PART I

THEORETICAL FRAMEWORK

CHAPTER 5. Modeling the different kinds of gossip

“Results from the newly emerging field of evolutionary psychology suggest that (i) explicit, well-specified models of the human mind can significantly enhance the scope and specificity of economic theory, and (ii) explicit theories of the structure of the human mind can be made endogenous to economic models in a way that preserves and expands their elegance, parsimony, and explanatory power.” (Cosmides & Tooby, 1994a: 327).

1 Introduction

Evolutionary biology not only has a tight connection with psychology, resulting in the field of evolutionary psychology, but can also be connected with economics. As Cosmides and Tooby (1994a) explained, natural selection is the blind process that slowly builds decision-making machinery in our minds, and these cognitive devices also generate economic behavior.

In the previous chapter, I focused on gossip as a noun, outlining how gossip as information can be classified in two well separated categories that each could solve adaptive problems occurring in the EEA. In this next step, I want to translate some of the different kinds of gossip in behavioral strategies, explaining what is going on when people exchange the kind of information that can be classified as gossip. For both Strategy Learning Gossip (SLG) and Reputation Gossip (RG) I will outline when it is advantageous to spread this kind of information around and when to pay attention to it. The stakes for SLG and RG are different. Costs and benefits for exchanging SLG are related to strategy knowledge, whereas the costs and benefits of RG concern both knowledge about and manipulation of reputations. The different costs and benefits involved, as well as other reasons I will discuss later, force me to outline different models for both.

This chapter is an exploratory part of my theoretical approach to gossip. I put forward some ideas about gossip that are new. Future research should investigate whether the models presented here are falsifiable. The primary scope of this chapter is to outline a manual to test whether the different kinds of gossip I distinguished in the previous chapter can be considered as adaptive or not. The focus of the previous chapter was to determine which functions could be attributed to gossip; this chapter tries to uncover the cognitive processes that underlie the different gossip adaptations.

2 Modeling human social behavior

2.1 Optimization models for human behavior

An evolutionary optimization approach is useful to construct a model about an adaptation. Parker & Smith (1990) set out some guidelines to construct optimization models. First of all, clear questions should be asked and these questions should be assumed to have an adaptive answer. Next, assumptions must be made about what should be maximized in terms of Darwinian fitness. Using optimization criterions, as indirect measures of fitness, assumptions must be made about the outcome of different strategies. This involves the construction of mathematical models to measure differences in outcomes. In a last step, the optimality approach should be tested, using observational data. Smith and Winterhalder (1992) give similar instructions, outlining as well that an optimization analysis is useful to compare different strategies an actor can choose between. For each alternative, costs and benefits have to be considered. An optimization analysis starts from an outline of which variables need to be maximized. Lastly, it is also important to recognize possible constraints (variables outside the actor’s control) that could determine the payoffs. There are however also some difficulties with these optimization models. For example, in real life an individual might not have access to all information needed to calculate the outcome (Parker & Smith, 1990).

2.2 Bounded rationality theory

2.2.1 The power of simple heuristics

Another critique on the optimization theory came from Herbert Simon (cited in Gigerenzer & Todd, 1999), who argued that humans are limited in their cognitive capacities, and optimization models are too complex to be considered as representations of human decision making. His ideas are used in the theory on Bounded Rationality, which I will use in this chapter to model how humans make decisions about “When to spread a certain gossip?”, “To whom should we tell the gossip?”, and “what do we have to pay attention to when confronted with gossip?”

The theory of Bounded Rationality focuses on fast and frugal heuristics that humans use to make decisions. “Fast and frugal heuristics employ a minimum of time, knowledge, and computation to make adaptive choices in real environments.” (Gigerenzer & Todd, 1999: 14). This theory builds on three (interconnected) domains of rationality: bounded rationality, ecological rationality and social rationality. The first domain of bounded rationality stresses the important fact that humans have limited time and capacity to make decisions. Ecological rationality refers to the fact that decision-making mechanisms (adaptations) exploit the structure of information in the environment, resulting in adaptive outcomes. Social rationality is a special form of ecological rationality and simply says that other agents are an important aspect of an agent’s environment. As Gigerenzer and Todd (1999) say, predators must make inferences about their prey, men and women must make decisions about others in the context of mating, etc. In the context of gossip, social rationality is obviously very relevant. Every decision that a sender or receiver of gossip has to make will always involve other agents.

