Social norms and learning theories

Quality and Quantity, 19 (1985) 279-291 279 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

Social Norms and Learning Theories

MARTTI KUOKKANEN

Department of Philosophy, University of Helsinki, Unioninkatu 40B, 00170 Helsinki, Finland

Introduction

The aim of this paper is to consider the possibility of coupling social norms with classical learning theories. From the point of view of the emergence of social norms in a social-interaction process, social loop beliefs play a central role. Methodologically, the fundamental idea of this paper is the following: in a social-interaction process or situation, there are certain fixed social loop beliefs which in the case of (fixed) small groups may generate relatively stable patterns of behaviour [1]. These patterns of behaviour in turn generate explicit or implicit social agreements. As patterns of behaviour or agreement are generated by the behaviour and goals of the members of a group, these transform into social norms, i.e., the behaviour of each member is controlled by other members of the group and deviations from the fixed pattern of behaviour are punished by the group (by the others). The aim is to show that classical learning theories may be applied to this process, at least theoretically.

It must be stressed that the scope of the theorizing is relatively limited. Firstly, this paper considers only small groups in the ordinary social-psychological sense. In general, it is very difficult to fix a value to decide whether a particular group is "small". Secondly, the results can be applied primarily in those types of social interaction where the group exists for a relatively long time in a state of anomaly. As in the case of fixing a criterion for the smallness of groups, it is also very difficult to specify an exact criterion for "relatively long time" in general terms. This problem is therefore left open. Moreover, I exclude situations where no division of labour is generated by the situation (hence, the members can change roles without any restriction). Also, situations where there are, so to speak, "ready" fixed social roles (or norms) relevant for the situation are excluded. The same also holds for situations where the members simply decide to do something (after a short period of communication).

Social-psychological concepts of social norms and social loop beliefs are very interesting philosophically and methodologically, but they are also very

0033-5177/85/$03.30 �9 1985 Elsevier Science Publishers B.V.

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problematic. It is beyond the scope of this paper to clarify these concepts or analyze them philosophically [2]. Instead, the concept of social norms is used in its ordinary pre-theoretical social-psychological sense (although it is clear that the term has many meanings).

Social Loop Beliefs

In the following I characterize approximately the concept of a social loop belief. It is assumed in these considerations that the small social group consists of m actors and that each actor has n possible types of action. It is assumed th~/t concrete social actions in a given social situation can be referred to in terms of social types of behaviour, which are specified by the common relevant sociolinguistic standards of the group. It is considered that any concrete social action can be labelled as a social type of action on the dimension "pure conflict ac t ions--mixed ac t ions- -pure common-interest actions" [3]. For the sake of simplicity, it is also assumed that each actor consists of only one individual, although this is not a necessary assumption. Thus, the methodological framework is individualistic.

Given these simple assumptions, the possibilities of action or behaviour for a small group can be represented objectively, or " f rom an outsider's point of view", by the following m x n matrix:

Xa X2 ... Xn . . . . . . . .

A 2 . . . . . .

The symbols A i refer to actors, i.e., to individuals in a given social situation (i = 1, 2 , . . . , m), and the symbols X k refer to different social types of action or behaviour in a given situation (k = 1, 2 , . . . , n). In principle, it is not necessary to assume that every actor in a given social situation recognizes "objectively" h i s / he r or others' possible modes of action. Such an assumption would not be very realistic from the dynamic social-psychological point of view. However, in general, for practical reasons this kind of assumption is made, because increasing the number of actors rapidly causes very serious computational difficulties when situations are analyzed using learning theories. In any case, it is not assumed that every actor has the same number of possible actions; rather, it is assumed that every actor has the same set of types of action from which to choose. Hence, the matrix above is of a very general nature, and in some aspects highly idealized and simplified. How- ever, it may be considered of heuristic value for recognizing the structure of

