“ Out of sight , out of mind ” : Social interactions and Smith ' s asymmetrical sympathy

Growing literature on Adam Smith’s system of sympathy has recovered an enriching view on our understanding of human interactions. Much attention has been placed on the construction of moral and social communities, the process of identification and recognition that Smith presents. But, the features Smith attributes to the intersubjective identification mechanism of sympathy can also lead to conceive of the possibility of exclusion of some members of a community. The asymmetry of sympathy allows explaining emulation of those seen as more fortunate as well as the exclusion of those perceived as miserable. Through a formal representation we try to illustrate the phenomena of inclusion and exclusion present in intersubjective relations and the construction of communities. Key-words: Adam Smith, sympathy, emulation, exclusion JEL Classification: B12, B31, D03


Introduction
Along with the increasing interest in human behavior, economics is searching for a deeper understanding of more complex human interactions.The construction of a "thicker" economic agent brought back to the forefront the analysis of mutual identification and recognition among individuals as a fundamental part of the description of their preferences and decisions.Beyond game theoretical strategic interactions, views on human interactions take into account fellow feelings, discrimination, reciprocity, segregation, and altruism, among others.Recent developments in experimental economics are also contributing substantially to this ever-growing movement towards the study of human interactions, and in particular on the analysis of altruistic, cooperative or evidence on specific forms of moral judgments 1 .
Most of these elements were present in Adam Smith's analysis of human behavior and interactions.Levy & Peart (2009) have shown that in the XVIIIth century such interactions were considered to be the result of extended sympathy.This gave a complex view of interactions forming individuals capable of recognizing their fellow-beings not only as others but also as extensions of their own selves.Such a view promoted cosmopolitanism, and a conception of social interactions as mostly pacific within a constructively competitive and ever thickening social network.However, Smith's view of commercial society is more complex.Even if he recognizes the advantages and progress associated with this social organization, as regards independence and self-sufficiency 2 , he also describes its possible shortcomings in terms of the construction of a community.Following O'Neill (2011), in this paper we would like to explore the pathologies of recognition that Smith analyzed in commercial society.
Both, the optimistic and the less optimistic side of recognition can be dealt with using Smith's sympathetic mechanism.Levy & Peart (2009) argue that with the arrival of social Darwinism sympathy faded away to give place to individual fitness, leading the way to a view of destructively competitive interactions among isolated individuals.The last half of the XXth century, and the first decades of the XXIst century have seen a regained interest in social interactions among individuals capable of going beyond mere self-interest, but sympathy has yet to regain its place.Seabright (2004) presents a complete overview of recent findings showing the peculiarity of the human species in being able to cooperate among strangers.He associates this form of spontaneous order with the division of labor that leads to specific forms of interactions between strangers that require trusting each other, that is, treating "strangers as honorary relatives or friends".Seabright (2004) associates this tendency to cooperate with two human characteristics: rational calculation and reciprocity.Both lead to the emergence of formal and informal institutions that allow this cooperation between strangers but which also is double-edged promoting cooperation within groups, and aggressive behavior between groups.Seabright (2004) traces research in economics, where this renewed interest has been based on the answers given to two questions: 'Who interacts?' and 'How does interaction take place?' (Manski 2000).To the first question, the answer has been that those who interact are agents defined as decision makers endowed with preferences, which form expectations, and face constraints.As to how, interactions take place through actions that influence preferences, expectations, and channels.This answer has been extended to include not only actions but also verbal communication.Both recognize how individuals influence each other, and how they respond to others' tastes and decisions in specific situations.
In the last fifteen years or so, the study of social interactions has been particularly active within behavioral economics, especially using economic experiments that have tried to reintroduce empathy and sympathy.Given this context, we believe it is particularly relevant to go back to one of the most complete elaborations of sympathy as the basis of social interaction: Adam Smith's system of sympathy, as presented in The Theory of Moral Sentiments (henceforth TMS).Smith's theory of moral sentiments places fellow-feeling, recognition, and the natural impulse to put one-self in the other's place at the center of social interactions.Moral sentiments, based on sympathy, explain human pro and anti-social behavior.In this case, going a step back might prove to be the way to move a step forward because in Smith's system, sympathy not 1 For a condensed review of the literature on altruism in experimental games see Andreoni et al. (2008).Ledyard's review on the literature about public goods (Ledyard 1995) is also a good reference on the subject.In his 2004 book P. Seabright synthesis in a non-specialized manner many of the recent findings on the cooperative character of human beings. 2Amongst many others, Hill's (2009) account of Smith's view emphasizes this particular optimistic side associated with the positive aspects of patterns of social distance and strangership.According to Hill the paradigmatic social interaction in commercial society, impersonal and ubiquitous exchange, supports a new civil society of amiable strangers.In this paper we would like to contest this extremely optimistic account including the failures of the recognition mechanism Smith himself acknowledged.only accounts for identification, recognition, inclusion, and community building, it can also be a rationale for the absence of recognition entailing social exclusion3 .Bréban (2012) and Mallory (2012) have explored this dual aspect of Smith's sympathetic system.As we do, they both deepen in the meaning and implications of the asymmetries Smith introduces in the sympathetic mechanism.Bréban (2012) deals with prosperity and adversity as symmetrical events producing asymmetrical effects on people's happiness, leading to a formal representation of a concave or convex happiness function if the individual is closer to the common state of happiness or to the lowest depth of misery.Using Smith's analysis of surprise in the History of Astronomy, Bréban (2012: 557) shows an asymmetric sensitivity associated with painful and pleasant experiences explaining why the sensation resulting from the former is more violent than the one resulting from the latter (Bréban 2012: 559).We will exploit this asymmetry to go a step further, and analyze the asymmetric sympathetic feelings arising with the identification processes with the rich and the poor, leading to emulation of the former and exclusion of the latter.
The possibility of exclusion brings our results closer to Mallory's (2012) analysis of strangership.Building on the idea that Smith presents commercial society as a society of strangers, Mallory (2012) shows there is a second, less amiable, form of strangership which Smith presents but avoids discussing its implications.According to Mallory (2012: 592, 600), this "obscures the links between strangership and inequality", in which we are interested.This second type of strangership, presents a social hierarchy where sympathy and fellow-feeling are not distributed equally (Mallory 2012: 601), leading eventually to the disappearance of sympathy and, therefore, of any social ties between individuals.Mallory (2012: 601) finds in Smith "a theory of obscurity or ignominy, or the disposition to 'despise or, at least, to neglect persons of poor and mean condition'".The possibility of exclusion is then very present in Smith's account, and we advance a formal representation of such a possibility.
The rest of the paper is divided into three sections.The second section first presents the basics of sympathy as a mechanism of identification and recognition leading to a self-regulated community.Then we deal with identification and recognition, focusing on the conditions in order for these processes to take place, in the absence of which exclusion or symbolic violence are possible.In section three, we show how property and poverty have an effect on identification and recognition, which allows assessing the limits of the sympathetic mechanism in the construction of a self-regulated community.In so doing, we discuss Sally's (2000Sally's ( , 2001) ) formal representation of sympathy and its consequences in strategic decision making environments.In particular, we are interested in the consequences of distance on identification and recognition, so we deal with asymmetric and extreme sympathetic passions in order to advance a formal representation of a sympathetic passion function.Such a function shows the sympathetic passion of a spectator, and depends on social distance and the subjective perception the spectator has of the observed agent's situation.Based on textual evidence, we find four features of this function: identification is always imperfect as the observer can never fully feel what the agent is experiencing; the sympathetic passion is decreasing on social distance; it presents an asymmetric intensity where perceived agreeable situations are more likely to lead to identification than disagreeable ones; and, finally, it is concave in sorrow and convex in happiness 4 .With these properties we present a graphical example of the mechanics of passion, and use it to further explore the effects of social distance.We believe this formal representation provides an interest-ing framework to understand social interactions between sympathetic individuals leading to a community where not necessarily all belong.

