that 2 must reject this offer. But would 2 want to do that? By rejecting, 2 gets nothing. By accepting, 2 gets the whole pie minus 2 cents, which is better than nothing. Indeed, 2 would NOT want to carry out the threat if push came to shove!

This simply says that rejecting the whole pie minus 2 cents is not a subgame perfect Nash equilibrium: the contingency where player 2 is offered the whole pie minus 2 cents is a subgame (with just one player, player 2). SPNE requires that player 2 must maximize his utility in this subgame. That requires accepting the offer, even though his strategy said he would reject it in this contingency.

(cont.)

998. Slackjaw - May 15, 1999 - 4:59 PM PT
(last for now)

A little more reflection will show that 2 does at least as well by accepting ANY offer as he does by rejecting it. That means that in EVERY subgame, it is a Nash equilibrium for 2 to accept the offer, whatever it was!

But now we have another subgame to consider, namely the whole game (which can, in a strange sematic twist, actually also be a subgame--in the sense that a set is necessarily a subset of itself). Now we know what player 2 will do in his subgame--accept any offer. But player 1 knows player 2's strategic environment and preferences, so 1 knows that 2 will do this. Thus, the best thing for player 1 to do is offer NOTHING!!

This offer, the whole pie for 1, none for 2, is the UNIQUE subgame perfect Nash equilibrium in this game. This is because 2 must accept any offer in equilibrium in the subgame starting after 1's offer, and 1 knows this. 1 must maximize utility in the subgame starting when she gets to make an offer, so she offers the mimimum possible.

This illustrates why subgame perfection is called a refinement of Nash equilibrium. A SPNE is still a Nash equilibrium, but there are many Nash equilibria that are not subgame perfect. Amazingly, this refinement in this game reduces the set of Nash equilibria from ALL possible allocations to just ONE of them!!

The bite of SPNE relative to Nash equilibrium is not always that huge. Consider the PD, for example, in extensive form. Imagine the subgame starting on player 2's move. We know that 2's strictly dominant strategy is to defect, so whatever 1 does, 2 will want to defect. 1 can of course look ahead and forecast this choice, because he can solve 2's problem just as well as 2 can. So in maximizing utility of the subgame starting at his move, player 1, knowing that 2 will defect, chooses to defect. Thus SPNE predicts exactly the same strategies here as Nash equilibrium.

999. Slackjaw - May 15, 1999 - 9:53 PM PT
actually, for people who followed this thread from the beginning (when it was "is philosophy dead?") may recognize the logic of subgame perfection. It is the process of "looking down the game tree," or what Dixit and Nalebuff in their book _Thinking Strategically_ call "look ahead and reason back."

It appeared in this thread as the logic underlying the paradox of the surprised prisoner presented by elliot. The formal name for this reasoning is "backward induction." Not because it is in some sense a backward style of reasoning, but because you start at the end of some decision problem and work your way back. In the problem elliot presented, it was a single person issue, but it is the same basic logic in the ultimatum game above.

Actually, the logic is much older than subgame perfection, but it has always been connected with decision theory and (more generally) game theory. It is, for example, how one solves tic tac toe: start at all the possible endings. Immediately prior to these, the person with the move (call her A) makes the decision leading to the outcome she prefers. Then immediately prior to that move, the other person (B) chooses which branch of the game tree he wants A to be on, taking account of the fact that A will choose her most advantageous move. Then A on the move prior to the one B just made, A can perfectly forecast how the rest of the game will be played, contingent on each of her possible actions. She thus chooses on this turn the action that leads to the outcome she likes best, given the optimal strategies in all future subgames. And so on, to the beginning of the game.

1000. Slackjaw - May 15, 1999 - 9:53 PM PT
Backward induction is also the backbone of dynamic programming, the branch of decision theory that deals with single-person decisions made over time, which was developed in the '50s. As with everything else in decision theory (and game theory), you convert the big problem into a series of littler problems, each of which is of the form of the only kind of problem we really know how to solve: one-person static decision problems. But that conversion has to be clever, so that the solutions to the littler problems lead to a coherent solution to the bigger one.

In principle, it is also how one would solve chess, and it is responsible for the implication that chess has a solution, in the same sense that tic tac toe does. Indeed, this is a special case of the very first theorem ever proved on game theory. Of course, chess is quite simply much much too complicated to be fruitfully analyzed in this way. There are far too many possible games to consider--as I've said before, rumor has it that there are more possible chess games than molecules in the universe.

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