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social groups and their possible ways of acting. The present characterization of the concept of a social loop belief is

philosophically and methodologically very approximate and unsatisfactory [4]. However, I believe it to be sufficient for the purposes of this paper. By a social loop belief (SLB) in a given social group I understand a situation in which:

some Ai's (1 < i < m) believe(s) (recognize(s), expect(s)), that some Aj's (1 <j<m; i--g j) believe(s) (recognize(s), expect(s)) that he / she (Ai) ought (want(s), intend(s)) to do X k and that the Aj's ought (want(s), intend(s)) to do X k (for the sake of some goal Y). The fundamental point of social loop beliefs is that they create and justify

some kind of distribution of labour in the group. I consider that social loop beliefs are at least necessary (and perhaps also sufficient), for the emergence of social norms and for the existence of a group as a small social group [5]. Hence, I consider social loop beliefs to be conceptually prior for small social groups: without social loop beliefs there are no social norms, no distribution of labour, and, hence, no small social groups.

The above concept of social loop belief implies that in a given social situation there are at least two different individuals. Each individual has certain propositional attitudes in respect of h i s /he r own role in the situation via beliefs concerning others' beliefs concerning himself/herself. The situation is structured as a social situation primarily by the actors' loop beliefs, and the actors as a collective in a given (social) situation are structured as a small social group by their behaviour, which in turn is generated by existing social loop beliefs [6]. Note that the above concept of social loop beliefs does not imply that actors' individual beliefs should be consonant with each other. In fact, it is possible to speak of the degree of divergence (or consonance) of social loop beliefs in a given group. One of the proposals here is that aspects or dimensions of small social groups such as "social pressure", "coherence", "consonance", etc., should be based conceptually on the concept of social loop belief. In the following I construct some very simple metricized concepts for measuring certain aspects of small social groups. Some of these concepts are applied later in this paper when coupling social loop beliefs and learning theories.

Group Measures

I now introduce four very simple functions, which are as follows: the function f(G) designates the quantity of those individuals in a given

group who have some social loop beliefs (relevant for some goal Y); the function f,(Xk) designates the quantity of individuals Aj in a given

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group who according to Ai's belief expect that A i ought to do Xk; the function f~(A) designates the quantity of those individuals Aj in a

given group who according to Ai's belief have some expectations concerning A i's behaviour;

the function f~(X~) designates the quantity of those individuals Aj in a given group who according to A,'s belief will do (want to do) X k.

It is clear that the concepts defined above are technically very simple, but from the point of view of methodology they are relatively problematic.

Notice that in the above definitions the functions f~(Xk) and f,(XL) refer to types of social action, not to concrete social actions. Moreover, these concepts and the function f, (A) are subjective: they tell something about the situation from Ai's point of view. The only "objective" concept so far is the function f (G) . The point is that, using these concepts, it is possible to express certain relevant aspects of small groups as subjective, experienced aspects. Consider, for instance, the notions of social pressure or social cross-pressure. These clearly reflect subjective properties.

Assuming that a given group consists of individuals A1,..., A,,, certain very simple measures and concepts result immediately for the description of certain aspects of the group. The present list of these aspects is not at all exhaustive, but I believe that at least some relevant social-psychological aspects of small groups can be represented by these concepts.

(1) If m~ designates the quantity of members from Ai's point of view, as m is the "objective" quantity of members, f ( G ) / m designates the relative quantity of individuals in a given group who have some social loop beliefs. This may be applied as a measure of the potential extension of social norms in a given group (in a given social situation). The possibility of mutual inconsistency of social loop beliefs justifies the epithet "potential". The measure varies in the range [0,1].

(2) The expression f,(A)/m~ designates the relative number of individuals in a given group who according to Ai's belief have some expectations concerning A~'s behaviour. This measure represents in some sense Ag's experienced subjective social pressure in the group. However, nothing about social pressure is indicated by behaving in one way or another. This aspect is caught by the following concept.

(3) The measure f ,( X k ) /m i designates the relative number of individuals in a given group who according to Ai's belief have expectations with respect to A~'s behaving by doing X k. Hence, this measure represents Ai's subjective social pressure to perform some concrete action X belonging to the type X k in a given social situation, which is caused by Ai's social loop beliefs concerning others' expectations about his /her own behaviour. It is clear that both measures (2) and (3) vary in the range [0,1] (as A~'s "self expectations" are allowed).