Beyond Self-Interest
In constructing a thicker economic agent, economists have looked, again, at social interactions; again, because this was the fundamental pillar of moral philosophy, the origin of modern economics.In particular, moral philosopher Adam Smith, grounded all his economic theory in a social theory, aimed at explaining how interactions took place.Smith, as other thinkers of his times, was concerned with social coordination, with how interactions between free individuals produced a self-regulating community.
More recently, behavioral and experimental economics, in close work with psychologists, has produced a huge amount of literature exploring social interactions in controlled environments, accounting for altruism, reciprocity, and empathy 5 .They have gone a long way from the caricature of the economic agent depicted with homo oeconomicus, and seem to have brought economics closer to its origins, and, especially, to the Scottish professor.Smith's description of human beings goes beyond mere self-interest, which might act as a "centrifugal force" that leads to a society of rent seeking individuals, incapable of, for example, self-sacrifice.Evenksy (1992) argues that if agents are supposed to exploit all resources most efficiently -as the standard model states-, there is no reason why, in the absence of a system of ethics, they would not do the same with power.Smith denies self-interest is the only driving force individuals follow.There is another force that counteracts self-interest called sympathy 6 (TMS I.i.1.1),which acts as a centripetal force, explaining commitment to community values (Evensky 1992: 27;Evensky 1993: 396).According to Smith, the chief part of human happiness comes from the consciousness of being loved (TMS I.ii.5.1), and this would explain self-sacrifice among many other committed, value-driven behaviors.Smith's theory allows thinking of an extended self by relying on sympathy, which allows him to explain why individuals transcend themselves (Evensky 1992: 24).
Using this device, Smith explains how a community is built, and how norms regulating such a community arise.He explains the origin of these norms, and how individuals, through their extended self, will internalize them.Hence, Smith explains the co-evolution of individuals and community (Evensky 1992: 21;1993: 40), showing how, as communities shape individuals, individuals also shape communities (Evensky 1992: 21-22).The mechanism is based upon what Smith presents as a natural tendency: Nature, when she formed man for society, endowed him with an original desire to please, and an original aversion to offend his brethren.She taught him to feel pleasure in their favourable, pain in their unfavourable regard.She rendered their approbation most flattering and most agreeable to him for its own sake; and their disapprobation most mortifying and most offensive.(TMS III.2.6) 5 Further evidence of the growing interest economists show for social interactions can be found in a 2010 issue of the American Economic Review.Two of the articles in the issue explore precisely this: David Baron analyzes self-regulation motivated by altruistic moral concerns associated with private provision of goods and private redistribution.The article shows, using a theoretical model, that altruistic moral concerns are weaker with growing social distance and are influenced by the expectation that others will reciprocate.D.J. Benjamin, J.J. Choi, and A.J. Strickland show that norms tied to social identities can help explain demographic differences in economic outcomes.Through different experiments they explore how ethnic, racial, and gender category norms influence time and risk preferences, showing how identity salience affects individual behavior. 6Thousands of pages have been published explaining, interpreting and re-interpreting Smith's sympathy.Historians of economic thought, in general, and Smithian scholars, in particular, have explored this mechanism, and pointed to its effects on market and social interactions.However, modern economic theory and economists seem to have taken little notice of this gigantic work.With the notable exception of David Sally, few references are found in modern economic theory to Smith's sympathy.
Individuals want to belong to their community, and they will behave in such a way that others will identify with them, accept them, and approve of them7 .Smith shows individuals change, and adapt in order to be accepted, because: Man naturally desires, not only to be loved, but to be lovely: or to be that thing which is the natural and proper object of love.He naturally dreads not only to be hated, but to be hateful: or to be that thing which is the natural and proper object of hatred.(TMS III.2.1)So people will adapt, their preferences will change according to what they perceive others expect from them.Individuals derive positive and negative utility from who they are, and who they are is determined by the sympathetic encounters they have with those around them: This natural disposition to accommodate and to assimilate, as much as we can, our own sentiments, principles, and feelings, to those which we see fixed and rooted in the persons whom we are obliged to live and converse a great deal with, is the cause of the contagious effect of both good and bad company.(TMS VI.ii.1.16)Thus, individuals are mostly the result of their social environment; evidencing what, in experimental economics, has been presented as the effect of mere exposure (cf.Sally 2000: 588).In this sense, Smith advances: "The objects with which men in the different professions and states of life are conversant, being very different, and habituating them to very different passions, naturally form in them very different characters and manners" (TMS V.2.4).
This marked social nature of individuals explains not only Smith's refusal of any such hypothetical state as the state of nature but also his rejection of characterizations of society as the result of private vices, such as greed and selfishness.There is a spontaneous order that emerges from what Smith calls natural tendencies in individuals.However, this spontaneous order is not the result of individuals trying to satisfy their material needs, and profiting from the increases of productivity due to the division of labor.Neither is it the consequence of individuals minding only their own business with no regard for others.It is their desire to belong, to be acknowledged and esteemed by their fellows that leads to an affective communication and thus to the possibility of a community of shared values.

