Mathematical Modeling Of Menopause

Some states of affairs are so ubiquitous in the natural world that – much like the air we breathe – we stop noticing their existence or finding them particularly strange. The effects of aging are good examples of this. All else being equal, we ought to expect organisms that are alive longer to reproduce more. The longevity/reproduction link would seem to make the previously-unappreciated question of why organism’s bodies tend to breakdown over time rather salient. Why do organisms grow old and frail, before one or more homeostatic systems start failing, if being alive tends to aid in reproduction? One candidate explanation for understanding senescence involves.considering the trade off between the certainty of the present and the uncertainty of the future; what we might consider the discount rate of life. Each day, our bodies need to avoid death from a variety of sources, such as accidental injuries, intentional injuries from predators or conspecifics, the billions of hungry microorganisms we encounter, or lacking access to sufficient metabolic resources. Despite the whole world seemingly trying to kill us constantly, our bodies manage to successfully cheat death pretty well, all things considered.

“What do we say to death? Not to..OH MY GOD, WHAT’S BEHIND YOU?”

Of course, we don’t always manage to avoid dying: we get sick, we get into fights, and sometimes we jump out of airplanes for fun. Each new day, then, brings new opportunities that might result in the less-than-desirable outcome, and the future is full of new days. This makes each day in the future that much less valuable than each day in the present, as future days come with the same potential benefits, but all the collective added risk. Given the uncertainty of the future, it follows that some adaptations might be designed to increase our chances of being alive today, even if they decrease our odds of being alive tomorrow. These adaptations may well explain why we age the way we do. They would be expected to make us age in very specific ways, though: all our biological systems ought to be expected to breakdown at roughly the same time. This is because investing tons of energy into making a liver that never breaks doesn’t make much sense if the lungs give out too easily, as the body with the well-functioning liver would die all the same without the ability to breathe; better to divert some of that energy from liver maintenance to lung function.

As noted previously, however, being alive is only useful from an evolutionary perspective if being alive means better genetic representation in the future. The most straightforward way of achieving said genetic representation is through direct reproduction. This makes human menopause a very strange phenomenon indeed. Why do female’s reproductive capabilities shut off decades before the rest of their body tends to? It seems that pattern of loss of function parallels the liver/lungs example. Further, as the use of the word ‘human’ suggests, this cessation of reproductive abilities is not well-documented among other species. It’s not that other species don’t ever lose the capacity for reproduction, mind you, just that they tend to lose it much closer to the point when they would die anyway. This adds a second part to our initial question concerning the existence of menopause: why does it seem to only really happen in humans?

Currently, the most viable explanation is known as “The Grandmother Hypothesis“. The hypothesis suggests that, due to the highly-dependent nature of human offspring and the risks involved in pregnancy, it became adaptive for women to cease focusing on producing new offspring of their own and shift their efforts towards investing in their existing offspring and grandoffspring. At its core, the grandmother hypothesis is just an extension of kin selection: the benefits to helping relatives begin to exceed the benefits of direct reproduction. While this hypothesis may well prove to not be the full story, it does have two major considerations going for it: first, it explains the loss of reproductive capacity through a tradeoff – time spent investing in new offspring is time not spent investing in existing ones. It doesn’t commit what I would call the “dire straits fallacy” by trying to get something for free, as some standard psychology ideas (like depressive realism) seem to. The second distinct benefit of this hypothesis is perhaps more vital, however: it explains why menopause appears to be rather human-specific by referencing something unique to humans – extremely altricial infants that are risky to give birth to.

A fairly accurate way to conceptualize the costs of the pregnancy-through-college years.

A new (and brief) paper by Morton, Stone, & Singh (2013) sought to examine another possible explanation for menopause: mate choice on the part of males.The authors used mathematical models to attempt and demonstrate that, assuming men have a preference for young mates, mutations that had deleterious effects on women’s fertility later in life could drift into fixation. Though the authors aren’t explicit on this point, they seem to be assuming, de facto, that human female menopause is a byproduct of senescence plus a male sexual preference for younger women, as without this male sexual preference, their simulated models failed to result in female menopause. They feel their models demonstrate that you don’t necessarily need something like a grandmother hypothesis to explain menopause. My trust in results derived from mathematical models like these can be described as skeptical at the best of times, so it should come as no surprise that I found this explanation lacking on three rather major fronts.

My first complaint is that while their model might show that – given certain states of affairs held – explanations like the grandmother hypothesis need not be necessary, they fail to rule out the grandmother hypothesis in empirical or theoretical way. They don’t bother to demonstrate that their state of affairs actually held. Why that’s a problem is easy to recognize: it would be trivial to concoct a separate mathematical model that “demonstrated” the strength of the grandmother hypothesis by making a different set of assumptions (such as by assuming that past a certain age, investments returned in existing offspring outweighed investments in new ones). Yes; to do so would be pure question-begging, and I fail to see how the initial model provided by Morton et al (2013) isn’t doing just that.

My second complaint is, like the grandmother hypothesis, Morton et al’s (2013) byproduct model does consider tradeoffs, avoiding the dire straits fallacy; unlike the grandmother hypothesis, however, the byproduct account fails to posit anything human-specific about menopause. It seems to me that the explanation on offer from the byproduct account could be applied to any sexually-reproducing species. Trying to explain a relatively human-specific trait with a non-human-specific selection pressure isn’t as theoretically-sound as I would like. “But”, Morton et al might object, “we do posit a human-specific trait: a male preference for young female mates“. A fine rebuttal, complicated only by the fact that this is actually the weakest point of the paper. The authors appear to be trying to use an unexplained-preference to explain the decline in fertility, when it seems the explanation ought to run in precisely the opposite direction. If, as the model initially assumes, ancestral females did not differ substantially in their fertility with respect to age, how would a male preference for younger females ever come to exist in the first place? What benefits would arise to men who shunned older – but equally fertile – women in favor of younger ones? It’s hard to say. By contrast, if our starting point is that older females were less fertile, a preference for younger ones is easily explained.