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(4) In general, Ai's experienced subjective pressure to behave in one way or another in a given social group, assuming that A i perceives n possible ways of acting, is expressed by the n-tuple (fl(Xi)/rng, f~(X2)/ m i . . . . . f i (Xn) /mi) . Here, every componen t f , ( X k ) / m i ( k = 1 . . . . . n) has a value in the range [0,1]. Assuming that according to A~'s belief every individual in the group has one and only one expectation concerning Ai's type of behaviour (including himself /herself) , the sum E" k=lfi( Xk)/m~ has the value 1. On these assumptions, measure (4) gives A~'s experienced subjective pressure to behave in one way or another as a probabili ty vector, or at least, probabili ty calculus can be applied to it. In any case, measure (4) can be thought to represent Ag's degree of belief with regard to his actions, if the above assumptions are not acceptable.

The measures (2)-(4) proposed so far have been individualistic, i.e., they have concerned only one individual, A~. It is easy to generalize them to the whole group by setting an approximate assumption that for each Ai,Aj it holds that m, = mj = m. The index of summation, i, ranges over m values, and it is useful to normalize the new measures by the multiplier 1/m, so that they vary in the range [0,1]. For practical reasons it is reasonable to assume that each A~ has the same set of possible types of actions [7]. Measure (5) is then obtained by summing measure (2) over the index i, giving (1/m)~i~=lfi(A)/rn, the experienced subjective social pressure in a given group. Similarly, measure (6) is (1/m)Eim= I ft ( Xk ) / m , the expected subjective social pressure in a given group to do X k. Coupling measures (4) and (5), the following n-tuple (7) is obtained as the measure for the total subjective social pressure to behave in one way or another in a given group:

y ~ m . . . , ( ( l / m ) ~=l[fi(X1)/m], (1/m)y'.m=l[fi(X2)/m], (1/m)ET'=l[fi(Xn)/m]). The definit ion of (7) implies that every one of its componen t s (1/m)E'f=lf,(Xk)/rn may vary in the range [0,1], depending on the other components . This feature of measure (7) couples in a natural way the social pressure and distribution of labour in a given group. Hence, if in measure (7) some component has a value near to one, this implies that the structure of action of the members in the group is "fixed". This fixed structure is generated by the individual social loop beliefs of the members. On the other hand, if the components of (7) have values near to zero, or the values are near to each other, a structure of action in the group has not emerged.

Social Status Structures

So far, it has been assumed implicitly that no individual in a given group has any "subjective" or "objective" structure of social status. Thus, all individuals are "equal" to each other in the group. However, f rom the point

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of view of social loop beliefs, and also from the point of view of social norms, it is realistic to assume that in a given group the expectations of some members have more "social weight" than others. It is also reasonable to assume that individuals themselves are not necessarily "equal" to others, i.e., the self-valuation of individuals with respect to others must be taken into account.

It is now assumed that each member A i of the group has a system of social status (SSS) of the following structure:

(P~, P~ . . . . . p ~ , . . . , p ~ )

where the components p / ( j = 1 . . . . , m) satisfy the conditions (i) 0 _< p / < 1 and (ii) m j _ Ej=lPi -- 1. For notational simplicity, no subscript i is used for m. It is allowed that the parameter rn may have different values for different individuals. Hence, it is not assumed that the shape of the group is same for every individual. By the SSS hierarchy every individual in the group fixes the social status of the members of the group, including himself/herself. Be- cause each component may vary in the range [0,1], it follows that social status is fixed via the evaluation of at least two different individuals. However, the SSS allows the situation where some members of the group are valued as zero. Moreover, no individual can have a negative social status. This assumption is critical, because individuals should differentiate between social status on the one hand, and preferences between members on the other. In general, it is rather problematic to determine values for the components p/ in practice. It is obvious that there are also many other serious methodological problems; the list above surely is not exhaustive. However, I believe that SSS's can be "operationalized" in a relevant way via social-psychological experiment situations.