Identification and Recognition
Contemporary economic literature8 on social interactions assumes individuals interact with someone they can imagine, someone who they affect and who affects them through their actions, resulting from their decisions, given their preferences, their constraints, and their expectations.Such interactions hardly include exclusion or violence: individuals decide to follow social norms or to stay in their community, or face the consequences of their decisions as a loss of utility.Segregation and exclusion look very much like isolation, but not as confrontation in the form of real or symbolic violence.
Collins & Lim (2010) have gone a step back reassessing the conditions that makes interactions possible.Drawing from political philosophy, the authors introduce recognition, that is, the identification process that leads to recognize another fellow-being with whom the agent might interact.The point here is that interaction requires being able to see the other as someone the agent might relate to.Including this aspect gives insights to understand exclusion, and violent phenomena.Such phenomena, according to Collins & Lim (2010), are not only the result of limited or null access to economic goods 9 .In fact, this limited access can be seen as the result of failed recognition.Within a framework of minimal liberty, the authors explore the relationship between recognition and redistribution, proving three propositions: first, recognition requires minimal liberalism; second, recognizing a group is a necessary but insufficient condition for redistribution; and, third, voluntary redistribution is sustainable in a liberal society in the presence of uncertainty, as long as transfers received are sufficiently large relatively to transfers given.Their results call our attention not only to the link between recognition and property but also to the conditions leading to recognition.Here we will focus our attention on these conditions reversing, so to speak, the causality Collins & Lim explore.Following O'Neill (2011), we believe Adam Smith's analysis allows assessing the effect of poverty on recognition, or the failed recognition of property-less individuals.
In this sense, Collins & Lim (2010) draw attention to the need of reassessing who interacts and how interactions take place; the identification process between individuals might prove relevant in understanding who, how, and why interactions take place.Adam Smith embedded all interactions within what could now be called social psychology, or within what he called a theory of moral sentiments, or what we have called his sympathy system.Smith's system of sympathy explains how individuals identify, and recognize each other as fellow-beings.Through an imaginary movement, the spectator places herself in the agent's situation, and experiences what she would feel if she were really in that situation.This imaginary movement is instantaneous, and triggered at the sight of someone else in specific circumstances.It implies an extended sense of self, because individuals are able to put themselves in someone else's place, and, to some point, experience what the agent is feeling.If their feelings coincide, the spectator will approve of the agent's behavior; if they don't, the spectator will blame it.Sympathy, not only allows identification, it is also the basis for moral judgments.Through this mechanism, individuals learn what is right and wrong, and which behaviors are accepted, permitted, required, rejected, or forbidden in their communities.However, here we will focus only on the conditions allowing recognition, and not on the moral results of the sympathetic process.
In placing herself in the agent's situation, the spectator develops a sympathetic feeling which can be of joy or of sorrow.She then observes if what she feels in the agent's circumstances is the same or not as what the agent seems to be experiencing.If it is, they will both enjoy the pleasure of mutual sympathy.If it isn't, they will both experience a negative feeling of reprobation and blame.The spectator is able to put herself in the agent's place because she recognizes in him a fellow-being; a sensible being capable of feelings.Hence, the sympathetic process has specific conditions for identification to take place: in the first place, the other, the one with whom we are sympathizing, must be able to produce some feeling in us, she must be visible, and we must be able to recognize her as our fellow-being; second, she must be able to feel herself; and, third, she must be able to produce feelings intentionally (TMS II.iii.6).If the agent is not visible, the process cannot take place: out of sight, out of mind 10 .
Moreover, the spectator will not feel exactly what the agent is feeling, because she never ceases to be herself; she only places herself in the other's place, she does not become the other, thus she can never have an exact impression of what the other is feeling (TMS I.i.1.2).Besides, her agreement or disagreement with the other's feelings varies according to circumstances.She may share the same feelings with one person in certain circumstances, and not share the feelings of the same person in other circumstances.Sympathy, then, is a case by case process, or rather a circumstance by circumstance process.In all cases, the process needs an encounter; it might not be a physical encounter, but it needs an image of the other in order for sympathy to operate.It is not an arranged encounter, and it does not need the agent to be aware of it 11 .
In what follows, we explore the implications of this identification mechanism, and especially, of the visibility condition we have presented, as a prior condition to any recognition, and thus, to any interaction.We advance, Smith's sympathy is a powerful mechanism to explore social phenomena that have been less visible in economic theory, such as social exclusion associated with the failure or the denial of recognition, and which entail, at least, symbolic violence.