No amount of math makes this an advisable idea.

Preferences are not explanations themselves; they require explanations. Much like aging, however, people can take preferences for granted because of how common they are (like the human male’s tendency to find females of certain ages maximally attractive), forgetting that basic fact in the process. The demonstration that male mating preferences could have been the driving force explaining the existence of menopause, then, seems empty. The model, like many others that I’ve encountered, seems to do little more than restate the author’s initial assumptions as conclusions, just in the language of math, rather than English. As far as I can see, the model makes no testable or novel predictions, and only manages to reach that point by assuming a maladaptive, stable preference on the part of men. I wouldn’t mark it down as a strong contender for helping us understand the mystery of menopause.

References: Morton, R., Stone, J., & Singh, R. (2013). Mate Choice and the Origin of Menopause PLoS Computational Biology, 9 (6) DOI: 10.1371/journal.pcbi.1003092

How Much Does Amanda Palmer Trust Her Fans?

A new TED talk was put out today (though it won’t be today anymore by the time you read this) by Amanda Palmer entitled, “The Art of Asking”, which you can watch here. If the comments on the YouTube page of the talk are to be believed, it truly was an inspiring affair. Professional cynic that I am, the talk didn’t do much to inspire me; at least not in the way that Amanda probably intended it to. Now, for those of who you don’t know her, Amanda is (primarily, I think) famous for her music in The Dresden Dolls. One of the main thrusts of her talk centers around the question she poses towards the end: how do we let people pay for music, rather than how do we get people to pay for music. Part of Amanda’s answer to this question was to allow people to download her music on her website and let them pay whatever price they wanted for the download. So, if someone downloaded Amanda’s music from her site, they had the option of paying $0, $1, $5, $10, $15, $20, or $100 for it. Amanda further suggests that she views this as a sort of “trust” in her fans, presumably because she had given people the option of paying nothing, which is the option most economists would consider the “rational” one. While her talk is delivered with a strong emotional tone and the message is ostensibly positive, Amanda is still a human, so my guess is that there’s more to her trust than meets the eye.

And more than meets the shaved-off eyebrows as well

Admittedly, I don’t know much about Amanda beyond what I just heard. Though I am familiar with her music to some degree, I’ve never followed her personal life at all. Here’s what I do know: a quick browsing of her website shows me that while she will indeed allow people to choose their own price for her music and download it, she doesn’t seem to have that same policy towards shirts, CDs, vinyl, posters, art books, or the shipping and handling required to send any of them out. Something (the tour section of her website) also tells me the venues she plays at – which I’m imagining represent a substantial proportion of her income – don’t allow anyone to come in to see the show and pay whatever they feel like for tickets. It would seem that telling people, rather than asking them, to pay is the norm; not her exception. This raises the inevitably question: to what extent does the choose-your-own-price option reflect a genuine leap of faith, and how much of her TED talk is actually cheap talk?

Cheap talk is just what it sounds like: it’s a signal that is easy to produce. Like all signals, it functions to attempt and persuade another individual to change their behavior. Cheap talk, however, is of very questionable value precisely because it’s so easy to manufacture. For instance, let’s say that a man tries to convince a woman at a bar to have sex with him. He tells her that he’s fabulously wealthy, will remain faithful to her throughout his life, and see to it that she wants for nothing if she agrees. Tempting offer no doubt, but what’s guaranteeing that any of the information that the man is sending is true? It costs the man almost nothing to say the words, and once the two have sex, he’s free to go back on his word without penalty. However, if that same offer is made after a month of courtship where the man has paid for multiple dates, consistently dressed in expensive clothes, and accompanies the offer with a diamond ring, wedding ceremony, and legal contract that entitles the woman to half of everything he owns, we’ve stepped out the realm of cheap talk into costly signals. Because of those high costs, the signal is much harder to fake, so its honesty can be better guaranteed.

Now Amanda would like us to think that her choose-your-own-price option represents a costly signal of trust towards her fans. Indeed, she may well consciously believe that it is one, just as most people consciously believe they’re better than average at things that the majority of other people or less likely to have bad things happen to them. Since her personal, potentially self-serving feelings about the whole thing don’t necessarily reflect reality, this brings us back to the “how costly is her gesture?” question. As the internet stands right now, whether a musician provides the option for free downloading on their own website or not, the option likely exists somewhere. It took me all of three seconds to find a list of websites where I could have downloaded Amanda’s album for free anyway. In other words, if someone wanted to download her album without paying, they likely could have. This suggests that her pay-nothing option isn’t as trusting as it initially comes across. Not only is she not creating that option where it didn’t exist before, but, in all likelihood, it would exist regardless of whether she wanted it to or not. Counting this as “trust” is a bit like my saying that I “trust” gravity to do what it does; I don’t really have a choice in the matter.