A classical example of a fast and frugal heuristic is the recognition heuristic. Goldstein and Gigerenzer (1999) put forward and tested a simple rule that can solve problems in which an individual has to make inferences about which of two objects has a higher value. “The recognition heuristic for such tasks is simply stated: If one of two objects is recognized and the other is not, then infer that the recognized object has the higher value.” (Goldstein & Gigerenzer, 1999: 41). For instance when, asking non-German people which city is the biggest, Dortmund or Munich, many answer (correctly) ‘Munich’, because they recognize this city, and mostly non-Germans have not heard of Dortmund. Goldstein and Gigerenzer (1999) concluded from an experiment where people were asked which cities they recognized that the media influence our recognition heuristics. Bigger cities, with higher population rates should be recognized by more people, according to the recognition heurist.

They tested this among American students, and the correlation between people recognizing a German city and the city’s population is .60. Additionally Goldstein and Gigerenzer traced down all articles that had mentioned the name of these German cities in the issues of the past 12 year of the Chicago Tribune. The correlation between the city’s population and the times it was mentioned in the newspaper was .70 (ecological correlation). The stunning finding was that the correlation between the times a city was mentioned in the newspaper and the number of people who recognized the city was .79. “These results suggest that individual recognition is more in tune with the media than with the actual environment, which indicates that city name recognition may come largely from the media.” (Goldstein & Gigerenzer, 1999: 55). In chapter 7 (gossip and media) I will come back to this finding and relate it to media gossip.

2.2.2 Fast and frugal decision trees

Because mathematical optimization models are too complex to describe how humans make fast decisions, I will focus in this chapter on another method that better portrays human decision making. Katsikopoulos and Martignon (2003) have suggested that human decision making most often involves classification of different options. We use cues, or criterions (c), to guide our decision making. For each criterion estimations have to be made. E is called the criterion estimator. If E(c)= 1 this means that what is subjected to the criterion estimator is classified as passing the criterion positively. If E(c)= 0 this means that what is subjected to the criterion estimator is classified as passing negatively.

Such classification rules can be presented graphically in a classification tree. Such trees classify decision rules. Each node of a tree represents a question regarding certain features of the objects that need to be classified. Each branch of these nodes leads to an answer of the question. The nodes below other nodes are called “children”, and the higher level nodes “parents”. So-called “leaf” nodes are nodes that have no children (Martignon, Vitouch, Takezawa & Forster, 2003). The convention rule is that all “yes” answers drop off the left part of the question node, and all “no” answers drop off the right part of the question node (Katsikopoulos & Martignon, 2003). Branches that drop off the left are given the label “1”, while branches that drop off the right part of the node are given the label “0” (Martignon et al, 2003). The algorithm for classification trees is as following:

Algorithm TREE-CLASS:

(1) Begin at root node.

(2) Execute rule associated with current node to decide which arc to traverse.

(3) Proceed to child at end of chosen arc.

(4) If child is a leaf node, assign to object the class label associated with node and STOP.

(5) Otherwise, go to (2). (Martignon et al, 2003: 191).

Within these classification trees “Fast and Frugal Decision Trees” are trees where parent nodes have two children each and that allow classifications to be made at each level. At each level a leaf node is present (Katsikopoulos & Martignon, 2003, Martignon et al, 2003):

A fast and frugal binary decision tree is a decision tree with at least one exit leaf at every level. That is, for every checked cue, at least one of its outcomes can lead to a decision. In accordance with the convention applied above, if a leaf stems from a branch labeled 1, the decision will be positive. […]” (Martignon et al, 2003: 197)

Such fast and frugal decision trees perform not as good as rational computational models, such as logistic regression. Still, their performance is not dramatically lower, and these trees are far more easy to use (Martignon et al, 2003). Full mathematical models might still have stronger accuracy, but can not represent how human make decisions in real life, and: “[i]n many decisional domains, we may be better off trusting the robust power of simple decision strategies rather than striving for full knowledge of brittle details.” (Martignon et al, 2003: 210).

In this chapter I will use mathematical models to explain why we share Strategy Learning Gossip and Reputation Gossip. Sharing (gossip) information requires some more explanation than acquiring information. For both sharing and acquiring Strategy Learning and Reputation Gossip I will put forward classification trees. I will try to make these trees fast and frugal, with binary options and a leaf node at each level. Before doing this, however, I present some theoretical background on the sharing and acquiring of information.