I now reconsider measures (3) and (4) by taking into account systems of social status. The measure f ,(Xk)/rn ~ represents the relative number of members in the group who according to A,'s belief expect h i m / h e r to behave by doing Xk, and the n-tuple (f/( X l ) / m i , fs( X 2 ) / m i . . . . , fi( X n ) / m i ) in turn gives Ag the structure of expectation for h i s /he r whole range of action types. Assuming that according to A~'s belief every individual's expectations (Ai himself included) consist of one and only one alternative for As's type of behaviour, and that A, can identify his behaviour alternatives and others' expectations concerning his behaviour with each other, every component f~(Xk)/rn ~ in the n-tuple above can be substituted in a natural way by the structures (p)(Xk), p~(Xk), . . . , p/(Xk) . . . . . pm(Xk)) ' where the p/ 's are determined by the SSS, and each X k has the value 1 or 0 depending on As's belief: i.e., X k has the value 1 in the case that A s believes Aj to expect him to behave by doing X k, and the value 0 in the alternative case. On these assumptions, multiplying each corresponding component p /

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and X k, a structure is obtained which consists of the values p / o r zero: for example, (p), 0, p2, 0 . . . . . p/, 0, 0, 0, ... ). Summing over the upper index j yields for each type of action X k the sum E7=1 p/(k) , k referring to action type X k. It is clear that this measure (3*) varies in the range [0,1]. This method can be iterated for all Ai's action types k, giving as a result the

~ m y~m p/(2), . Em p / (k ) . . . . ZT=lp/(n)) . In this structure ( j = l p / ( 1 ) , j=l � 9 s=l �9 measure (4"), the definition of SSS ensures that the sum of the components is 1. Measure (4*) defines for A~ the social pressure to behave in one way or another via A~'s social loop beliefs and via Ag's system of social status. Note that in contrast, measure (4) above does not take into account A~'s system of social status.

Measure (4*) is highly problematic and idealized in one respect, relating to an assumption concerning the concept of social loop belief. It is assumed that Ai believes absolutely the others' expectations concerning Ai's behaviour, and that each As's expectations concern exactly one of A~'s possible types of behaviour at a time. Epistemically this might be interpreted as a social situation where A, is absolutely sure in h i s / he r belief of what others are expecting h im/he r to do. In principle, this assumption can be superseded by representing Ai's beliefs concerning each A / s expectation as a probability vector defined over A~'s possible types of action, instead of the situation where A~ is sure about each A / s expectations concerning himself/herself. After this has been done, the structure of Ai's social status is applied to each Aj's expectation probability vector concerning A~'s behaviour as assumed or believed by A,. For the sake of technical simplicity, this revision for measure (4*) is not developed here.

Social Loop Beliefs and Learning Theories

I now consider the possibility of coupling the concept of social loop beliefs developed above and certain classical learning theories, or simple modifications of them. I do not deal with any technical problems relating to the estimation of parameters for these theories, nor with the problems of "operationalizing" such theories. The notation in this Section is partly independent of the notation above.

The first theory modification is as follows. First, assume that each individual A i has only two altemative types of behaviour in a given social situation. Let them be X 1 and )(2: X 1 refers to the class of cooperative actions, and X 2 to the class of noncooperative actions [8]. Hence, X 1 and X 2 are so-called "open classes", or action types which are sufficiently specified linguistically in the social context of individuals A i, and in practice they generate potentially infinite sets ( Xl, , X12 . . . . ) and { X2, , X22 . . . . } of concrete

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actions depending on the concrete social situation and accepted sociolinguistic rules.

Next, postulate for each individual A i two inner states, which are referred to by the symbols s o and s r s~ refers to the state of inner social certainty, and s o to the state of inner social uncertainty. The symbol p~(t) designates the probability that individual Ai is in state s~ at moment t (trial t), and po(t) the probability that individual A i is in state s o at moment t. The parameter fl (0 < fl < 1) refers to A~'s propensity to move from the state s o to the state sl: hence fl might be interpreted social-psychologically as the propensity to cooperate, to agree, etc.