The mechanism of sympathy and social distance: a formal representation
In order to understand the way in which the mechanism of sympathy works, we need to understand the way in which the extent to which the other's feeling of joy or of sadness affects a spectator.Smith considers the intensity of the effect of observing others, or taking the others' place, as fundamental in understanding how sympathy leads to the natural emergence of prosocial rules of conduct, and to the blockage of social interactions.Sympathy explains how we build a community, and how this community survives over time.It is not our concern for social order which preserves our community: Our regard for the multitude is compounded and made up of the particular regards which we feel for the different individuals of which it is composed.(…) The concern which is requisite for this, is no more than the general fellow-feeling which we have with every man merely because he is our fellowcreature.TMS II.ii.3.10However, when the distance between us is large enough, the general fellow-feeling might prove insufficient: Men, though naturally sympathetic, feel so little for another, with whom they have no particular connexion, in comparison of what they feel for themselves; the misery of one, who is merely their fellowcreature, is of so little importance to them in comparison even of a small conveniency of their own; they have it so much in their power to hurt him, and may have so many temptations to do so, that if this principle did not stand up within them in his defence, and overawe them into respect for his innocence, they would, like wild beasts, be at all times ready to fly upon him; and a man would enter an assembly of men as he enters a den of lions.TMS II.ii.3.4 The principle Smith is referring to is justice, which acts as the social glue in a community of strangers.The need for such a principle points to our inability to identify with distant others, showing the possible failures in identification and recognition, leading to discrimination, segregation, and exclusion.
In modern economics, to our knowledge, David Sally (2000) and ( 2001) has given the most attention to sympathy and its consequences in strategic decision making environments.He explores the consequences of the intensity of feelings involved in the sympathy mechanism, giving particular attention to the influence of the distance between agents on their interactions.This distance has to do with objective and subjective assessments that Smith posits as causes of the possibility or impossibility of identification and recognition.These assessments or perceptions are objective in that distance is physical, reflecting geographical or demographical conditions.The isolation of members of a community due to distance in space and time, or to the extent of the population has a direct relation with their possibility of sympathizing with others.The assessments are subjective in that they respond to the individuals' perception of the difference or psychological distance between them.The absence of identification with someone else, the failure to recognize someone as another, due to physical or psychological distances is a powerful mechanism that affects social interactions.
In Chapter 1, section II, part VI of the TMS, Smith explains the "Order in which individuals are recommended by nature to our care and attention".In this chapter it is clear that what Smith calls habitual sympathy plays a major role in how we relate to each other and how much we care for each other.Smith establishes a direct connection between this habitual sympathy or affection between individuals, and its importance for what he calls their common happiness.When the survival of those involved is at stake, habitual sympathy makes their well-being a matter of concern for those around them.So it is that, the well-being of the individual, of her family and close relatives comes first for her, and these close relationships imply "a more precise and determinate" (TMS VI.ii.1.2) sympathy, which allows her to have a better approach "to what he feels for himself" (TMS VI.ii.1.2)12 .We sympathize and agree more easily with those with whom we share our daily lives: our families, friends, neighbors and colleagues (TMS VI.ii.1.15-16),or, in other words, with whom we have a "physical connection" (TMS VI.ii.1.17).This physical connection can also, we advance, may be extended to a psychological connection, making physical and psychological distance between individuals play a key role in the sympathetic process.
Going a step further than Sally, we believe a more complete representation of Smith's sympathy can give insights into issues Sally does not address.In particular, he does not deal with what Smith calls the disagreeable sympathetic passion that explains how sympathy can be blocked, causing recognition to fail.Imagine, for example, a situation where parents try to keep their children from terrible news; they might decide to do so in order to prevent them from feeling the pain they felt when learning of a tragedy.It they believe the children will not be able to cope with such news, or that they might be traumatized by them, parents might decide not to tell the children, preventing them from sympathizing, let alone approving or not, with those in tragic circumstances.The sufferers will not exist for the children; they will not be recognized by them in their suffering.The same happens when we turn our eyes away from extreme misery, distress, despair or pain.This could be the case even when physical distance is very small, or when we try to increase psychological distance to avoid seeing ourselves in undesirable circumstances.

Social Distance and the Neutralization of Sympathy
Sally emphasizes the role of psychological and geographical distance as determinants of the intensity of the sympathetic passion.As he aims at incorporating common cases and not the extreme cases mentioned above, his formal representation avoids the complexity of disagreeable sympathetic passions producing sorrow in the observer, and thus the possibility of a blinding mechanism of sympathy explaining social exclusion.Furthermore, Sally's representation ignores the asymmetric form of the sympathetic mechanism Smith explains, and which will play an important part in our own representation.However, it is useful to use his notion of social distance, and its consequences on the intensity of the sympathetic passion as a starting point for a more general representation.
For our purposes, it is particularly interesting to note the role of psychological distance.Sympathy can only operate within a group of agents that recognize each other, that is, who can identify with the other´s circumstances, in particular, and with her place or situation within the community, in general.With increasing social distance, the other's identity becomes distorted.At the extreme, this distortion produces social exclusion, defined here as the inability to recognize someone else as a fellow-being.From the point of view of the spectator, sympathy would not work because she is unable to put herself in the agent's situation.
Figure 1 shows the inverse relationship between sympathy (namely sympathetic passion) and social distance as represented in Sally's (2000) model.The thick continuous line represents this idea.

Figure 1: Sally's sympathy mechanism
Here distance is a composite coefficient containing both geographical and psychological distance.Let be the distance coefficient between agents i and j as perceived by agent i. Sympathy is related with distance by a convex and decreasing function.Let be the sympathetic passion of agent i when observing the situation of agent j.The first argument of this function being the subjective idea that agent i has of j's situation.
As far as the simple idea of the effects of distance on the intensity of the sympathetic passion is concerned, this inverse relation accurately represents Smith's idea.However, Sally considers the relationship between distance and sympathy as an asymptotic function.Moreover, the domain over which sympathy is defined in Sally's model only takes into account a positive valuation of feelings.Both characteristics imply the impossibility of considering the blinding effect of extreme sorrow and thus the existence of exclusion present in Smith's analysis of sympathy.
Sympathy produces what Tugendhat (1998) has called affective communication, because it refers to a non verbal contact resulting from observation, and imaginary transfer.When social distance increases (decreases), this communication is more (less) difficult and inaccurate (accurate).Thus, distance has a direct influence on the possibility of communicating, and when this communication is not possible, individuals will not recognize others and will not be recognized by them.Furthermore, psychological distance may be related to a form of denial of the other's humanity due to his particular situation within society.Many explanations of slavery or ethnic violence are based on the dehumanization of slave or discriminated populations.Dehumanization can be considered to be an external element acting on individual judgment; a sort of perverse habit or custom that is transmitted through cultural information or social norms within a group, and which leads individuals to accept ethnic violence, and the denial of the humanity of those perceived as different and alien.Nevertheless, using Smith's sympathy mechanism, it is possible to point out another element of exclusion.An element that operates at an individual level and that accompanies, nurtures, and reinforces social norms.This element is the rejection of the pain the sympathetic passion might cause in the spectator.
In order to capture this idea, in Figure 1 we introduce as a dotted line a necessary modification of the relation between social distance and the sympathetic passion: from a certain level of social distance onwards, sympathy is neutralized.This represents the possibility of the absence of any fellow-feeling among agents and its consequent impossibility for the sympathetic mechanism to operate.
This mechanism does not operate as a form of neutral and objective assessment of the actor's situation.It is chiefly a mechanism involving feelings of sorrow and happiness linked to the identification process.Someone who sees someone else in pain, through the identification process of sympathy, might feel some degree of pain.Thus, the mechanism includes a direct effect on the spectator's well-being.It is precisely this sympathetic passion which is presented as the foundation of moral judgments, and it is this passion which defines the social interactions resulting from sympathetic encounters.As mentioned in the first section, the spectator will approve of the agent's behavior if she feels the same when putting herself in the agent's circumstances.She will disapprove of his behavior if she does not feel the same in his situation.In  general, approbation (disapprobation) depends on the coincidence (divergence) between the feelings of the spectator and those of the agent13 .Here we will concentrate only in the cases where coincidence arises, that is, when the spectator would approve of the agent.We believe these cases are particularly interesting because when this happens, acceptance or exclusion of the other does not arise from blame; it is not because we do not approve of the other, or because we envy them, or because we find her behavior reprehensible that we do not want them in our community.
Even in the case of coincidence, because the sympathetic encounter produces a feeling in the spectator, she may block the sympathy mechanism trying to avoid an extremely discomforting sympathetic passion.Such blockage can explain the invisibilization, exclusion, and even the failure or denial of recognition, of those in extreme situations of physical or psychological misery.On the other end, situations perceived as of extreme joy may lead the spectator to overestimate such situation, and to want to become the other, producing emulation in search of individual fusion.In brief, when a sympathetic encounter takes place with people in extreme misery or extreme joy, it distorts our image of the other, and has lasting consequences on social interactions.An important conclusion that can be derived from Smith's analysis of the sympathetic mechanism in extreme situations of joy and sorrow is that social order and the determination of the frontiers of the social community are related.Sympathetic encounters determine how individuals identify themselves, and the way they recognize or not someone else.

