Interdependence via reference groups and social want

18 H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 This two-step procedure should be contrasted with one suggested by Kornai 1971, in which a single element is chosen from the set of eligible alternatives at the final stage of an elementary process with no deterministic decision rules for this selection. Final choices are randomly made with a decision distribution being defined on the set of eligible alternatives. In our model, the criterion of how best to meet social want narrows the choices from the satisficing feasibility set.

6. Interdependence via reference groups and social want

With the role of social want made explicit, we next turn to the modeling of interdependence via reference groups that endows social want with a useful structure to decision making at the final stage. Since an individual guides his behavior by perceiving, in a bundle of goods, certain properties or qualities that contribute to the satisfaction of his social want, we need to measure such properties somehow. Recall that our scheme of social interdependence had three features Section 3: 1 an individual belongs to a social group and takes a number of social groups as his reference groups in the process of seeking upper status identification; 2 some of these groups are to be emulated positive orientation and others are to be avoided negative orientation; and 3 these reference groups are ordered in terms of their social statuses. These features were then consolidated into the notion of a reaction function defined on a set of well-ordered reference groups. This scheme associates each bundle of goods with a vector of non-functional attributes derived from its popularity across social groups. Therefore, to what extent a given bundle of goods meets social want can be measured, to a first approximation, by convoluting a reaction function with vectors of such non-functional attributes. To formalize this measurement, we start with the following postulates. Postulate 6. There are a finite number of social groups in the society, ˆ S ≡ {g 1 , g 2 , . . . , g n }. An individual is oriented to a subset of these groups, S ≡ {g 1 , g 2 , . . . , g k } ⊂ ˆ S. Groups in S are referred to as the individual’s relevant social groups or reference groups. S is individual-specific and depends largely on his position in the social field. The individual belongs to at least one group in S. Postulate 7. The set of relevant social groups, S, is divided into two disjoint subsets, S 1 and S 2 S=S 1 ∪S 2 , S 1 ∩S 2 =∅: S 1 = {g i : g i ∈ S and g i is a group of positive orientation}, S 2 = {g j : g j ∈ S and g j is a group of negative orientation}. That is, g i ∈S 1 is a group to be emulated, and g j ∈S 2 is a group to be avoided. Postulate 8. An individual has orderings, R 1 on S 1 and R 2 on S 2 , defined as follows: 1. For any two groups, g i and g j , in S 1 , g i R 1 g j if and only if g i has emulation effects stronger than or equal to g j . H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 19 2. For any two groups, g i and g j , in S 2 , g i R 2 g j if and only if g i has avoidance effects stronger than or equal to g j . We assume that there is a continuum of social status levels over the range [0, h] alter- natively, one may assume that there are only a finite number of such levels. It is important that there exists a social-status ranking function that is accepted by most members of the society, so that the status disparity between any two groups can be measured with little personal biases. Postulate 9. There exists a social-status ranking function r : ˆ S → [0, h] which satisfies 1. rg i rg j if and only if g i is higher than g j in social status, and 2. rg i =rg j if and only if g i and g j are identical in social status, where ˆ S is the set of all social groups. This social-status ranking function makes it possible to measure the social status disparity between any two groups. Definition 1. A social-status disparity function is a real-valued function d : ˆ S × ˆ S → R that associates each pair g i , g j ∈ ˆ S × ˆ S with a real number dg i , g j = rg i − rg j . The absolute value |dg i , g j | is referred to as the social distance. A social-status disparity function is analogous to a distance function a metric in math- ematics, but it differs in that it is allowed to take both positive and negative values. If the function takes a positive negative value for a pair of groups, the first is ranked higher lower than the second in social status. If there is little risk of confusion, we shall use social status disparity and social distance interchangeably. An individual’s orientation to social groups for emulation or avoidance is in general limited to a subset S ⊂ ˆ S. Without loss of generality, let it be assumed that the elements of S are ordered by the social-status ranking function with the larger subscript indicating the higher social status, so that r g i r g j if and only if ij. We assume that no two groups in S have an identical social status rank. With this convention, g 1 takes the lowest value rg 1 and g k the highest value r g k among all g i ∈S. Suppose that group g m ∈S is a group of an individual’s current belonging; the case of multiple group belonging is excluded. From the vantage point of g m , the above disparity function, when restricted to his relevant set S, takes its maximum value at some social group and its minimum value at some other group with all other groups taking their values in between. Definition 2. Let an individual belong to a group g m ∈S. For his relevant set of social groups, S, define δ min ≡ min{dg i , g m : g i ∈ S, i = 1, . . . , k; g m is fixed}, δ max ≡ max{dg i , g m : g i ∈ S, i = 1, . . . , k; g m is fixed}, and Ω ≡ {dg i , g m : g i ∈ S, i = 1, . . . , k; g m is fixed}. With our convention, it holds that dg 1 , g =δ min and dg k , g =δ max . 