3 Acquiring and sharing information

Both Strategy Learning Gossip (SLG) and Reputation Gossip (RG) involve the exchange of information. Certain costs and benefits are common for both kinds of gossip. I will outline these first, and then focus more specific on SLG and RG separately when translating these costs and benefits in optimization models and fast and frugal decision trees. In general, I will pay more attention to the sharing of both SLG and RG, because in evolutionary terms acquiring fitness-relevant information has clear benefits, but sharing this with others needs some more explanation.

3.1 Acquiring information

According to Michele Scalise Sugiyama (1996), it is the receiver of a story who benefits most from storytelling, because he or she gains social information about his or her environment. In her view, gossip is most beneficial for recipients. Or at least, this should be true for Strategy Learning Gossip (SLG), which in function is closely related to the function Scalise Sugiyama (1996, 2001) attributes to storytelling. Indeed, acquiring information, both behavior focused (SLG) or person focused (Reputation Gossip) requires very little investment of the listener. He or she just has to devote some of his or her time to the one who wants to share the gossip with them, knowing that they can gain a lot form this transaction.

Yet, besides this little cost of investing time to listen, the higher price people pay for new knowledge is the struggle with the question how reliable their news source is. Reliability is a major issue when we talk about gossip. Gossip has been called ‘cheap’, because it is so easy to lie (Barkow, 1989; Power, 1998). Even more troubling is the fact that true/not-true is no matter of black and white, but covers different shades of gray. There are might-be-true, what-others-believe-is-true, once-was-true, might-become-true, what-they-want-me-to-believe-true etc. (Tooby & Cosmides, 2001).

The first time you are presented a gossip story the news value will be high, but the credibility value might be low (depending on the credibility status of the source as well). Hearing the same piece of gossip multiple times might still be beneficial to add up credibility value (see chapter 1 as well). Hess and Hagen (2002) already noticed from their research on gossip among sorority girls that when the girls heard the same gossip story twice, it is when a reiteration effect is present, they were more likely to believe the gossip story. When independent sources spread the same gossip information, the believability of the gossip story still increases. Independency of the sources is important. When girls hear the same gossip story from several others who are close to each other, they were less likely to believe the gossip story, Hess and Hagen noticed. In sum, gossip, reported by multiple female sources, is more likely to be believed when these sources are independent instead of dependent of each other. Wilson et al (2000) found similar results for both male and female students, using paper-and-pencil test to investigate the importance of the reliability of the source(s) of a gossip story.

The importance of the reliability of the resource of gossip is not only important in the context of interpersonal gossip, as above described studies have shown, but also with media gossip. Kaufman, Stasson and Hart (1999) analysed the importance of source credibility of media gossip messages by comparing a rather untrustworthy newspaper (National Enquirer) with a more trustful one (Washington Post). Controlling for need-for-cognition they used a group of respondents who were low in need-for-cognition, meaning that those people rely on simple heuristics to process information (such as a reliability cue) and a group of respondents who were high in need-for-cognition. Those last always process information very thoroughly, and do not rely on peripheral cues. Those who score high on need-for-cognition are always cautious about information, but those who are low on need-for-cognition, are only sensible about the information when the source is rather unreliable. “When articles are attributed to low-credibility sources, the untrustworthy source may motivate greater scrutiny among individuals low in need for cognition.” (Kaufman et al, 1999: 1994.).

3.2 Sharing information

3.2.1 Low cost of sharing non-rival goods

In evolutionary terms, it is highly beneficial to get information, but less beneficial to share valuable knowledge with others. Sharing needs an explanation in evolutionary terms, as I explained in the previous chapter. The important difference between sharing goods, and sharing knowledge (which is the case with gossiping) is, as Romer (1994) outlined, that gossip can be considered as a non-rival good, for which the cost of sharing is relatively cheap. Sharing knowledge with others does not imply you lose it yourself, as is the case when you share goods. The costs of sharing non-rival goods, such as information, are low, while the benefits can be large, and basically concern reciprocal actions.

3.2.2 Multiple benefits of sharing gossip

3.2.2.1 Gossiping and kin selection

Following Hamilton’s (1964) thoughts on kin selection theory, I argue that gossiping can contribute to an individual’s inclusive fitness. Sharing fitness-relevant information (SLG) with kin, or increasing the status of kin related members through reputation gossip (RG), both rebound to individual benefits. You can secure or increase the fitness of relatives through SLG, and increase the reputation of relatives through RG.