Asymmetric and extreme sympathetic passion
As   (. ) is defined over a positive domain in Sally's model, it represents sympathy with joy and with sorrow as if they were equivalent, and always pleasurable, hence leading to the approval of the other's feelings.It does not allow us to make a distinction between two elements Smith differentiates, and to which he referred to in a remark he added to the second edition of the TMS: It has been objected to me that as I found the sentiment of approbation, which is agreeable, upon sympathy, it is inconsistent with my system to admit any disagreeable sympathy.I answer, that in the sentiment of approbation there are two things to be taken notice of; first, the sympathetic passion of the spectator; and, secondly, the emotion which arises from his observing the perfect coincidence between this sympathetic passion in which the sentiment of approbation properly consists, is always agreeable and delightful.The other may either be agreeable or disagreeable, according to the nature of the original passion, whose features must always, in some measure, retain.(Footnote added in ed.2 (1761) to TMSI.iii.1.9)So, as we already saw, the greater or lesser coincidence between the feelings of the spectator and those of the agent in a specific situation produces the pleasure of mutual sympathy, because they share, to a greater or lesser extent, their feelings.But in order for this to happen, a prior feeling is aroused in the spectator: that which she herself would feel if she were in the agent's situation.In a joyful situation, she will feel joy; in a sad situation, she will feel sorrow.These sympathetic feelings make her happy or sad, feelings that in themselves are, as Smith calls them, agreeable or disagreeable14 .These are the feelings we would like to include in a formal representation aiming at illustrating the possibility of non-recognition.
As Bréban (2012: 559) recalls adversity generates a more violent sensation than prosperity because it is less usual.People will have to make a greater effort to imagine the feelings of those in misery than those of the ones in joyous situations because the distance between the ordinary emotional state of most people "and the highest pitch of human prosperity […] is but a trifle; between it and the lowest depth of misery the distance is immense and prodigious" (TMS I.iii.1.8) 15.
Following this idea, the pain that a situation of extreme misery would cause in the spectator would be so intense that she would try to avoid it.Sympathy is thus blocked, in a more or less conscious manner, to escape the extreme pain that the sight of an extremely miserable situation generates.On the contrary, facing situations of extreme joy, the spectator overrates them, just as in the case Smith presents of the poor man's son (TMS IV.i.8).This individual, who, as most of us, confuses wealth and power with happiness (TMS I.iii.3.1),strives at reaching the higher ranks of his community in order to enjoy the same situation of the wealthy and the powerful.However, his confusion prevents him from seeing that these individuals may be no happier than the most simple of human beings (TMS IV.i.10), and that the level of happiness he longs for, might even be humanly unattainable 16 .When the spectator disapproves of the actor's feelings in situations of extreme joy, meaning she does not share them, this overestimation of such situations also has an important effect: spectators are less tolerant with the failings of those they perceive in enviable circumstances 17 .The asymmetry would explain why "Our respect for the great, accordingly, is most apt to offend by its excess; our fellow-feeling for the miserable by its defect."(TMS VI.ii.1.20).
Consequently sympathy does not operate in a symmetric way.In the beginning of the TMS, when he is defining sympathy, Smith asserts that it has been currently associated with compassion but that it can be related to a wider sentiment of fellow-feeling, which denotes our capacity of accompanying our fellow-beings in whatever sentiment they might be experiencing (TMS I.i.1.5).It had been taken for compassion because there is an asymmetry in this fellow-feeling: we have a stronger propensity to sympathize with happier and agreeable situations than with sorrow or misery.This happens because the spectator takes more notice of the effort she makes in entering the situation of those in sorrow and pain, than of the effort of placing herself in the opposite circumstances.
As we struggle to keep down our sympathy with sorrow we take more notice of it.This process does not take place with joy, even when we feel envy because we are ashamed of it and we prefer to ignore it.(TMS I.iii.1.4).
Incorporating the disagreeable and agreeable sympathetic passion within the same model requires also taking into account its asymmetric intensity whether it is aroused by joy or by sorrow.This allows us to propose a more general framework including other elements that have currently been left aside in most of the literature.