Physics has yet to disappoint

On top of that preexisting problem of music downloads already being available, there’s another: to the best of my knowledge, the costs to letting someone download her album are minimal. While one could argue about how much money she would lose on account of people not paying, I’m talking more about the physical costs of sending the information to someone’s computer. Since there really is no cost there – and because the option to download for free would exist with or without Amanda’s seal of approval – Amanda is essentially undertaking zero risk in providing her ostensibly-trusting option. It requires no investment and no need for desire. Without that risk, assessing the credibility of the signal becomes very difficult, as was the case with the sex example above. How trusting would Amanda be when there are some actual risks involved? When she has the ability to create that trusting option, will she? This is where Amanda’s other merchandise comes to the rescue.

Things like shirts, posters, and physical copies of CDs cost actual money to produce, and the option to get these things for free doesn’t already exist. Nothing is stopping Amanda from paying out of pocket to have these items made and allowing her fans to pay whatever they want for them (from $0 a shirt a $100, for instance), yet this isn’t what she does. Once actual risk enters the picture – once Amanda needs to make a real initial investment – her trust sees to dry up in a hurry. Apparently, she doesn’t trust her fans enough to adequately compensate her on a shirt and the shipping cost when she has the option to. One could argue, I suppose, that a handful of amoral people could, in principle, ruin her financially by ordering dozens or hundreds of shirts from her for free online, and that same risk isn’t posed by the downloading of a CD. That would be a fair point, except there are multiple ways around it: the requirement of a credit card for the purchase (whatever the purchase price ended up being), a limit on the number of free or cheap items, or the option available to pay whatever you want for the merchandise, but only at live concerts. Admittedly, I don’t know if she does the last one; I just suspect she doesn’t offer it as default option.

Forgetting about the merchandise, we could also discuss ticket prices to the shows as well. A quick browsing of the links for tickets on her tour schedule shows tickets that can range from $15 to $60. Now of course ticket prices aren’t being set by Amanda herself, but, then again, venues aren’t set in stone either. Presumably Amanda could, if she wanted to, only schedule herself to play at venues where ticket prices could be determined (at least largely) by the willingness of the people who show up to pay. I’m sure there are plenty of venues – though not necessarily traditional ones – that would at least consider such an offer. Rather than take this approach, however, Amanda’s “art of asking” seems to involve first demanding people pay full price for tickets and merchandise and, in addition, asking them to then pay more, whether that more came in the form of additional money placed into a hat she passes around the crowd, giving her food, places to stay, practice space, or other items of interest.

“How can we let people pay $7 for a cup of coffee and then let them pay us even more?”

Now none of this is to say that Amanda is a bad person. As I said, I don’t know nearly enough about her to make that judgment one way or the other. This is merely to point out that the “trust” Amanda has in her fans certainly has its limits – many of them – as pretty much anyone’s does. That’s just the point though; there doesn’t seem to be anything particularly special going on here. Despite there being nothing special about it, Amanda seems to be trying to play it off as if it’s some great exercise in trust. The impossible-to-assess pretense is the part of the talk that inspired this post. There’s also the matter of the kickstarter she mentions. Amanda asked for $100,000 on kickstarter and ended up making over a million. Now I don’t find anything particularly egregious about that; if her fans wanted to support her, nothing was stopping them. What I did find curious, though, what her analysis of how that money would be spent. It seemed that she had a legitimate need for almost the full million. While that’s fine if she does, what’s curious about that was is if she needed the full million, why didn’t she ask for, well, the full million? Why only ask for the hundred thousand that clearly would have been grossly insufficient for her plans? Something about that analysis strikes me as off as well. Then again, if a pretense of trust is easy to manufacture, so is a pretense of need.

“Nice Guys”, The Friend Zone, And Social Semantics

A little over a year ago, a video entitled, “Why men and women can’t be friends” was uploaded to YouTube. In the video, a man approaches various men and women and presents them with the question, “can men and women just be friends?”. While many of the woman answered in the affirmative, most of the men seemed to answer in the negative, suggesting that men would generally be interested in something more; something sexual. When asked about whether their male friends were interested in having sex them, many of the women seemed to similarly acknowledge that, yes, their male friends probably were interested, so maybe there was more lurking behind that “just friendship”. In a follow-up video, the same man asked whether it would be alright for people in relationships to hang out alone with same-sex friends. While the men seemed to be of relatively one mind (no, it would not be appropriate), women, again, initially stated that opposite-sex friends are fine. However, when confronted with the possibility of their significant other hanging out alone with a member of opposite-sex, the tune seemed to change dramatically: now men and women agreed that they would, indeed, be bothered by that state of events.

“And here I thought his sudden interest in jogging was purely platonic”

So why the discrepancy in women’s responses, but not men’s? Perhaps it’s simply due to the magic of video editing, where only certain responses were kept to make a point, but, working under the assumption that’s not happening, I think there’s something interesting going on here. Understanding what that something is will require us to dig deeper into two concepts that have been floating around for some time: “the friend zone” and “Nice guys”. The friend zone, as many of you know, refers to the context where someone wants a relationship with another, but that other doesn’t return the affection. Since the interest isn’t mutual, the party interested in the relationship settles for a friendship with the target of their affections, often with the hope that someday things will change. “Nice guys” on the other hand, are typically men who are stuck in the friend zone and, upon the eventual realization that their friendship will probably not transition into a relationship, become irritated with the person they were interested in, resulting in the friendship being called off and feelings being hurt. The friendship, after all, is not what they were after; they wanted the full relationship (or at least an occasional hook up).