I even expand this benefit of gossiping to coalitions. Individuals do not solely benefit from manipulating knowledge (SLG) and reputations (RG) of kin related members of their band, but also by doing this for coalition members. Increasing the knowledge and reputations of your own band (coalition) and securing that information is withheld from other bands (non-coalitions) or sharing false, deceitful knowledge with non-coalition members (false SLG), and decreasing the reputations of non-coalition members (negative RG) all rebound to relative benefits for an individual. If the level of truthful knowledge or the reputations of non-coalition members go down, the relative knowledge and reputation of the individual (and his coalition members) goes up.

3.2.2.2 Gossiping and reciprocal altruism

Though focusing on rumors, rather than on gossip, Rosnow and Fine’s (1976) ideas about rumors as a social exchange paradigm are applicable to gossip as well; “[…] like rumormongering, gossiping has definite functions that might best be understood within the framework of social exchange.” (Rosnow & Fine, 1976: p. 93). Indeed, Trivers’ (1971) simple principle of you-scratch-my-back-and-I’ll-scratch-yours can in this context be translated as you-tell-me-something-and-I’ll-tell-you-something.

But the returns go beyond informational benefits. Reciprocity in the context of gossiping has a broader perspective, say Rosnow and Fine (1976). We not only gossip to get information in return, but also to get money, power, status, etc.:

“From the broader perspective of social exchange, one can readily visualize rumormonging as a transaction in which someone passes a rumor for something in return – another rumor, clarifying information, status, power, control, money, or some other resource. When information is scarce, the rumormonger can exact a high price for his tales.” (Rosnow & Fine, 1976)

Sharing gossip can also assure the sender that the content is true: “What, in economics of gossip, is offered, what is received? Point of view, information; also reassurance. Participants assure one another of what they share: one of gossip’s important purposes.” (Spacks, 1985: 22).

3.2.2.3 Gossiping and the show-off hypothesis

Being rewarded with an increase of status, fits in the show-off hypothesis of explaining human sharing. The reason why we attribute status to people who share gossip with us, is according to Miller (2000), because having exclusive social knowledge signals high social status and intelligence. Therefore Miller claims that spreading gossip must have been favored by sexual selection. Pinker (1994) as well mentions that the leaders of current hunter-gatherer societies are often those who know most about what is going on in their band; they have information, power, and have high social intelligence skills.

This benefit of gossip sharing, however, involves a potential cost. One can loose exclusive social knowledge, if others run of with the gossip story (see below as well). To reduce this cost as much as possible, the sender must assure that he is recognized as the source of information. The easiest and most reliable way to achieve this is to spread the word around himself or herself to as many people as possible. “Hey, have you heard… but do not tell this to others” is a classical utterance when gossip is shared and can be associated with the thought “Because I will tell the others.”

Another important remark here is that prestige will only be given to those who spread true gossip. Spreading lies about other people will not increase your status, and can even harm your reputation. People are aware of this, because they are less likely to spread information of which they doubt the reliability. Jaeger, Anthony and Rosnow (1980) found that the reliability of the source and the content of information spread around influences the dissemination. The subject of their research were ‘rumours’, which they defined as “A rumor is a proposition for belief in general circulation without certainty as to its truth.” (Jaeger, et al, 1980: p. 473). Nevertheless, the ‘rumor’ they used concerned the smoking of marijuana by some students. So it is information about (a) person(s), which makes it very close to my definition of gossip. They called their information rumors, because they manipulated the believability of the story, by adding a confirmation (believable) or counter-statement (unbelievable) from an extra source. Their “[…] results suggest that a rumor perceived to be false is less likely to be transmitted than one perceived to be true.” (Jaeger et al, 1980: p.476).

3.2.2.4 Gossiping and tolerated scrounging

A fourth model that explains human sharing is tolerated scrounging (Gurven, in press). In this case people share their goods because the costs of defending them are too big. For instance, it is better to share large game that cannot be consumed alone. The cost of defending it would be big, and hungry others can benefit a lot if you give some away. In the context of gossip transactions this is an interesting way to explain why people tolerate that others run away with their knowledge. This is, if you share exclusive social knowledge with others, this can result in (1) an increase of social status and (2) the potential of getting return-information. It is in the interest of every individual to secure that he or she shares his or her knowledge with as many others as possible, so that the returned benefits are maximized. In reality however, recipients of gossip ‘run away’ with this knowledge, because they can profit from an increase in social knowledge and potential returned-information as well. People seem to tolerate this, and I guess tolerated scrounging can explain why. The cost of securing others that they will not spread around your knowledge are too high, because this would mean that an individual should spy on all his recipients, to secure that they do not run away with their knowledge. Additional, if others run off with the knowledge, this can increase the credibility of the gossip message, because hearing the same gossip story from multiple sources increases credibility (see above).