The formal properties of the sympathetic passion function
The above elements allow us to define a function of the sympathetic passion of a spectator with two arguments: social distance and the subjective perception of agent i, the spectator, of the situation of the observed agent j: .ℝ 2 , meaning sorrow or painful feelings have negative values and joy or pleasure have positive values. 15We will come back to this quote in section 4.3. 16Smith also says that "it is well that nature imposes upon us in this manner" because this deception "rouses and keeps in continual motion the industry of mankind."(TMS IV.i.10). 17The way in which the sympathetic mechanism operates in these circumstances is similar to what has been identified in modern behavioral and experimental economics.The literature on altruistic punishment, initiated by Fehr and Gächter, finds a link between individual evaluation of other's rank or situation, and the negative sentiments towards defection or no-cooperative behaviors: "The evidence indicates that negative emotions towards defectors are the proximate mechanism behind altruistic punishment" (Fehr & Gächter, 2002).
According to our interpretation of Smith's theory, function has the following characteristics: 1. Imperfect identification: Smith considers sympathy not as a perfect matching between the observer's feelings and her perception of the other's, implying only in particular cases: Mankind, though naturally sympathetic, never conceive, for what has befallen another, that degree of passion which naturally animates the person principally concerned.TMS I.i.4.7 So we can resume this property by supposing there are two values for ̂  such that: (1) ̂   ≡ Ω ∈ ℝ − :   (. ; Ω) = ̂   and ̂   ≡ Φ ∈ ℝ + :   (. ; Φ) = ̂   Imperfect matching implies that for an individual, the sympathetic passion is most of the time different from what she considers the other is feeling in a particular situation.This could be above or below what the other is feeling.We shall show that this imperfect coincidence of sympathy explains interesting cases, as the one referred above as the "poor man's son", or our sympathy with the dead: That our sympathy can afford them no consolation seems to be an addition to their calamity; and to think that all we can do is unavailing, and that, what alleviates all other distress, the regret, the love, and the lamentations of their friends, can yield no comfort to them, serves only to exasperate our sense of their misery.TMS I.i.1.13 Or our sympathy with the mentally ill: The compassion of the spectator must arise altogether from the consideration of what he himself would feel if he was reduced to the same unhappy situation, and, what perhaps is impossible, was at the same time able to regard it with this present reason and judgment.TMS I.i.1.11Furthermore, Smith insists on the possibility of a lack of sympathy for what an individual considers is an excessive reaction of others facing little sorrow.

Decreasing on social distance:
The intensity of the sympathetic passion diminishes on the perceived social distance between the observer and the observed agent 18 .Thus: (2) 3. Asymmetric intensity: perceived agreeable situations of the observed agent are more likely to produce identification with the observer's feelings than disagreeable situations: Pain is a more pungent sensation than pleasure and our sympathy with pain, though imperfect, is a more lively perception than that of pleasure, which can be more perfect.(TMS I.iii.1.3) 18For the sake of simplicity, we suppose   to be independent from the sympathetic passion.However, in some passages Smith advances the idea of a sort of endogeneity of the psychological distance.
This implies a non monotonic function of sympathetic passion depending on the sign of Let and be two functions representing respectively the influence of social distance on agreeable and disagreeable situations of the observed agent.Where and .Let and be two different functions relating respectively the perceived agreeable and disagreeable situations19: The asymmetric property can be resumed according to the partial derivatives on (3) Functions g and f increase in because we are only considering the mechanics of sympathy when there is a coincidence of feelings between spectator and actor.Furthermore, f(0)=0 and g(0)=0, because the sympathy mechanism facing no situation or no sentiment is inactive.
In order to complete our scheme, we need to construct some assumptions about the curvature of the function.

Concavity in sorrow and Convexity in happiness:
Logically related with property 3, Smith describes a nonlinear relation between and as noticed above.The reasons for these curvatures are related with two elements of Smith's description of the way in which an observer reacts facing sorrow and joy.Concerning the former case, what an observer considers as little pain or sorrow triggers a greater sympathetic effort from the spectator, making her feel more intensely.Whereas concerning little joy the observer's feelings are more akin: Joy is a pleasant emotion and so it is pleasurable to sympathize with it.Grief is painful and we try to avoid it, so we do not sympathize with it when caused by frivolous objects, plus there is the natural malice which renders little uneasiness diverting (TMS I.ii.5.3)Such asymmetry in effort occurs because the average state of mind is closer to happiness than to pain: "The greater part of men, therefore, cannot find any great difficulty in elevating themselves to all the joy which any accession to this situation can well excite in their companion" (TMS I.iii.1.7).Therefore, Smith concludes that: It is agreeable to sympathize with joy; and wherever envy does not oppose it, our heart abandons itself with satisfaction to the highest transports of that delightful sentiment.But it is painful to go along with grief, and we always enter into it with reluctance (TMS I.iii.1.9)This is not a prosaic observation because it has implications for the construction of self identity and social rank structures.This asymmetry leads individuals to agree more, in everyday preferences and even in politics, with those who are happier or richer than with those in sorrow and misery.Smith explains this difference in a straightforward manner: 19 The properties of these functions will be described below following other aspects of Smith's theory.
Mankind, however, more readily sympathize with those smaller joys which flow from less important causes.(TMS I.ii.5.2) (…) It is quite otherwise with grief.Small vexations excite no sympathy, but deep affliction calls for the greatest.(TMS I.ii.5.3) The asymmetry of the sympathetic passion implies a more complex mechanics of the formation of social rules than the common cases of sympathy as pure identification with other's feelings or situation.The importance of this asymmetry is also linked with the extreme cases described above.In fact, the sympathetic passion has different limits and leads to different reactions whether it is produced by a negative or a positive feeling.
Not only is sympathy with joy and sorrow asymmetric, it also happens that the distance between the sympathetic passion and the perceived one is greater in the case of sad circumstances than in the case of happy ones.Extending a quote we already used above, we find: Though between this condition and the highest pitch of human prosperity, the interval is but trifle; between it and the lowest depth of misery the distance is immense and prodigious.Adversity, on this account, necessarily depresses the mind of the sufferer much more below its natural state, than prosperity can elevate him above it.[…] It is on this account, that though our sympathy with sorrow is often a more pungent sensation than our sympathy with joy, it always falls much more short of the violence of what is naturally felt by the person principally concerned.(TMS I.iii.1.8).
The partial derivatives for those functions are not constant because the "marginal sympathetic passion" is increasing in .Furthermore, the sympathetic passion when considering sorrow or pain converge to a coincidence of feelings ( ) only for "great pain", whether it is easier to match the observer's feelings with the observer's joy: (..) I will venture to affirm, that, when there is no envy in the case, our propensity to sympathize with joy is much stronger than our propensity to sympathize with sorrow; and that our fellow-feeling for the agreeable emotion approaches much more nearly to the vivacity of what is naturally felt by the person principally concerned, than that which we conceive for the painful one.TMS I.iii.1.5 The form of g and f are thus described by the following properties: (4) These four properties allow us to represent a general idea of the mechanics of sympathy.We shall apply these properties and propose a particular illustration using simple functional forms verifying them.As we are particularly interested in the cases of exclusion and emulation, we will focus our attention on these extremes cases.Nonetheless, it is worth noticing that other cases can be easily studied from this formal representation of sympathy.