20 H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 To formalize the notion that an individual is oriented positively to some groups and negatively to others, we introduce the notion of a reaction function defined on set Ω. 3 Definition 3. The reaction function of an individual who belongs to group g m is a real-valued function V : Ω → R such that 1. Vdg i , g m 0 if g i is in S 1 , 2. Vdg i , g m 0 if g i is in S 2 , 3. for any two groups, g i and g j , in S 1 , Vdg i , g m ≥Vdg j , g m if and only if g i R 1 g j , and 4. for any two groups, g i and g j , in S 2 , Vdg i , g m ≤Vdg j , g m if and only if g i R 2 g j , where S 1 and S 2 are the sets of groups for emulation and avoidance in Postulate 7. The last two conditions require that the reaction function V : Ω → R agree with orderings R 1 and R 2 defined on S 1 and S 2 , respectively. Listing the images Vdg i , g m , g i ∈S, gives a reaction vector, whose first and last components are Vδ min and Vδ max , respectively. Definition 4. A reaction vector, denoted [Vg i , g m ], is a vector defined by [V g i , g m ] ≡ [V dg 1 , g m , V dg 2 , g m , . . . , V dg k , g m ], where Vdg 1 , g m =Vδ min and Vdg k , g m =Vδ max . An example is useful to illustrate graphically what has been captured by Postulates 6–8 and Definitions 1–4. Consider a case in which an individual belongs to group g 4 and has seven relevant social groups including g 4 . In Fig. 1, the social-status disparity of each group from g 4 is plotted on the x-axis. Since the disparity of g 4 from itself is zero i.e., dg 4 , g 4 =rg 4 −rg 4 =0, the origin corresponds to the social-status rank of g 4 . The individual emulates groups g 3 , g 4 , g 5 , and g 6 and avoids groups g 1 , g 2 , and g 7 . The reaction function V : Ω → R, therefore, takes positive values at dg 3 , g m , dg 4 , g m , dg 5 , g m , and dg 6 , g m , and negative values at dg 1 , g m , dg 2 , g m , and dg 7 , g m . The absolute value of Vdg i , g m measures the intensity of the individual’s emulation and avoidance. Capturing the nature of the orientation to social and cultural norms, Vdg i , g m , i∈S or a reaction vector characterizes the individual’s social want. The shape of reaction functions is not a matter of personal tastes. Because orientation to social and cultural norms grows out of the need for reciprocal expectations and workable heuristic solutions to otherwise complex problems, it is contrary to the notion of social want itself to assume that such functions are idiosyncratically formed. But, if they are to have a common structure, some principles must be identified that contribute to its formation. At least four such principles can be identified along the psychological, social, communicational, and economic dimensions Ray, 1973, pp. 284–288. 3 We define a reaction function on the social status disparities of relevant social groups rather than directly on the set of such groups, although a reaction function defined as such, together with a social-status disparity function, induces an indirect reaction function on the set of relevant social groups. The reason for this definition is that the extent to which one emulates or avoids a reference group depends largely on how disparate the group is in social status from his own. That is, if a relevant reference group is replaced with another one of a similar status, the group should be emulated or avoided to a similar degree. H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 21 Fig. 1. A reaction function: an example. The psychological principle. Under interdependence via reference groups that is em- bedded in success-oriented moral values, psychological motives that drive emulation and avoidance should be closely related to the rewards of upward status identification as well as to the threat of lower status identification. The psychic satisfaction from such motives will, most likely, be an increasing function of the gains in social status. Written as a function of the social status disparity defined above, this function will be positive in its positive range and negative in its negative range, but increasing over the entire range. This satisfaction will be subjected to the law of diminishing marginal satisfaction analogous to the law of diminishing marginal utility. The social principle. Group norms tend to sanction positively favor those activities that are in vogue among members of own and similar status groups and to sanction negatively penalize those that deviate from these activities. Peer group pressures are often very strong and cannot be ignored e.g., Evans et al., 1992. The fear of a loss of reputation by acting differently from norms e.g., Akerlof, 1980 or the fear of inviting envy from others by doing too well Mui, 1995 can be strong enough to coerce individuals to behave in conformity with group norms. Viewed as a function of the social status disparity, these sanctions will therefore be positive around zero disparity but will fall to negative values in a bell-shaped fashion as the social distance increases in either direction. 