4 Exchanging Strategy Learning Gossip

The different kinds of SLG I differentiated between in the previous chapter (Survival, Mating, and Social SLG) all concern the sharing and acquiring of fitness-relevant information. Costs and benefits for all three kinds of gossip involve the manipulation of fitness-relevant knowledge of the receivers. Central to SLG is that the costs and benefits relate to information about fitness relevant strategies (knowledge) and this both for the sender and the receiver. The gossipees of SLG are mere carriers of information and are not subject to benefits of costs of the gossip transaction about their experiences.

In what follows, I put forward a general model that describes when it is optimal to share SLG. I pay more attention to explaining why we share SLG than to why we acquire SLG. This for the simple reason, as already explained, that sharing needs more explication from an evolutionary point of view. I first outline an optimisation model to clarify the costs and benefits of the sharing of SLG-exchange and then turn to classification trees that present a more realistic view on how humans make decisions about their daily gossip exchange. With these classification trees I also pay attention to the receiver’s side. Next to presenting classification trees that show how human decision-making occurs when SLG is shared, I also set up classification trees that clarify what receivers of SLG need to decide when hearing SLG, and how they best act on this acquired information.

4.1 Sharing Strategy Learning Gossip

Because the sender of SLG can manipulate the knowledge about fitness-relevant strategies of others, sharing SLG returns benefits. When sharing SLG the sender manipulates the knowledge of receivers. It is important to keep this in mind, and I remind again that the gossipees of SLG are no subjects of manipulative costs and benefits; gossipees are not at stake in the costs and benefits of sharing SLG. As I will discuss later, this is different for Reputation Gossip, where gossipees are at stake. I will first outline the costs and benefits of sharing SLG, and then put forward a fast and frugal decision tree to explain how humans decide when to share their fitness-relevant knowledge with others or not.

4.1.1 Costs and benefits of sharing Strategy Learning Gossip

4.1.1.1 Benefits of sharing SLG

The benefits of sharing SLG with others are twofold. First of all, the sender of SLG gets merit from people who believe him or her. Reason for this is because he or she shows off to have exclusive social knowledge. This happens regardless of the fact that the gossip story is true or not, but depends on the fact whether the gossip message is believed to be true or not. If everybody knows already what a sender of SLG is sharing, he or she does not signal exclusive social knowledge of course, and will not be merited for this. But, in a situation where some know the SLG message and a sender shares this SLG message with a receiver who knew about this already, this sender can still gain some merit. He or she does not show off complete exclusive knowledge, but rather exclusive knowledge (only some know about this).

Secondly, the one who shares SLG can manipulate the knowledge of others. Beneficial for the sender is to spread true-SLG to coalition members and withhold this from non-coalition members. Similar, he or she should withhold untrue-SLG from coalition members and make sure this reaches non-coalition members. Extra benefits are expected for the sender of true-SLG when he or she is kin related to the receiver of his or her SLG. He or she then increases his or her own inclusive fitness. Sharing SLG, the sender can manipulate (increase or decrease) the waste of time, energy and risks of receivers, by giving them strategy learning information that third parties (gossipees) have acquired by investing their time, energy and risks. The most beneficial for an individual in manipulating SLG is to secure that his or her relatives, friends, and other allies will increase future opportunities for fitness-promoting strategies and decrease future risks of fitness-endangering strategies. Likewise, an individual benefits from securing that non-allies will miss out on future opportunities for fitness-promoting strategies and will increase fitness-endangering strategies. If non-allies’ fitness goes down, the individual and his or her allies’ relative fitness goes up.

4.1.1.2 Costs of sharing SLG

The costs a sender of SLG has to take into account are threefold. A first cost is that when recipients do not believe the SLG, the sender can loose social status for having exclusive knowledge. If recipients do not believe the sender, and consider him or her as a liar, this decreases his or her social status for knowledge. Secondly he or she risks spreading around false knowledge. Doing this, he or she can decrease the fitness of others, if he or she causes them to use a strategy that will harm them in stead of being beneficial. This implies a cost if this happens to coalition members, and especially if this happens to kin related members (because of inclusive fitness). A third cost occurs when others run-off with the knowledge.