A graphical example of the mechanics of passion
A simple case of the general properties of the sympathetic passion function is represented in The red curve represents the form of the sympathetic passion when the observer perceives joy and the black one when it is the case for sorrow.As the 45 degrees dotted line represents perfect matching of feelings, property 1 is verified because there exist Φ and Ω showing respectively the coincidence of joy and sorrow.Furthermore, the red and black curves take values below and above the 45 degrees line because of the curvatures implied by properties 3 and 4. We will analyze the effects of social distance over the sympathetic passion (property 2) in another figure (Figure 3) as this produces the curves to shift.
The whole portion of the red curve below the 45 degrees line is closer to this line than the portion of the black curve above it.This stands for the asymmetric relation of the sympathetic passion with joy and sorrow.The spectator's feelings are closer to the agent's joy than to her sorrow.However, as the absolute value of the second derivative of g depends on ̂  , so when perceived pain increases, the convergence of feelings becomes more possible.The black curve's slope is higher the higher is the perceived pain.Thus, it is worth noticing that the red curve cuts "faster" the dotted line but the slope of this curve increases "more slowly" than for the black curve.This illustrates the fact that little pains are less noticed than stronger ones, but joyous feelings match more easily.This is related with the fact that, comparing the absolute values of those levels: |Ω| > |Φ|.For the coincidence with other's pain requires a higher level of it than the coincidence in joy.Taking into account the fact that approbation or reprobation of an action depends on the matching of feelings, we can observe that this formal representation of the sympathetic passion accurately represents one of Smith's main characterizations of sympathy: the sympathy with situations causing small joys is easier than the one with those producing small pains.
On the contrary, he always appears, in some measure, mean and despicable, who sunk in sorrow and dejection upon account of any calamity of his own.We cannot bring ourselves to feel for him what he feels for himself, and what, perhaps, we should feel for ourselves in his situation: we, therefore, despise him; unjustly, perhaps, if any sentiment could be regarded as unjust, to which we are by nature irresistibly determined.(TMS I.iii.1.15) 20  The rapid increase in the slope (going from 0 to negative values) of the black curve represents precisely the way in which this mechanism operates.
We can now turn our attention to what happens when an agent observes levels of pain such that ̂  < Ω.These cases represent situations of unbearable levels of pain caused by the observed misery.For levels of pain higher than Ω (i.e.̂  more negative than this level), agents in an intended or unintended way cover their eyes and hinder the sympathetic mechanism.Smith says: "We often feel a sympathy with sorrow when we would wish to be rid of it;" (TMS I.iii.1.4).This produces what we have described as a process of non-recognition.In order to illustrate this, let us present a long quotation: The poor man, on the contrary, is ashamed of his poverty.He feels that it either places him out of the sight of mankind, or, that if they take any notice of him, they have, however, scarce any fellow-feeling with the misery and distress which he suffers.He is mortified upon both accounts; for though to be overlooked, and to be disapproved of, are things entirely different, yet as obscurity covers us from the daylight of honour and approbation, to feel that we are taken no notice of, necessarily damps the most agreeable hope, and disappoints the most ardent desire, of human nature.The poor man goes out and comes in unheeded, and when in the midst of a crowd is in the same obscurity as if shut up in his own hovel.Those humble cares and painful attentions which occupy those in his situation, afford no amusement to the dissipated and the gay.They turn away their eyes from him, or if the extremity of his distress forces them to look at him, it is only to spurn so disagreeable an object from among them.The fortunate and the proud wonder at the insolence of human wretchedness, that it should dare to present itself before them, and with the loathsome aspect of its misery presume to disturb the serenity of their happiness."(TMS I.iii.2.1) Remark that misery renders individuals invisible.The sufferer is aware of this, and the invisibility augments her suffering; whereas the spectator tries not to see her to avoid the disagreeable sympathetic passion, and even blames her for altering her state of mind.Mallory (2012: 600) explores this kind of relation as a type of strangership based "on exclusion and the denial of sympathy and recognition".Recognition cannot take place because the spectator does not want to see, she does not want to engage in the affective communication involved in the sympathetic encounter.She would rather avoid any contact with the sufferer, who is made invisible, ignored, left aside, and, in the end, excluded.
In our formal representation, as showed in Figure 2, another discontinuity appears along the function .This function is asymptotic to Ω, graphically represented by the continu- 20 As we tend to associate sorrow and misery with poverty, this also happens regarding the poor: "The mere want of fortune, mere poverty, excites little compassion.Its complaints are too apt to be the objects rather of contempt than of fellow-feeling.We despise a beggar; and though his importunities may extort an alm from us, he is scarce ever the object of any serious commiseration."(TMS III.3.18) ) ; ( ij ij ij s S  ous curve going along this value and showing the excessive or even the intolerability of levels of sorrow beyond that limit.Formally: ̂  < Ω (5) Note that the dotted line in black in Figure 2 represents the value of the function going beyond that limit value.These values are impossible to attain because agents refuse to observe or refuse to imagine a greater level of suffering.We shall come back to this idea to show an interesting conclusion of Smith's theory concerning the invisibility of extreme poverty.
On the other side of the sentiments, Φ represents the perfect convergence with a joyful situation.Levels of joy above this limit do not imply a blockage of the sympathetic mechanism but a perturbation, leading the observer to overestimate the intensity of the observed happiness.The dotted portion of the red curve above the 45 degrees line represents the actual impossibility of someone going beyond that limit.
In a certain way Φ represents the maximum possible joy that an agent can reach.However an important characteristic of the sympathy mechanics is its being an exercise of the imagination.This leads agents to be victims of a form of illusion considering other's joy.Smith relates these phenomena with a form of disproportionate willingness to agree with powerful or rich people, because we consider their situation "to be almost the abstract idea of a perfect and happy state", and this state is "the final object of all our desires" (TMS I.iii.2.2).In Figure 2, we observe that becomes identical to the 45 degrees line as: This discontinuity in the function implies agent i misperceiving the possibility to be happier or even wealthier than a certain limit.Agent i is thus victim of an illusion and imagines agent j situation beyond this limit.As any level of joy beyond Φ is a pure invention of i's imagination, there is a perfect coincidence of the perception and the perceived sympathy.Smith deduces an interesting conclusion from this type of situations: The spectator wishes to become the one she observes, opening the way to social fusion, or loss of individuality: "To approve of another man's opinions is to adopt those opinions, and to adopt them is to approve of them" (TMS I.i.3.2).And as with opinions, the same happens with sentiments or passions, and the spectator will adopt the agent's passions to become more like her.This creates incentives to imitate or to try to attain this imaginary state of richness associated with maximum happiness.It can even explain fanaticism and the voluntary acceptance of arbitrary decisions from powerful people.Exclusion and power abuse are thus the product of a similar mechanism, operating on the limits of human perception of sorrow and happiness.