“Nice guys”, in other words, are only being nice because they want to get sex, so they’re not really nice, people seem to feel; hence the quotation marks. Further, “nice guys” are frequently socially maligned, seemingly because of their (actually held or assumed to be held) attitude that women are obligated to have sex or start a relationship with them because they are nice (whether any substantial number of them consciously think this is another matter entirely). Alternatively, “nice guys” are looked down on because they view the friendship – or the friend zone – as, at best, a consolation prize to what they were actually going after or, at worst, something they couldn’t care less about having. The nerve of these people; insisting that just a friendship isn’t enough! There are some very peculiar things about the label of “nice guy”, though; things that don’t quite fit at first glance. The first of these is that the earning of the “nice guy” label appears to be contingent on the target of the affections not returning them. If whomever the “nice guy” is interested in does return the affections, there is no way to tell whether he was “nice guy” or one of those actually nice guys. In other words, you could have two identical guys enacting identical sets of behavior right up to the moment of truth: if the target returns the man’s affections, he’s a nice guy; if she doesn’t and the man doesn’t find that state of affairs satisfactory, he is now a “nice guy”; not a nice guy.

That, however, is only a surface issue. The much more substantial issue is in the label itself, which would, given its namesake, seem to imply that the problem is the nice behavior of the guys, rather than the attitude of entitlement that the label is ostensibly aimed at. This is very curious. If the entitled attitude is what is supposed to be the problem of the people this term is aimed at, why would the label focus on their otherwise nice behavior; behavior that might not differ in any substantial way from the behavior of genuine nice guys? Further, why is the label male-specific (it’s “nice guys” not “nice people”, and even when it’s a woman doing it, well, she’s just being a “nice guy” too)? With these two questions in mind, we’re now prepared to begin to tackle the initial question: why do women’s response to the friendship questions, but not men’s, seem discrepant?

“Thanks for taking me shopping; I’m so lucky to have a friend like you…”

Let’s take the questions in a partially-reversed order: the first is why the term focuses on the nice behavior. The answer here is would seem to revolve around the matter of cooperation and reciprocity more generally. In the social world, when an altruistic individual provides you with a benefit at a cost to themselves, the altruist generally expects repayment at some point down the line. It’s what’s called reciprocal altruism – or, less formally, cooperation – and forms the backbone of pretty much every successful social relationship among non-kin (Trivers, 1971). However, sometimes relationships are not quite as reciprocal in nature: one individual will continuously reap the benefits of altruism without returning them in kind. Names for those types of individuals abound, though the most common are probably exploiters or cheaters. Having a reputation as a cheater is, generally speaking, bad for business when it comes to making and maintaining friendships, so it’s helpful to maintain a good reputation amongst others.

The implications for why the “nice guy” label focuses on otherwise nice behavior should be immediately apparent: if someone is behaving nicely towards you – even if that nice behavior might be unwanted – it creates the expectation of reciprocity, both among the altruist and potentially other third parties. Failing to return the favor, then, can make one look like a social cheater. This obviously puts the recipient in a bind: while they would certainly like to enjoy the benefits of the nice individual’s behavior (free meals, social support, and so on), they don’t want to have the obligation to repay it if it’s avoidable (it’s that expectation that makes people uncomfortable about accepting gifts; not because they don’t want said gifts). So how can that obligation be effectively avoided? One way seems to be to question the altruist’s motives: if the altruist was only giving to get something else (like sex), and if that something else is viewed to be of substantially more valuable than what was initially given (also like sex tends to be), one can frame the ostensible altruist as the exploiter, the cheater, or, in this case, the “nice guy”. If a woman wants to either (a) reap the benefits of nice guys, (b) avoid the costs in not reciprocating what the nice guy wants, or (c) both, then the label of “nice guy” can be quite effective. Since there behavior wasn’t actually nice, there’s no need to reciprocate it.

Bear in mind, none of this needs to be consciously entertained. In fact, in some cases it’s better to not have conscious awareness of such things. For instance, to make that reframing (nice to “nice”) more successful, the person doing the reframing has to come off as having innocent motives themselves: if the woman in question was explicit about her desire to take advantage of men’s niceness towards her with no intentions of any repayment, she’s back to being the cheater in the situation (just as the “nice guy’s” behavior is back to just being plain old nice, if a bit naive). Understanding this point helps us answer the third question: why are women’s responses to the friendship question seemingly discrepant? Conscious awareness of these kinds of mental calculations will typically do a woman no favors, as they might “leak out” into the world, so to speak. To think of it in another way, you’ll have an easier time trying to convince people that you didn’t do something wrong if you legitimately can’t access any memories of you doing something wrong (as opposed to having access to those memories and needing to suppress them). To relate this to the answers in the videos, when a woman is receiving benefits from her male friends, keeping the knowledge that her male friends are trying to get something more from her out of mind can help her defend against the criticism of being a social cheater, as well as avoid the need to pay her male friends back. On the other hand, when it’s her boyfriend who’s now being “nice” to other women, there are benefits to her being rather aware of the underlying motives.

“I swear I was just giving her my opinion about her new bra as a friend!”

Finally, we turn to the answer to second question, the answer to which ought to be obvious by now: why is the “nice guy” term male-specific? This answer has a lot to do with the simple fact that, all else being equal, women do prefer men who invest in them, both in the short and long term, but investment plays a substantially lessened role for women in drawing and maintaining male interest (Buss, 2003). Put simply, males invest because females tend to find that investment attractive. So, to sum up, women want to receive investment and males are generally willing to provide that investment. However, male investment typically comes contingent on the possibility or reality of mating, and when that possibility is withdrawn, so too does male investment wane. The term “nice guy” might serve to both avoid the costs that come with receiving that investment but not returning it, as well as a potential shaming tactic for men who withdraw their niceness when it becomes clear that niceness will not pay off as intended. Similarly, a woman might doubt her partner’s “niceness” when it’s directed towards another. This analysis, however, only examines the female-end of things; males face a related set of problems, just from a different angle. Further, the underlying male strategy is, I assure you, not any less strategic.