The inner, nonobservable behaviour of individuals is determined as a Markov chain by the following three axioms [9]:

p l ( t ) = p l ( t - 1 ) + f l p o ( t - 1)

po( t ) = (1 - f l ) p o ( t - 1)

p0(0) = 1; p,(0) = 0

Public, observable behaviour is coupled with the inner states s o and s~ by the following two axioms or correspondence assumptions: at every t,

if s 1, then P * { x 1) = 1

[ e * ( x, } = p if then So, x

e*(z2}=l-p In the above formulas, x~ refers to a concrete action of type X 1, and x 2 to a concrete action of type X 2. P* designates a probability measure defined over the set of possible types of action in a given social situation, conditioned by the two inner states s~ and s 0. The proposal here is that the probability measure might in a very natural way be specified by either measure (4*) or measure (4) above. In both cases, the probability measure P* might be interpreted social-psychologically as Ai's propensity to behave in a cooperative way, if h e / s h e is in the state of social uncertainty, generated via h i s / h e r social loop beliefs (and in the case of (4*) also via h i s / h e r system of social status).

The second theory modification is based on a four-state Markov chain. Independent of formal analogies with the model above ("enrichment"), its social-psychological substance may be interpreted differently. Assume that there are four types of action, X1, X 2, X 3 and X 4, which are specified, say, by moral or ethical categories. As before, x~, . . . , x 4 are concrete actions which are modified by the social contexts corresponding respectively to types X 1 . . . . , X 4. The inner states So,. . . , s 3 refer to A~'s cognitive moral states or levels such that the state s o indicates A / s being wholly " immoral" , s 3

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indicates Ai's being wholly "moral" , and S 1 and s 2 lie respectively between the states s o and s 3 according to given moral s tandards in a given group. Now A,'s "mora l development" is determined by two groups of axioms, of which the first is

p3(t)=p3(t - 1 ) + fl2p2(t- 1)

p2( t ) = (1 - fl2)P2(t- 1) + f l lp l ( t - 1)

p l ( t ) = (1 - f l l )p l ( t - 1 ) + floPo(t- 1)

po(t)= ( 1 - flo)Po(t - 1)

These axioms specify A~'s " inner" development. Each pi(t) (i = 0 , . . . , 3 ) designates A~'s propensi ty to be in the i th moral level at m o m e n t t. The parameters fl, (0 < fl~ < 1; i = 0 . . . . ,2) refer to Ai's propensity to "develop morally", i.e., propensi ty to transit from one state to another. Ai's "mora l level" is tested at each momen t t via Ai's public behaviour. This is done exactly by the following four correspondence assumptions which couple each of A, 's "mora l states" and his possibilities of behaving according to existing moral standards: at every t,

if s 3, then P * ( x 4 ) = ]

if s 2, then P * ( x 4, x 3} = 1

if sl, then P * ( x 4 , x3, x2) = 1

if s o , then P * ( x 4, x 3, x 2, x 1} = 1

Now, the proposal here is that the probabili ty measure P* might be fixed by measure (4*) or by measure (4). Hence, in the model above, A~'s inner moral development is generated by A~'s social loop beliefs concerning the given social situation. The others create A~'s inner moral categories in a social way, by allowing h i m / h e r to behave in the way corresponding to h i s / h e r moral state of development. The whole development process passes through "quali tat ive changes" and "quanti tat ive processes". In the model above it is assumed that development progresses to the state s 3. This is not necessary if "regressions" or "mora l degenerations" are allowed. Hence, by suitable modificat ions to the axioms concerning the inner process, the model might be applied in social situations where given social norms, morali ty and the whole social structure are in a state of destruction.

Both of the models above are unsatisfactory, in that they do not take into account the effects of social contacts or actions during the process. That is, they behave as if the individuals of a given group fix their expectations concerning others and themselves a priori, and these a priori beliefs do not change at all (this fact is reflected by the parameters p and fl, which are constants). In the following model this is not the case.