The effects of social distance revisited
Going further in the analysis of this psychological mechanism, we can now explain the effects of property 2. As it has been explained in Smithian literature (remember Sally among others), social distance is an important variable to understand sympathy.Using our formal representation, Figure shows21 the effects of changes in social distance22 : .Let's imagine an agent observing a similar action or situation affecting two different individuals.When the spectator perceives the agent to be closer (psychologically or geographically) her ability to sympathize with him increases, and their feelings are more similar.This is represented by the red and black lines being closer to the 45 degrees line for lower levels of .The dotted curves on Figure 3 shift, pointing to this exogenous effect of social distance on the sympathetic passion.When we move down the curve relating sympathy with distance in Sally's representation (Figure 1), we witness a shift of our sympathetic passion function getting closer to the 45 degree line.


Three important implications can be derived from this representation.The first one is that social proximity produces a paradoxical effect on exclusion.In Figure 3 Ω( 1 ) > Ω( 2 ) as  2 >  1 implies that a spectator would be more sensible to the sorrow and misery when she perceives a greater social proximity.For instance, when an agent observes that someone very close to her, which could even be herself, is in an extremely miserable situation, she will be shocked by this situation and then prefer to turn her eyes away from it.This may seem paradoxical but it is easy to understand that, for example, middleclass white people would tend to ignore the existence of white poor people in developed countries, just as sociological studies showed in the US during the sixties.
The second implication concerns the delusive situation created by an overestimation of the joyful situation of an agent.Think about the case of the "poor man's" son considering the possibility attaining someone else's imagined level of wealth and happiness.When he considers this person to be socially closer to him, as someone from his same social group or neighborhood, he thinks it is possible to become that rich.The mirage is closer and the poor man's son will make incredible efforts to attain that imaginary state of happiness.As we are all more or less subject to this form of delusion, leading us to confuse wealth and power with happiness and virtue, and to imagine the rich and the powerful to live in a perfect state of happiness, this figure of the poor man's son is more general that would appear at first sight.When this attitude is accompanied by an industrious spirit, we will obtain the image of what Smith calls the "projec-tors".This is a form of compulsive entrepreneurial attitude causing growth but also instability in the economy 23 .
Finally, as we mentioned above, Smith considers the cases when social distance leads to another form of exclusion: the spectator is incapable of evaluating the other's situations because she cannot put herself in the other's shoes.In Figure 1 this is represented by the level of distance where the decreasing curve cuts the horizontal axis.In Figure 3 this will be the case when  → 0. It is easy to observe that at the limit the red and the black curve tend to be closer to the horizontal axis or to be further apart from the 45 degrees line.Social exclusion is then explained by two different reasons: the social distance and thus our incapacity to recognize the other as a similar, and the exclusion of extreme misery.Mallory (2012: 602) asserts Smith does not question the fact that unequal access to property and wealth leads to unequal recognition "even if it leads to what he considers unjust regard for the rich and the poor".Smith would privilege a type of strangership "imbued by a generalized atmosphere of good will, generosity and trust and where interactions are predictable, civil, calm and friendly" (Mallory 2012: 599), and therefore "Smith provides a depoliticized notion of strangership where the sympathy that animates it generates only weak ethical demands" (Mallory 2012: 602).Smith, then, would fall short in his assessment of a commercial society because he does not deal with "asymmetrical power relations between strangers" (Mallory 2012: 603).Even if we share Mallory's conclusions, we believe Smith provides an insightful framework that allows tackling these precise relations and their consequences on the assessment of justice in commercial society.In this paper we have tried to formalize such framework.

Concluding Remarks
Smith's sympathy proves to be a simple and powerful mechanism to assess social interactions.Through a formal representation we have tried to account for this mechanism, and show how it explains recognition and its conditions, as well as emulation, and exclusion.Within this simple framework, we believe it is possible to develop insights that can further our understanding of social interactions as relationships between sensitive individuals defined by an extended sense of self.Such individuals strive at being recognized; as human beings have a tendency to sympathize more easily with joy than with sorrow, and to associate wealth and power with happiness and virtue, such individuals will pursue fortune and success, and avoid poverty and misery: As to become the natural object of the joyous congratulations and sympathetic attentions of mankind is, in this manner, the circumstance which gives to prosperity all its dazzling splendour; so nothing darkens so much the gloom of adversity as to feel that our misfortunes are the objects, not of the fellow-feeling, but of the contempt and aversion of our own brethren."(TMS I.iii.2.9)Through this analysis we hope to offer a better understanding of Sally's statement: "Smith appeared to place great faith in the aphorism, 'Out of sight, out of mind'" (2001: 3), showing it was not only faith that moved Smith, but a convincing model of human interactions.

Figure
Figure , with the following functional forms , and and being linear functions.It is easy to verify that quadratic and cubic functions verify the four properties, in particular:

Figure
Figure 2: General representation of : the sympathy mechanism ) ; ( ij ij ij s S 

Figure 3 :
Figure 3: Effects of social distance on Sympathy