References: Buss, D. (2003). The evolution of desire: Strategies of human mating. Basic Books: New York

Trivers, R. (1971). The Evolution of Reciprocal Altruism The Quarterly Review of Biology, 46 (1) DOI: 10.1086/406755

Should You Give A Damn About Your Reputation (Part 2)

In my last post, I outlined a number of theoretical problems that stand in the way of reputation being a substantial force for maintaining cooperation via indirect reciprocity. Just to recap them quickly: (1) reputational information is unlikely to be spread much via direct observation, (2) when it is spread, it’s most likely to flow towards people who already have a substantial amount of direct interactions with the bearer of the reputation, and (3) reputational information, whether observed visually or transmitted through language, might often be inaccurate (due to manipulation or misperception) or non-diagnostic of an individual’s future behavior, either in general or towards the observer. Now all of this is not to say that reputational information would be entirely useless in predicting the future behavior of others; just that it seems to be an unlikely force for sustaining cooperation in reality, despite what some philosophical intuitions written in the language of math might say. My goal today is to try and rescue reputation as a force to be reckoned with.

In all fairness, I did only say that I would try

The first – and, I think, the most important – step is to fundamentally rethink what this reputational information is being used to assess. The most common current thinking about what third-party reputation information is being used to assess would seem to be the obvious: you want to know about the character of that third party, because that knowledge might predict how that third party will act towards you. On top of assuming away the above problems, then, one would also need to add in the assumption that interactions between you and the third party would be relatively probable. Let’s return to the example of your friend getting punched by a stranger at a bar one night. Assuming that you accurately observed all the relevant parts of the incident and the behavior of the stranger there was also predictive of how he would behave towards you (that is, he would attack you unprovoked), if you weren’t going to interact with that stranger anyway, regardless of whether you received that information or not, while that information might be true, it’s not valuable.

But what if part of what people are trying to assess isn’t how that third party will behave towards them, but rather how that third party will behave towards their social allies. To clarify this point, let’s take a simple example with three people: A, B, and X. Person A and B will represent you and your friend, respectively; person X will represent the third party. Now let’s say that A and B have a healthy, mutually-cooperative relationship. Both A and B benefit form this relationship and have extensive histories with each other. Person B and X also have a relationship and extensive histories with one another, but this one is not nearly as cooperative; in fact, person X is downright exploitative over B. Given that A and X are otherwise unlikely to ever interact with each other directly, why would A care about what X does?

The answer to this question – or at least part of that answer – involves A and X interacting indirectly. This requires the addition of a simple assumption, however: the benefits that person B delivers to person A are contingent on person B’s state. To make this a little less abstract, let’s just use money. Person B has $10 and can invest that money with A. For every dollar that B invests, both players end up making two. If B invests all his money, then, both him and person A end up with $20. In the next round, B has his $10, but before he gets a chance to invest it with A, person X comes along and robs B of half of it. Now, person B only has $5 left to invest with A, netting them both $10. In essence, person X has now become person A’s problem, even though the two never interacted. All this assumption does, then, is make clear the fact that people are interacting in a broader social context, rather than in a series of prisoner’s dilemmas where your payoff only depends on your own, personal interactions.

Now if only there was a good metaphor for that idea…

With the addition of this assumption, we’re able to circumvent many of the initial problems that reputational models faced. Taking them in reverse order, we are able to get around the direct-interaction issue, since your social payoffs now co-vary to some extent with your friends, making direct interaction no longer a necessary condition. It also allows us to circumvent the diagnosticity issue: there’s less of a concern about how a third party might interact with you differently than your friend because it’s the third party’s behavior towards your friend that you’re trying to alter. It also, to some extent, allows us to get around the accuracy issue: if your friend was attacked and lies to you about why they were attacked, it matter less, as one of your primary concerns is simply making sure that your friend isn’t hurt, regardless of whether your friend was in the right or not. This takes some of the sting out of the issues of misperception or misinformation.

That said, it does not take all the sting out. In the previous example, person A has a vested interest in making sure B is not exploited, which gives person B some leverage. Let’s alter the example a bit, and say that person B can only invest $5 with person A during any given round; in that case, if X steals $5 from B’s initial $10, it wouldn’t affect person A at all. Since person B would rather not be exploited, they might wish to enlist A’s help, but find person A less than eager to pitch in. This leaves person B with three options: first, B might just suck it up and suffer the exploitation. Alternative, B might consider withholding cooperation from A until A is willing to help out, similar to B going on a strike. If person B opts for this route, then all concerns for accuracy are gone; person A helping out is merely a precondition of maintaining B’s cooperation. This strategy is risky for B, however, as it might look like exploitation from A’s point of view. As this makes B a costlier interaction partner, person A might consider taking his business elsewhere, so to speak. This would leave B still exploited and out a cooperative partner.