4.1.2 Mathematical model for sharing Strategy Learning Gossip

If I line up these costs and benefits in a mathematical optimization model, this looks as follows:

SK.(bCM + bNCM) + t.(bCM +k1 + dNCM - k5 + eNCM – k6) + u.(bNCM –k4 + dCM +k2 + eCM +k3)

 >

SK.(dCM + dNCM) + u.(bCM +k1 + dNCM –k5 + eNCM –k6) + t.(bNCM –k4 + dCM +k2 + eCM +k3)

Where:

CM = coalition member receivers

NCM= non-coalition member receivers

b = number of people who believe you

d = number of people who disbelieve you

e = error (people who do not hear the gossip)

b + d + e = n = total number of coalition or non-coalition members (band)

 nCM = bCM + dCM + eCM

 nNCM = bNCM + dNCM + eNCM

SK= Social Knowledge

Senders of SLG show of exclusive Social Knowledge.

SK can vary from 0 to 1.

SK = 0 if everyone already knows the gossip information

SK = 1 if the sender has exclusive gossip information

Note that SK at the left side of the ‘>’ (benefits) means bonus points, or benefits to the sender: he or she gets merit for having Social Knowledge in the eyes of the receivers who believe him. The more receivers believe him, the more merit the sender gets (SK gets multiplied with (bCM + bNCM)

SK at the right side of the ‘>’ (costs) means punishment for being seen as a liar, or costs to the sender: he or she gets punishments from all receivers who do not believe the gossip message (SK here gets multiplied with (dCM + dNCM)

t = true SLG knowledge

u = untrue SLG knowledge

k1; k2; k3; k4; k5; k6 = corrections for kin relatedness with coalition and non-coalition members

where:

r= Wright’s coefficient of relatedness, with r(.5) for parents and siblings, r(.25) for aunts, uncles, and grandparents , r(.125) for cousins and stepsiblings, …and r(0) for non relatives

and:

k1 = n1.bCM.r(.5) + n2.bCM.r(.25) + n3.bCM.r(.125) + …

Where:

n1.bCM = number of coalition members who believe sender and with whom r = .5

n2.bCM = number of coalition members who believe sender and with whom r = .25

n3.bCM = number of coalition members who believe sender and with whom r = .125

k2 = n1.dCM.r(.5) + n2.dCM.r(.25) + n3.dCM.r(.125) + …

Where:

n1.dCM = number of coalition members who disbelieve sender and with whom r = .5

n2.dCM = number of coalition members who disbelieve sender and with whom r = .25

n3.dCM = number of coalition members who disbelieve sender and with whom r = .125

k3 = n1.eCM.r(.5) + n2.eCM.r(.25) + n3.eCM.r(.125) + …

Where:

n1.eCM = number of coalition members who do not receive the SLG and with whom r = .5

n2.eCM = number of coalition members who do not receive the SLG and with whom r = .25

n3.eCM = number of coalition members who do not receive the SLG and with whom r = .125

k4 = n1.bNCM.r(.5) + n2.bNCM.r(.25) + n3.bNCM.r(.125) + …

Where:

n1.bNCM = number of non-coalition members who believe sender and with whom r = .5

n2.bNCM = number of non-coalition members who believe sender and with whom r = .25

n3.bNCM = number of non-coalition members who believe sender and with whom r = .125

k5 = n1.dNCM.r(.5) + n2.dNCM.r(.25) + n3.dNCM.r(.125) + …

Where:

n1.dNCM = number of non-coalition members who disbelieve sender and with whom r = .5

n2.dNCM = number of non-coalition members who disbelieve sender and with whom r = .25

n3.dNCM = number of non-coalition members who disbelieve sender and with whom r = .125

k6 = n1.eNCM.r(.5) + n2.eNCM.r(.25) + n3.eNCM.r(.125) + …

Where:

n1.eNCM = number of non-coalition members who do not receive the SLG and with whom r = .5

n2.eNCM = number of non-coalition members who do not receive the SLG and with whom r = .25

n3.eNCM = number of non-coalition members who do not receive the SLG and with whom r = .125

This formula outlines most of the costs and benefits I summed up earlier. First of all the sender’s knowledge status is at stake. If recipients believe the sender of SLG, they will attribute knowledge status to the sender. The SK.(bCM + bNCM) in the formula simply stands for the total amount of people (coalition and non-coalition members) who believe the SLG sender. Likewise the SK.(dCM + dNCM) stands for the total amount of people who received the gossip and did not believe the sender.