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For simplicity, define two types of results of individuals' actions. Type E 1 refers to results which are classified by the sociolinguistic standards of a given group as cooperative actions, and type E 2 refers to results which are classified as noncooperative actions. Hence, the result of individual actions is at every moment t (at every trial t) either cooperative or noncooperative in nature.

The symbol p~ (t) denotes the probability that an individual i will behave cooperatively at moment t, i.e., the result of his action will be classified by the sociolinguistic standards of the group as belonging to the cooperative category of behaviour. Hence, A i, so to speak, is "doing his part", the result being cooperative by nature [10]. Whether or not the result is cooperative depends in turn on whether or not the others behave cooperatively. The symbol P2(t) denotes the probability that an individual i will behave noncooperatively at moment t.

Ai's behaviour at moment t is conditioned with respect to results at the previous moment t - 1 by the two axioms

p ~ ( t ) = a z p , ( t - 1), if E z occurred at moment t - 1

p l ( t ) = a l p , ( t - 1) + (1 - ai))~, if E 1 occurred at moment t - 1

Hence, the occurrence of E 1 "reinforces" (or "rewards") A~'s behaving in a cooperative way, and the occurrence of E 2 "disreinforces" (or "punishes") A~'s behaving in a cooperative way, i.e., it "reinforces" A~'s behaving noncooperatively. The parameters a I and a 2 might be interpreted as representing A~'s social sensitivity to the behaviour of the group as a social entity.

The model above entails a very unrealistic assumption. It implies that the classification of types of action results is dichotomous: E1 designates a cooperative result, E 2 designates a noncooperative result. Assume now that the group consists of n individuals each of whom has two types of behaviour (cooperative--noncooperative) with respect to the results of the action of the group, The group can generate 2" different results of action via its members ' behaviour, reflecting lesser or greater extents of cooperation (or noncooper- ation).

Assume now that each member of the group is able to differentiate among the degrees of cooperation in the group by common sociolinguistic standards [11]. This case might be generalized from the above model by the following axiom scheme:

Pa ( t ) = a ~ p I (t - 1) + (1 - am) )~m, if E,, occurred at moment t - 1

There are at least two possible ways to couple the model above with the concept of social loop belief. First, measure (4) or measure (4*) may be used to fix the values of the parameters a m. Because it was assumed that A~ has

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only two possible types of behaviour, the results E i are in this case irrelevant with respect to the values of a,,. In other words, the application of (4) or (4*) for fixing the values of a m leads to the case where a m has the same value independent of the result E i. Hence, the model reduces to the form

p l ( t ) = a p ~ ( t - 1) +(1 - a)X,, , if Em occurred at moment t - 1

The second possibility for coupling the above model and social loop beliefs is based on the idea of fixing the parameters X m by measure (4) or (4*). This case presupposes a slight modification of the concept of social loop belief analyzed above. The social loop belief expressed by (4) or (4*) is based on expectations concerning individual actions. Instead of this, social loop beliefs here should be based on the expectations concerning the results E, of actions of the members of the group. Hence, each individual's recogni- tion of the results E i is primary for his behaviour, instead of individual actions in the group. In this case the social loop beliefs take the form " A i

believes that some A j ' s expect Ae to do h i s /he r part to achieve El". In the general case of the model above this might be done by fixing the X,,'s by measure (4) or (4"), reflecting A~'s beliefs concerning others' expectations about himself and the goals of the group.

Assumptions

In the above text some critical assumptions have been adopted. It is worth discussing them here briefly. The most critical, idealized and unrealistic assumption made in general concerns the shape of a given small social group, and hence also the structure of the social situation. The problem is how to take into account the possible distance between a situation recognized objectively (" from an outsider's point of view") and the same situation recognized subjectively ("from the actors' point of view"). Moreover, it is realistic to take into account that the recognitions of different actors may differ from each other. This type of assumption may be termed the Objectiv- ity assumption.