22 H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 The communicational principle. The more distant in social status are the groups that are being emulated or avoided, the more difficult it becomes to obtain useful factual information about their life styles. People who belong to identical or similar social groups tend to communicate more often through socializing activities, and knowing more about what significant others are doing makes emulation and avoidance easier and more effective. Therefore, the quantification of this principle as a function of the social status disparity will be analogous to a density function of a normal distribution in probability. The economic principle. A life style is mediated by a certain set of complementarity relationships among goods and services. Hence, trying something new always runs the risk of threatening to break some of these relationships. To the extent that the disparity in life style becomes more pronounced with the social distance, such costs will rise as a function of this distance. Furthermore, successful emulation and avoidance requires factual information about life styles to be emulated and avoided, but information gathering is costly. Because sources of such information diminish in availability with the social distance, this cost will also increase with the same distance. An individual’s reaction function is the net outcome of these four and possibly more principles working underneath. The function will take 1 negative values in the extreme negative range of the social-status disparity, 2 positive values in the neighborhood of zero social status disparity, and again 3 negative values in the extreme positive range of the same disparity. That it takes negative values at the extreme positive and negative ranges of the social status disparity can be attributed to the dominating influences of the social and economic principles. Moreover, because the psychological principle is not symmetric in its effect i.e., the psychic satisfaction from higher status identification is positive while that from lower status identification is negative, a reaction function will generally take a skewed bell shape, tilted toward the upper status identification, as in Fig. 1. A word of caution is in order: It is by no means easy to construct a reaction function without running into a normalization problem. To anchor the position of a reaction function, it would be necessary to introduce some additional hypotheses that help fix the position of its underlying component functions including those representing the four principles above. But, such positioning cannot be left to the whim of personal tastes because one’s social orientation has to be reciprocated by similar orientation by others if social norms are to be sustained. The empirical testing of a reaction function, therefore, would require that some additional restrictions be imposed on its component functions in order that these functions may yield a normalized reaction function that can be tested empirically in actual situations see Ray, 1973, for a specific example. We have now demonstrated that social want can be represented by a reaction function. The importance of this function is twofold. First, expressed as a function of the social-status disparity, it structures social want itself i.e., the pattern and the intensity of emulation and avoidance against relevant social groups. Second, combined with another piece of information, it becomes possible to quantify the social want-satisfying property of choice objects. We now turn to this quantification. If orientation to social norms and seeking of upper status identification is what constitutes social want, the quantification of the social want-satisfying property requires information or perception regarding the whereabouts of these norms, in particular, information about how vogue choice objects are perceived to be among members of various social groups. H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 23 This information is essential in determining whether consumption of a particular choice object enhances the image of being part of those groups that are being emulated or puts distance to those that are being avoided. We, therefore, need to characterize choice objects in terms of their popularity across relevant social groups. Definition 5. Take an individual with set S of his relevant social groups, and consider commodity y j . Let zy j , g i be a popularity indicator index of commodity y j for group g i ∈S. For certain commodities, such as most household durables and semidurables, the pop- ularity in group g i can be measured by the proportion of the group’s population actually using them. Because such commodities are normally not purchased in bundles, the quanti- ties purchased are close to the number of the purchasing households. For others, however, measuring their popularity in this fashion can only be a rough approximation. In general, individuals do not possess accurate information on such proportions, nor do they have exact information on any other popularity measure. To that extent, the content of popularity indi- cators will be short of being objective; it may also be affected by channels of information diffusion such as advertising and word-of-mouth. Again, what is important here is that an individual has a certain perception on how popular any choice object is in each of his rele- vant social groups. Given the cost of information gathering and cognition, this perception is bound to be subjective and biased. But, by actually observing or hearing what significant others are purchasing, individuals will develop some idea on the social desirability of their choice alternatives, without which norm-orientation becomes an empty endeavor. Given a reaction vector and popularity indicators