There is another potential way around the issue, though: person B might attempt to persuade A that person X really was interfering in such a way that made B unable to invest; that is, person B might try to convince A that X had really stolen $8 instead of $5. If person B is successful in this task, it might still make him look like a costlier social investment, but not because he is himself attempting to exploit A. Person B looks like he really does want to cooperate, but is being prevented from doing so by another. In other words, B looks more like a true friend to A, rather than just a fair-weather one or an exploiter (Tooby & Cosmides, 1996). In this case, something like manifesting depression might work well for B to recruit support to deal with X (Hagen, 2003). Even if such behavior doesn’t directly stop X from interfering in B’s life, though, it might also prompt A to increase their investment in B to help maintain the relationship despite those losses. Either way, whether through avoiding costs or gaining benefits, B can leverage their value with A in these interactions and maintain their reputation as a cooperator.

“I’ll only show back up to work after you help me kill my cheating wife”

Finally, let’s step out of the simple interaction into the bigger picture. I also mentioned last time that, sometimes, cooperating with one individual necessitates defecting on another. If person A and B allied against person X, if person Y is cooperating with X, person Y may now also incur some of the punishment A and B direct at X, either directly or indirectly. Again, to make this less abstract, consider that you recently found out your friend holds a very unpopular social opinion (say, that women shouldn’t be allowed to vote) that you do not. Other people’s scorn for your friend now makes your association with him all the more harmful for you: by benefiting him, you can, by proxy, be seen to either be helping him promote his views, or be inferred to hold those same views yourself. In either case, being his friend has now become that much costlier, and the value of the relationship might need to be reassessed in that light, even if his views might otherwise have little impact on your relationship directly. Knowing that someone has a good or bad reputation more generally can be seen as useful information in this light, as it might tell you all sorts of things about how costly an association with them might eventually prove to be.

References: Hagen, E.H. (2003). The bargaining model of depression. In: Genetic and Cultural Evolution of Cooperation, P. Hammerstein (ed.). MIT Press, 95-123

Tooby, J., & Cosmides, L. (1996). Friendship and the banker’s paradox:Other pathways to the evolution of adaptations for altruism. Proceedings of the British Academy (88), 119-143

Should You Give A Damn About Your Reputation? (Part 1)

According to Nowak (2012) and his endlessly-helpful mathematical models, once one assumes that cooperation can be sustained via one’s reputation, one ends up with the conclusion that cooperation can, indeed, be sustained (solely) by reputation, even if the same two individuals in a population never interact with each other more than once. As evidenced by the popular Joan Jett song, Bad Reputation, however, one can conclude there’s likely something profoundly incomplete about this picture: why would Joan give her reputation the finger in this now-famous rock anthem, and why would millions of fans be eagerly singing along, if reputation was that powerful of a force? The answer to this question will involve digging deeper into the assumptions that went into Nowak’s model and finding where they have gone wrong. In this case, not only are some of the assumptions of Nowak’s model a poor fit to reality in terms of the one’s he makes, but, perhaps more importantly, also poor in regards to what assumptions he doesn’t make.

Unfortunately, my reply to some current thinking about reputation can’t be expressed as succinctly.

The first thing worth pointing out here is probably that Joan Jett was wrong, even if she wasn’t lying: she most certainly did give a damn about her reputation. In fact, some part of her gave so much of a damn about her reputation that she ended up writing a song about it, despite that not being her conscious intent. More precisely, if she didn’t care about her reputation on any level, advertising that fact to others would be rather strange; it’s not as if that advertisement would provide Joan herself with any additional information. However, if that advertisement had an effect on the way that other people viewed her – updating her reputation among the listeners – her penning of the lyrics is immediately more understandable. She wants other people to think she doesn’t care about her (bad) reputation; she’s not trying to remind herself. There are a number of key insights that come from this understanding, many of which speak to the assumptions of these models of cooperation.

The initial point is that Joan needed to advertise her reputation. Reputations do not follow their owners around like a badge; they’re not the type of thing that can be accurately assessed on sight. Accordingly, if one does not have access to information about someone’s reputation, then their reputation, good or bad, would be entirely ineffective at deciding how to treat that someone. This problem is clearly not unsolvable, though. According to Sigmund (2012), the simple way around this problem involves direct observation: if I observe a person being mean to you, I can avoid that person without having to suffer the costs of their meanness firsthand. Simple enough, sure, but there are many problems with this suggestion too, some of which are more obvious than others. The first of these problems would be that a substantial amount – if not the vast majority – of (informative and relevant) human interactions are not visible to many people beyond those parties who are already directly involved. Affairs can be hidden, thieves can go undetected, and promises can be made in private, among other things (like, say, browsing histories being deleted…). Now that concern alone would not stop reputations derived from indirect information from being useful, but it would weaken its influence substantially if few people ever have access to it.

There’s a second, related concern that weakens it further, though: provided an interaction is observed by other parties, those who most likely to be doing the observing in the first place are the people who probably already have directly interacted with one or more of the others they’re observing; a natural result of people not spending their time around each other at random. People only have a limited amount of time to spend around others, and, since one can’t be in two places at once, you naturally end up spending a good deal of that time with friends (for a variety of good reasons that we need not get into now). So, if the people who can make the most use of reputational information (strangers) are the least likely to be observing anything that will tell them much about it, this would make indirect reciprocity a rather weak force. Indeed, as I’ve covered previously, research has found that people can make use of indirectly-acquired reputation information, and do make use of it when that’s all they have. Once they have information from direct interactions, however, the indirect variety of reputational information ceases to have an effect on their behavior. It’s your local (in the social sense; not necessarily physical-distance sense) reputation that’s most valuable. Your reputation more globally – among those you’re unlikely to ever interact much with – would be far less important.

See how you don’t care about anyone pictured here? The feeling’s mutual.