There are two essential aspects to the objectivity assumption: the first concerns the number of individuals in a given group, and the second concerns the types of possible action. So far as t y p e s of actions are concerned, there is no problem of objectivity. On the contrary, it is in the case of concrete social actions that problems arise. I think it realistic to assume that the individuals in a given social situation have sufficiently similar sociolinguistic standards in order to classify concrete social actions as belonging to the same type. This does not imply that each individual has the same (potential) set of concrete social actions. In fact, it is realistic to assume that some

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concrete actions are excluded or "forbidden" via types of other's given concrete actions.

The primary motive for introducing the notions of action type and concrete action has been to avoid the problems generated by the objectivity assumption. In fact, for each of the three classical learning theories applied above to the generation of social norms, these problems were avoided. The point is simply as follows: instead of the ordinary "operationalizing" use of such theories, i.e., fixing concrete action alternatives for individuals, only types of alternatives are fixed. Hence, concrete actions may vary given some fixed action type. In applying theories to concrete (experimental) situations this approach is much m~re realistic than the "tradit ional", i.e., "concrete action", approach. There is no problem in classifying individuals' various concrete actions as given action types in a given (experimental) situation: for instance, as cooperative or noncooperative. This kind of (experimental) situation is also more realistic from the point of view of (experimental) individuals.

The problem of the number of members in a given group arises only in the case of measures (5), (6) and (7). However, nothing in the above theorizing depends on these measures. Instead, a comparison of the subjective measures (2), (3), (3"), (4) and (4*) and the objective measures (1), (5), (6) and (7) provides relevant information concerning the structure of the group both from the subjective and objective points of view. There are also other possibilities for constructing measures of group structure based on the four "primitive" functions. However, these are not considered here.

Acknowledgements

Thanks for critical comments are due to Prof. K. Rainio, Prof. R. Tuomela, Prof. I. Niiniluoto and especially to Mr. I. Patoluoto.

NoEs

1 Tuomela (1984) has analyzed conceptually the methodological and philosophical role of social loop beliefs from the point of view of his theory of social action.

2 See, for instance, Tuomela (1982, 1984) for a lucid logical analysis of these concepts. 3 This classification of action types is based on Schelling's proposal concerning a reclassifi-

cation and reorientation of games (see Schelling, 1970, pp. 88-89). 4 Compare, for instance, Tuomela (1982, pp. 7-12, 21-23). It is worth noting that the

concept of social loop belief is easily representable, for instance, in terms of Rainio's (1970) theory. There are also many nonequivalent ways of formalizing mathematico-logi- cally the concept of social loop belief in Rainio's theory.

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5 See Tuomela (1984) for an analysis of the role of social loop beliefs. 6 Compare, for instance, Tuomela (1984) for a relevant interpretation of the term "gener-

ated by existing social loop beliefs". 7 This assumption implies that the Ai's have the same sociolinguistic standards, and that

each of them recognizes a given social situation as similar and symmetrical for each of the others' action types. However, the assumption does not imply that each A,, Aj has the same set of possible concrete actions, because it simply destroys the distance between objective and subjective social situation. Although in the following the applications of certain classical learning theories rest on subjective aspects of social pressure, there remain certain "objectivist" assumptions concerning the structure and action possibilities of a given social situation.

8 Rainio (1981) has recently studied empirically the dynamics of two-person prisoner's-dilemma-type interaction. His simulation experiments were based on the one hand, on Galanter's (1966) stochastic theory of choice behaviour, which Rainio (1970) redeveloped and formalized, and on the other hand, on classical learning theories (Bush and Mosteller, 1955).

9 This model and all other models in this paper are classical learning theories or simple versions of them (see Bush and Mosteller, 1955). Cohen and Lee have applied these to social conformity via classical Ash experiments (see Cohen, 1963; Cohen and Lee, 1975).

10 Compare Tuomela's (1982, 1984) lucid analysis of "doing his part of social action". 11 This is the same assumption as in Note 7.

References

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Social norms and learning theories