of choice objects, the social want-satis- fying property of a given commodity bundle y=[y 1 , y 2 , . . . , y n ] can be measured, as a first approximation, by multiplying each component of the reaction vector with a correspond- ing popularity indicator and summing this product over all relevant social groups and all components of the commodity bundle; this is a mapping from the commodity space G to the set of real numbers, F : G → R; i.e., x s = F y ≡ n X j =1 X i∈S zy j , g i V dg i , g m , where zy j , g i is a popularity indicator of commodity y j for relevant social group g i , Vdg i , g m the ith component of the individual’s reaction vector, subscript m denotes the group of the individual’s belonging and x s denotes the social want-satisfying property. Such imputation summarizes the total serviceabilities of a commodity bundle to the goal of getting better social status identification through emulation and avoidance of the life styles of relevant social groups. In this vein, Hirsch’s 1976 positional goods can be interpreted as those that take relatively high values in this imputation. The imputation of the social want-satisfying property completes the two-step choice process of the preceding section. According to this process, an individual first identifies his satisficing feasibility set through a sequential satisficing decision rule applied to his physical wants, and then selects from this set those objects that yield the highest satisfaction of his social want. Since each commodity bundle is associated with its social want-satisfying 24 H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 property through mapping x s =Fy, this process yields the following choice set: CB ≡ {y : y ∈ Ax ∗ ∩ BP , M and F y ≥ F y ′ ∀y ′ ∈ Ax ∗ ∩ BP , M}, where Ax ∗ ≡ {y: y∈G and Φy≥x ∗ } and BP, M≡{y: y∈G and P·y≤M}. It is possible to rationalize this choice set by an ordering defined on the goods space. To demonstrate this point, we first define on G a relation that is induced by function F. Call this relation a social want relation and denote it by R S . Definition 6. For any two commodity bundles, y i and y j , in G, y i R S y j if and only if Fy i ≥Fy j . This relation can be combined with our composite relation R G above to form a new relation R ∗ G on G. Definition 7. For any two commodity bundles, y i and y j , in G, y i R ∗ G y j if and only if any one of the following conditions holds: 1. y i ∈Ax ∗ , y j ∈Ax ∗ , and y i R S y j , 2. y i ∈G−Ax ∗ , y j ∈G−Ax ∗ , and y i R G y j , or 3. y i ∈Ax ∗ and y j ∈G−Ax ∗ , where G−Ax ∗ ≡ {y: y∈G and y ∈Ax ∗ }. Under this definition, the choice set CB consists of the R ∗ G -greatest elements of B: CB = {y : y ∈ B and yR ∗ G y ′ ∀y ′ ∈ B}. Consider now the goods space G and the set β of all possible budget sets of the form BP, M≡ {y: y∈G and P·y≤M}, where P is a price vector and M is income. The two constitute a so-called budget space G, β. The question is whether an individual h is rational in the sense of having a preference relation R defined on G such that the choice set hB is the set of the R-greatest elements of B for every BP, M∈β Richter, 1971. We have seen that with two relations, R G and R S , combined, there essentially is a preference relation R ∗ G on space G such that for each budget set BP, M∈β the choice set CB is the set of the R ∗ G -greatest elements of BP, M. Thus, the individual is rational; in fact, he is regular rational since R ∗ G is reflexive, transitive, and complete. Proposition 4. A system G, R ∗ G is a preference ordering relational system i.e., R ∗ G is reflexive, transitive, and complete. This result confirms that orientation to social and cultural norms is no less rational than behavior based on idiosyncratic tastes. Faced with the bounded rationality, an individual is motivated to cut the cost of problem-solving. In our modeling, this motivation takes the form of positive and negative orientation to social groups as an individual allows his choice decisions to be guided by the life styles of his relevant social groups. In this sense, the life styles as social norms are serving as real sources of low-cost heuristics to complex problems. An individual acting in this fashion is perfectly rational in the formal sense of Proposition 4, because the act of referring to social norms facilitates comparison of choice objects in a socially meaningful way. But, the resulting behavior differs from what the traditional utilitarian individualism envisions in that social norms are now internalized into an individual’s preferences. Among many possible modes of behavior, it is sensible and H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 25 meaningful to adopt this particular mode when an individual looks for heuristic solutions that not only saves the problem-solving cost but also are effective to the goal of upper social status identification. Proposition 4 implies that it is misleading to distinguish tastes-driven behavior in eco- nomics and norm-oriented behavior in sociology by the litmus test of the existence of a well-defined preference relation on the goods space. Whether behavior is guided by per- sonal tastes or social norms, individuals would have to have some idea as to which alterna- tives are more desirable than others. Orientation to social norms provides a guide no less effective on such comparison than personal tastes. The essence of Proposition 4 is that it is entirely possible for an individual to form a consistent ordering of his choice objects when his preferences are guided by social and cultural norms. It can be viewed as an