The problems don’t end there, though; not by a long shot. On top of information not being available, and not being important, there’s also the untouched matter concerning whether the information is even accurate. Potential inaccuracies can come in three forms: passive misunderstandings, active misinformation, and diagnosticity. Taking these in order, consider a case where you see your friend get punched in the nose from across the room by a stranger. From this information, you might decide that it’s best to steer clear of that stranger. This seems like a smart move, except for what you didn’t see: a moment prior your friend, being a bit drunk, had told the stranger’s wife to leave her husband at the bar and come home with him instead. So, what does this example show us? That even if you’ve directly observed an interaction, you probably didn’t observe one or more previous interactions that led up to the current one, and those might well have mattered. To put this in the language of game theorists, did you just witness a cooperator punishing a defector, a defector harming a cooperator, or some other combination? From your lone observation, there’s no sure way to tell.

But what if your friend told you that the other person had attacked them without provocation? Most reputational information would seem to spread this way, given that most human interaction is not observed by most other people. We could call this the “taking someone else’s word for it” model of reputation. The problems here should be clear to anyone who has ever had friends: it’s possible your friend had misinterpreted the situation, or that your friend had some ulterior motive for actively manipulating your perception that person’s reputation. To again rephrase this in terms of game theorist’s language, if cooperators can be manipulated into punishing other cooperators, either through misperception or misinformation, this throws another sizable wrench into the gears of the reputation model. If one’s reputation can be easily manipulated, this, to some extent, will make cooperation more costly (if one fails to reap some of cooperation’s benefits or can offset some of defection’s costs). Talk is cheap, and indirect reciprocity models seem to require a lot of it.

This brings us to the final accuracy point: diagnosticity. Let’s say that, hypothetically, the stranger did attack your friend without provocation, and this was observed accurately. What have you learned from this encounter? Perhaps you might infer that the stranger is likely to be an all-around nasty person, but there’s no way to tell precisely how predictive that incident is of the stranger’s later behavior, either towards your friend or towards you. Just because the stranger might make a bad social asset for someone else, it does not mean they’ll make a bad social asset for you, in much the same way that my not giving a homeless person change doesn’t mean my friends can’t count on my assistance when in need. Further, having a “bad” reputation among one group can even result in my having a good relationship with a different group; the enemy of my enemy is my friend, as the saying goes. In fact, that last point is probably what Joan Jett was advertising in her iconic song: not that she has a bad reputation with everyone, just that she has a bad reputation among those other people. The video for her song would lead us to believe those other people are also, more or less, without morals, only taking a liking to Joan when she has something to offer them.

The type of people who really don’t give a damn about their reputation.

While this in not an exhaustive list of ways in which many current assumptions of reputation models are lacking (there are, for instance, also cases where cooperating with one individual necessitates defecting on another), it still poses many severe problems that need to be overcome. Just to recap: information flow is limited, that flow is generally biased away from the people who need it the most, there’s no guarantee of the accuracy of that information if it’s received, and that information, even if received and accurate, is not necessarily predictive of future behavior. The information might not exist, might not be accurate, or might not matter. Despite these shortcomings, however, what other people think of you does seem to matter; it’s just that the reasons it matters need to be, in some respects, fundamentally rethought. Those reasons will be the subject of the next post.

References: Nowak, M. (2012). Evolving cooperation. Journal of Theoretical Biology, 299, 1-8.

Sigmund, K. (2012). Moral assessment in indirect reciprocity Journal of Theoretical Biology, 299, 25-30 DOI: 10.1016/j.jtbi.2011.03.024

The Tension Between Theory And Reality

“In theory, theory and practice are the same. In practice, they are not.”

There is a relatively famous quote attributed to Michelangelo who was discussing his process of carving a statue: “I saw the angel in the marble and carved until I set him free”. Martin Nowak, in his book SuperCooperators (2011), uses that quote to talk about his admiration for using mathematical models to study cooperation. By stripping away the “noise” in the world, one can end up with some interesting conclusions. For instance, it was through this stripping away of the noise that led to the now-famous programming competition that showed us how successful a tit-for-tat strategy can be. There’s just one hitch, and it’s expressed in another relatively famous quote attributed to Einstein: “Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed.” Imagine instead that Michelangelo had not seen an angel in the marble, but rather a snake: he would have “released” the snake from the marble instead. That Michelangelo “saw” the angel in the first place seemed to preclude his seeing the snake – or any number of other possible images – that might have potentially been representable by the marble as well. I should probably also add that neither the snake nor the angel were actually “in” the marble in the first place…

“You see a medium for high art; I see new kitchen countertops”

The reason I bring up Nowak’s use of the Michelangelo quote is that both in his book and a recent paper (Nowak, 2012), Nowak stresses the importance of both (a) using mathematical models to reveal underlying truths by stripping away noise from the world, and (b) advocates for the readdition of that noise, or at least some of it, to make the models better at predicting real-world outcomes. The necessity of this latter point is demonstrated neatly by the finding that, as the rules of the models designed to assess cooperation shifted slightly, the tit-for-tat strategy no longer emerged as victorious. When new variables – ones previously treated as noise – are introduced to these games, new strategies can best tit-for-tat handily. Sometimes the dominant strategy won’t even remain static over time, shifting between patterns of near universal cooperation, universal defection, and almost anything in between. That new pattern of results doesn’t mean that a tit-for-tat strategy isn’t useful on some level; just that it’s usefulness is restricted to certain contexts, and those contexts may or may not be represented in any specific model.