As I explained above, SK can vary from value ‘0’ to value ‘1’. SK gets value 0 if everyone already knows the information, then the sender cannot show off exclusive social knowledge. SK gets the maximum value of ‘1’ if he or she is (almost) the only one who knows the gossip information. That is why senders must secure to spread the news to as many people as possible as the first sender; the more people know the information, the higher the chances that potential receivers will have already heard the information (the cost of runaway knowledge). SK can have a value in between ‘0’ and ‘1’ if the receiver already knew the information, but knows that only a few people know about the gossip information. The sender does not get maximum merit, but still gets some merit because he or she signals he or she is one of the few people who know about this.

If for instance a sender has exclusive social knowledge (SK= 1), he or she only gets merit from those who believe him or her. A sender gains social knowledge status from every receiver who believes him or her and looses social knowledge status from every disbeliever. If for instance a sender tells a SLG to 20 people, of which 15 believe the SLG and 5 do not, the sender gets an increase of 15 points from the 15 believers, and loses 5 points from those who disbelief him or her. His or her net benefit is 10 points of social knowledge credit.

Next, the knowledge of the receivers is at stake. If the SLG is believed to be true (t=1 and u=0), the sender must secure that this true-SLG, which has clear fitness benefits, reaches coalition members who believe the sender, and does not reach non-coalition members or if it reaches non-coalition members they best do not believe this true-SLG. This is formula with t.(bCM + dNCM + eNCM). For true-SLG the number of coalition members who believe the SLG (bCM) -and therefore benefit from fitness relevant true information- should be maximized. If the SLG is true, then the sender benefits most by not telling his or her non-coalition members (maximize eNCM) or securing that the non-coalition members disbelieve the information (maximize dNCM).

If the SLG is believed to be untrue by the sender (lie), then u=1 and t=0. In this case u.(bNCM + dCM + eCM) states that the number of non-coalition members believing the untrue SLG should be maximized (bNCM). And, if the SLG is untrue the sender benefits most if his or her coalition members do not hear the SLG (eCM) or disbelieve the false information (dCM).

Further, the formula also calculates corrections for kin relatedness. If the information is true (t=1) and a coalition member believes the SLG (bCM) then extra benefits comes from kin-relatedness: (t.k1). If a coalition member disbelieves the SLG (dCM) or does not hear the SLG (eCM) and the SLG is true, then a cost comes from the kin-relatedness (t.k2) or (t.k3). In this same situation where t=1 some benefits gets lost for non-coalition members who disbelieve (dNCM) or not hear the SLG (eNCM): (-t.k5) and (-t.k6). Still in this situation where t=1, some costs are reduced because of kin-relatedness: (-t.k4) for non-coalition members who do believe the SLG.

If the information is untrue (u=1) kin-relatedness increases some benefits and decreases a benefit. The fact that coalition members do not hear (eCM) or disbelieve (dCM) false SLG are benefits, to which kin-relatedness adds extra benefits: (u.k2) and (u.k3). In the situation that the SLG is untrue (u= 1) kin-relatedness increases a cost and reduces two costs. The fact that coalition members believe false SLG is a cost, and this costs is even higher for kin-related coalition members (u.k1). The fact that non-coalition members do not hear (eNCM) or disbelieve (dNCM) untrue SLG are costs as well, but if these non-coalition members are kin-related to the sender, the costs get a little reduced: (-u.k5) and (-u.k6).

4.1.3 Visual translation of domain of the model

What I described above can be visualized as follows:

An individual X who sends a SLG about Y to a population Z, has a number of coalition members (yellow) and a number of non-coalition members (purple). Among X’s coalition members, some will hear the SLG from X (green and blue), and some will not (red). Among those X reaches, some will believe him (green) and some will not (blue). And for all these three groups (believers, disbelievers, non-receivers) some individuals will be kin related to X, and this with a varying degree (here black is r=.5; dark grey r=.25; light grey r=.125), and others will not be related to X (white r=0). Similar to the population of coalition members, the non-coalition members has believers, disbelievers, and non-receivers, with for each group kin-related and non kin-related individuals. In the EEA non-coalition members will have been mostly not kin-related. This will only be the case after relocation of individuals, which was mostly the case for women (at marriage).

4.1.4 Fictive examples of the mathematical model for sharing Strategy Learning Gossip

Let me illustrate and clarify this cost/benefit analysis with some fictive examples. I will present an optimal strategy example of sharing truthful SLG and an optimal strategy example of sharing untrue SLG (where the sender spreads a lie). I illustrate the formula in the context of simple coalition structures, as was the case in the EEA. I do admit that nowadays our living structures are more complex, and it is difficult to define who our coalition members are and who are not (see next chapter).