ordering that prevails over a zone of socially meaningful flexible responses in the social field in Day’s terms or as an ordering that justifies the practice of intentional rationality in Beckert’s terms. The existence of such a norm-guided ordering is an answer to Hodgson’s call that human behavior be characterized as a purposeful norm-oriented behavior. With this ordering, an individual’s decision-making autonomy is exercised at two levels, first at the level of assign- ing priorities to different physical wants and setting their aspiration levels, and second at the level of identifying relevant social groups for emulation–avoidance purposes and eval- uating the social merits of choice objects by way of a reaction function and the perceived popularity indicators of choice objects. A norm-guided ordering reflects one’s position in the social field, the multiple principles that underlie reaction functions, and the percep- tion on the whereabouts of social norms. This implies that one’s choice behavior changes whenever any one of the underlying forces of his reaction function shifts and whenever his perception of social norms is influenced by advertising, word-of-mouth, and other diffusion processes of information. On this point, it is useful to recall that Corneo and Jeanne 1997 have examined the possibility that norms may be intentionally created by investment in social norms by producers with market power and that if social pressures for conformity transmitted via the feeling of envy by others become excessive, healthy efforts aimed at upper status identification may be seriously hampered Kolm, 1995; Mui, 1995. Thus, the social disposition and cultural value orientation, jointly, absorb bounded ratio- nality by suggesting how to integrate preferences around social and cultural norms. If the deliberation costs and other limits to rationality are substantial, norm-guided behavior will be an effective way of adapting to the environment in a socially meaningful way. 4 4 Sometimes a model of bounded rationality reduces to a model of unbounded rationality as a special case. No simple relationship of this kind exists for our model, because deliberation costs are not explicitly considered in individuals’ optimization problems as in Conlisk 1988, Day and Pingle 1991, and Pingle 1992. Rather than presuming that social orientation or status seeking is an end in itself dictated by invariant utility-measurable preferences regardless of the limits to rationality, we have maintained that because rationality is seriously bounded, individuals see the need to develop social capital of life styles collectively as real sources of low-cost heuristics to otherwise complex choice problems and that in so doing they simultaneously develop the desire to act in socially meaningful ways by internalizing social norms and cultural values into their preference formation. We leave undefined what the world would be like if individuals were completely unbounded in their rationality, hence were not in need of any instrument, social or otherwise, by which to absorb the boundedness of rationality. Therefore, our model of norm-guided preferences and socially-oriented behavior under bounded rationality cannot be related in simple terms to a model of unbounded rationality in the limit as the limits to rationality are lifted. 26 H. Hayakawa J. of Economic Behavior Org. 43 2000 1–34 What has been confirmed here, therefore, is that human behavior reflects endogenizes and thereby reinforces the social structure of the decision-making environment. As in- dividuals are oriented to social and cultural norms, such norms become internalized in their preferences. Norm-guided preferences, in turn, serve as an instrument to the repro- duction and evolution of these norms. Moreover, to the extent that social orientation is a consequence of the imperfect decision-making environment, the social structure reflects the nature of bounded rationality. Human behavior in society, therefore, rests on a triad of relations involving bounded rationality, the existence of social and cultural norms, and the formation of norm-guided preferences. We close this section with an observation that the above norm-oriented choice behavior of an individual who belongs to social group g m and has k-relevant social groups, S= {g 1 , . . . , g m , . . . , g k } can be viewed formally as a demand correspondence D : R n+1 + → G such that DP , M; x ∗ ; zy j , g i , V dg i , g m , i = 1, . . . , k, j = 1, . . . , n = {y : y ∈ BP , M ∩ Ax ∗ and F y ≥ F y ′ ∀y ′ ∈ Ax ∗ ∩ BP , M}. This correspondence does not presume that relevant social groups and reaction functions are exogenous to decision makers. To the extent that reference group taking is very much influenced by one’s economic and social status, which groups to emulate or avoid for social status identification is as much part of one’s choices as commodity bundles. For this reason, the reference group taking itself should be viewed as a choice correspondence Ψ g m ; Z : ˆ S → ˆ S such that Ψ g m ; Z = S ⊂ ˆ S, where Z is an indicator of one’s economic resources such as income and wealth. A reaction function is then formed vis-a-vis the selected reference groups. Such static characterizations of norm-oriented behavior and the reference-group taking are incomplete and should be supplemented by their dynamic features. But, taken as snapshots, these correspondences capture choice behavior and reference group taking within a zone of flexible responses that is tied to a position in the social field.

7. Leibenstein and Duesenberry revisited