Like Michelangelo, then, these theoretical models can “see” any number of outcomes (as determined by the initial state of the program and its governing rules); like Einstein, these models can also only “see” what they are programmed to see. Herein lies the tension: these models could be excellent for demonstrating the many things (like group selection works), but many of many those things which can be demonstrated in the theoretical realm are not applicable to the reality that we happen to live in (also like group selection). The extent to which those demonstrations are applicable to the real world relies on the extent to which the modeller happened to get things right. For example, let’s say we actually had a slab of marble with something inside it and it’s our goal to figure out what that something is: a metaphorical description of doing science. Did Michelangelo demonstrate that this something was the specific angel he had in mind by removing everything that wasn’t that angel from an entirely different slab of marble?  Not very convincingly; no. He might have been correct, but there’s no way to tell without actually examining the slab with that something inside of it directly. Because of this, mathematical models do not serve as a replacement for experimentation or theory in any sense.

On top of that concern, a further problem is that, in the realm of the theoretical, any abstract concept (like “the group”) can be granted as much substance as any other, regardless of whether those concepts can be said to exist in reality; one has a fresh slab of marble that they can “see” anything in, constrained only by their imagination and programming skills. I could, with the proper technical know-how, create a mathematical model that demonstrates that people with ESP have a fitness advantage over those without this ability. By contrast, I could create a similar model that demonstrates that people without ESP have a fitness advantage over those with the ability. Which outcome will eventually obtain depends entirely on the ways in which I game my model in favor of one conclusion or the other. Placed in that light, (“we defined some strategy as working and concluded that it worked”) the results of mathematical modeling seem profoundly less impressive. More to the point, however, the outcome of my model says nothing about whether or not people actually have these theoretical ESP abilities in the first place. If they don’t, all the creative math and programming in the world wouldn’t change that fact.

Because, eventually, Keanu Reeves will stop you.

As you can no doubt guess by this point, I don’t hold mathematical modeling in the same high esteem that Nowak seems to. While its theoretical utility is boundless, its practical utility seems extremely limited, relying on the extent to which the assumptions of the programmer approach reality. With that in mind, I’d like to suggest a few other details that have not yet seemed to have been included in these models of cooperation. That’s not to say that the inclusion of these variables would allow a model to derive some new and profound truths – as these models can only see what they are told to see and how they are told to see it – just that these variables might help, to whatever degree, the models better reflect reality.

The first of these issues is that these cooperation games seem to be played using an identical dilemma between rounds; that is to say there’s only one game in town, and the payoff matrices for cooperation and defection remain static. This, of course, is not the way reality works: cooperation is sometimes mutually beneficial, other times mutually detrimental, and still others only beneficial for one of the parties involved, and all that changes the game substantially. Yes, this means we aren’t strictly dealing with cooperative dilemmas anymore, but reality is not made up of strictly cooperative dilemmas, and that matters if we’re trying to draw conclusions about reality. Adding this consideration into the models would mean that behavioral strategies are unlikely to ever cycle between  “always cooperate” or “always defect” as Nowak (2012) found that they did in his models. Such strategies are too simple-minded and underspecified to be practically useful.

A second issue involves the relative costs and benefits to cooperation and defection even within the same game. Sometimes defecting may lead to great benefits for the defector; at others, defecting may only lead to small benefits. A similar situation holds for how much of a benefit cooperation will bring to one’s partner. A tit-for-tat strategy could be fooled, so to speak, by this change of rules (i.e. I could defect on you when the benefits for me are great and reestablish cooperation only when the costs to cooperation are low). As cooperation will not yield identical payoffs over time more generally, cooperation will also not yield identical payoffs between specific individuals. This would make some people more valuable to have as a cooperative partner than others and, given that cooperation takes some amount of limited time and energy, this means competition for those valuable partners. Similarly, this competition can also mean that cooperating with one person entails simultaneously defecting against another (cooperation here is zero-sum; there’s only so much to go around). Competition for these more valuable individuals can lead to all sorts of interesting outcomes: people being willing to suffer defection for the privilege of certain other associations; people actively defecting on or punishing others to prevent those others from gaining said associations; people avoiding even trying to compete for these high value players, as their odds of achieving such associations are vanishingly low. Basically, all sorts of politically-wise behaviors we see from the characters in Game in Thrones that don’t find themselves represented in these mathematical models yet.

We might also want to add a stipulations for in-game beheadings.

A final issue is that information that individuals in these games are exposed to: it’s all true information. In the non-theoretical realm, it’s not always clear as to whether someone you’ve been interacting with cooperated or defected, or the degree of effort they put into the venture even if they were on the cooperating side of the equation. If individuals in these games could reap the benefits of defecting while simultaneously convincing others that they had cooperated, that’s another game-changer. Modeling all of this is, no doubt, a lot of work, but potentially doable. It would lead to all sorts of new set of findings about which strategies worked and which one didn’t, and how, and when, and why. The larger point, however, is that the results of these mathematical models aren’t exactly findings; they’re restatements of our initial intuitions in mathematical form. Whether those intuitions are poorly developed and vastly simplified or thoroughly developed and conceptually rich is an entirely separate matter, as they’re all precisely as “real” in the theoretical domain.

References: Nowak, M. (2011). SuperCooperators: Altruism, evolution, and why we need each other to succeed. New York: Free Press

Nowak, M. (2012). Evolving cooperation Journal of Theoretical Biology, 299, 1-8 DOI: 10.1016/j.jtbi.2012.01.014