4.1.4.1 Example 1: sharing exclusive (SK= 1) eye witness (t= 1) SLG

Imagine for instance that X has 100 coalition members and 200 non-coalition members he can gossip with. This is 100 people he lives with, and 200 he meets on visits, or at larger meetings, gatherings. He witnesses how a man is killed by an unknown snake. Seeing this he has knowledge of 100% true-SLG (t= 1 > u= 0). He is the only one who witnessed this, so has exclusive social knowledge, no one else has (SK= 1). He starts to spread the news around, to 110 people in total, of which 60 are coalition members (CM), and 50 are non-coalition members (NCM). He does not tell his other 40CM (eCM= 40), and 150NCM (eNCM= 150) with whom he has contact. Of the 60CM he tells the information, 50 believe him (bCM= 50), and 10 do not (dCM= 10). Of the NCM, 30 believe him (bNCM= 30) and 20 do not (dNCM= 20). His relatives are scattered over all groups. For an overview and calculations of k1 to k6 see table V.1.

Table V.1. Population overview of fictive examples and calculations of k’s.

If I fill in all values from this fictive example 1 into the formula to estimate the cost/benefits of spreading this gossip, this gives:

SK.(bCM + bNCM) + t.(bCM +k1 + dNCM - k5 + eNCM – k6) + u.(bNCM –k4 + dCM +k2 + eCM +k3)

 >

SK.(dCM + dNCM) + u.(bCM +k1 + dNCM –k5 + eNCM –k6) + t.(bNCM –k4 + dCM +k2 + eCM +k3)

1.(50 + 30) + 1.(50 + 7.5 + 20 - .25 + 150 – 1.875) + 0.(30 – 1.5 + 10 + .70 + 40 + 2.5)

>/<?

1.(10 + 20) + 1.(30 – 1.5 + 10 + .70 + 40 + 2.5)

1.(50 + 30) + 1.(50 + 7.5 + 20 - .25 + 150 – 1.875)

>/<?

1.(10 + 20) + 1.(30 – 1.5 + 10 + .70 + 40 + 2.5)

80 + 225.375

>/<?

30 + 81.70

305.375 > 111.70

The sender of this example gained 50 points of social knowledge status (80 -30), the benefits of manipulating the knowledge of others is 225.375, which have to be reduced with 81.70 costs of manipulating the true knowledge of others.

4.1.4.2 Example 2: sharing untrue (u= 1) exclusive (SK=1) SLG

Now consider X spreads a lie to the same audience (see table V.1). He knows a man got killed by an unknown snake and shares with the receivers that he encountered an unknown snake. He is the only witness of this happening. He describes the snake accurately (he has exclusively witnessed the snake) and tells his friends and foes this animal is not dangerous. He therefore endangers the life of those who hear and believe this information. Here u=1. Let me now illustrate that this is a bad strategy of X:

SK.(bCM + bNCM) + t.(bCM +k1 + dNCM - k5 + eNCM – k6) + u.(bNCM –k4 + dCM +k2 + eCM +k3)

 >

SK.(dCM + dNCM) + u.(bCM +k1 + dNCM –k5 + eNCM –k6) + t.(bNCM –k4 + dCM +k2 + eCM +k3)

1.(50 + 30) + 0.(50 + 7.5 + 20 - .25 + 150 – 1.875) + 1.(30 – 1.5 + 10 + .70 + 40 + 2.5)

>/<?

1.(10 + 20) + 1.(50 + 7.5 + 20 - .25 + 150 – 1.875) + 0.(30 – 1.5 + 10 + .70 + 40 + 2.5)

1.(50 + 30) + 1.(30 – 1.5 + 10 + .70 + 40 + 2.5)

>/<?

1.(10 + 20) + 1.(50 + 7.5 + 20 - .25 + 150 – 1.875)

80 + 81.70

>/<?

30 + 225.375

161.70 < 255.375

Costs outscore the benefits for X by sharing this lie with his friends and foes.

If he would have shared this information only with the foes, and not with the friends, then bCM=0 and dCM= 0, while eCM= 100, and the model would give the following results:

SK.(bCM + bNCM) + t.(bCM +k1 + dNCM - k5 + eNCM – k6) + u.(bNCM –k4 + dCM +k2 + eCM +k3)

 >