Chapter 1 Preface MORAL SCIENCE AND MORAL ALGEBRA Comments are most welcome. 22norman22@gmail.com Moral science can be developed on a foundation of mathematical law. Three algebraic laws—averaging, adding, multiplying—have received extensive support in several moral areas. Dedicated investigators have made applications to deserving and fairness/unfairness (Chapter 2), blame and punishment (Chapter 3), legal psychology (Chapter 4), and moral development (Chapter 5).

Establishing these laws depended on concomitant development of a theory of psychological measurement, a long-recalcitrant problem whose nature is illustrated with the basic blame law of Equations 1a,b (p. 7). The success of this functional theory of measurement is detailed in the cited empirical chapters. Two fundamental problems are solved by these laws: valuation of stimulus variables to construct their functional values for operative goals; and integration of multiple, goal-oriented values into a unified response, as with the basic blame law. These three laws have done well in many different areas of human psychology: person science, social attitudes, judgment–decision, and learning/memory. These areas have largely ignored moral psychology. And vice versa. Unification has much to offer all (Chapter 8).

FUNCTIONAL THEORY (3) THEORY OF INFORMATION INTEGRATION (4) PARALLELISM THEOREM (9) THREE INTEGRATION MODELS (12) EXPERIMENTAL EVIDENCE (15) MORAL ALGEBRA (17) MORAL SCIENCE (19) NOTES (23)

2 Chapter 1

Chapter 1 MORAL SCIENCE AND MORAL ALGEBRA

Copyright Norman H. Anderson April 22, 2012 Comments are most welcome. 22norman22@gmail.com A general theory of moral cognition, grounded on moral laws, is present-ed in this book. These laws are mathematical; they describe how people valuate and integrate multiple considerations involved in moral thought and action. Many right/wrong reactions result from this cognitive alge-bra, much of which is nonconscious. This moral algebra is a foundation for developing moral science.

The moral rule—people should get what they deserve—is the classic example. Writers from Aristotle to modern equity theorists have conjec-tured algebraic formulas for fair shares. But these conjectures remained conjectures; they were untestable because psychological theory to meas-ure people’s judgments of deserving was lacking.

This measurement obstacle was overcome with the functional theory of measurement. Exact analysis thus became possible. Aristotle’s alge-braic formula for fair division was found psychologically superior to its most prominent modern alternative. A different algebraic model was necessary, however, especially to study related questions including the important issue of unfairness (Chapter 2).

A second domain of moral algebra concerns blame, a too-common moral judgment in everyday life. Young children follow an algebraic blame law that persists in adult life, a novel base for developmental comparison (Chapters 3 and 5). Indeed, young children showed far high-er cognitive capabilities than had previously been recognized.

Moral algebra has double value. First, moral psychology provides an effective base for studying cognitive processes common in every area, from person science to learning/memory. Moral algebra can thus con-tribute to unification of cognitive theory (see Chapter 8).

Second, moral algebra can help with the paramount goal of improv-ing the moral level of society. This difficult goal requires combined effort of all social sciences. The present work is a modest, hopeful con-tribution to a better society.

MORAL ALGEBRA 3

FUNCTIONAL THEORY A functional perspective is adopted in this book: moral systems are stud-ied in terms of their dual functions—for individuals and for society. These two functions are intimately related. Society consists of individu-als who have self-interests that need to be harmonized enough to allow social groups to persist and accomplish social goals.

One function of moral systems is thus to entrain self-interest to the interest of the group. This function appears in everyday beliefs and cus-toms about friendship, fairness/unfairness, obligation, and blame, as well as in legal/regulatory systems. These have done reasonably well for they allow existence of societies of many millions of individuals, immeasura-bly aided by developments in utilizing natural resources, in farming and manufacturing, and in socioeconomic organization.

Moral systems have a second function. Society should subserve the good of its individual members. In substantial part, of course, individual good is subserved by the general social good, notably with economic, educational, and legal systems. Nevertheless, individual self-interests have their own moral priority.

Moral systems should seek to promote individual self-interest with-out detracting from others’ interests. Instilling positive attitudes of help-fulness and job performance, as well as respect for law, can contribute to both goals. No less important is to encourage pursuit of individual goals, not merely those that benefit society, but also those that enhance individ-ual accomplishments and feelings of worth without necessary regard to social benefit. This latter function has fundamental moral significance. Society should serve its members.

This function of individual self-fulfillment has been relatively neglected in moral theory. One reason is the primary need to implement the first function. This neglect has been fostered by many writers, espe-cially by moral philosophers who maintain that self-interest can never truly conflict with social morality (see Moral Philosophy, Chapter 7).

Moral theory should seek to learn how to achieve these two goals. At present, social–moral education is haphazardly dependent on family, schools, and social groups. These leave much to be desired.

Morality has been peripheral in the psychological field. Current person science, social attitude theory, learning/memory, and judgment–decision are largely silent on this basic social phenomenon. In colleges and universities, education about family life, the primary locus of social-ization, is close to nonexistent.

4 Chapter 1

Cognitive process is the main concern of this book. Three mathemat-ical laws govern much moral thought and action. These laws give unique insight into cognitive processes. Such understanding can help develop social programs to improve both functions of moral systems.

THEORY OF INFORMATION INTEGRATION

Moral thought and action are here considered within the framework of a general theory of information integration (IIT). This theory is grounded on two propositions whose self-evident nature warrants the term axiom. The Axiom of Purposiveness recognizes that thought and action are motivated toward goals. The Axiom of Integration recognizes that thought and action result from integration of multiple determinants.

AXIOM OF PURPOSIVENESS The purposiveness of our everyday activities is one manifestation of general goal-directedness of organic life. Purposiveness goes far deeper than consciousness to include biological and affective–cognitive processes developed in evolution. The Axiom of Purposiveness recog-nizes that moral systems have biosocial grounding.

One major function of purposiveness is to place subjective, goal-oriented values on objective stimulus informers. Judgments of deserving, whether positive as in praise or negative as in blame, are an important function, common in daily life.

The Axiom of Purposiveness has an important analytical implica-tion: purposiveness imposes a one-dimensional, approach–avoidance metric on much thought and action. This metric is considered to have an evolutionary origin in sensory–motor processes for survival action in the external world. Approach–avoidance tendencies of everyday life, the moral right–wrong axis in particular, are considered to involve melding of this general metric sense with particular affective qualities (see Metric Cognition, Chapter 7).

Purposiveness has obvious attractions as a base for general theory. This teleological attractiveness appeared in Aristotle’s concept of final cause and reappears in modern attempts to understand thought and action in terms of their goals. Various conjectures about goal-oriented motiva-tions in social science, hopeful analogs to the concept of force in physics, are one manifestation. These conjectures pointed to important problems, but they lacked analytic power. An effective approach is available with the three laws of information integration.

MORAL ALGEBRA 5

AXIOM OF INTEGRATION Information integration is fundamental in cognition. Moral thought and action, in particular, generally depend on joint influence of two or more variables. Thus, blame for a harmful act may depend on intent behind the act as well as on amount of harm. A judge’s sentence, similarly, may depend on past record as well as present crime. Blame theory must address the problem of how intent and harm are integrated. Similar integration considerations hold for all moral thought and action.

The Axiom of Integration is basic in every field of psychology; multiple variables are generally operative. How are these multiple varia-bles integrated to arrive at a unified response? An answer to this integra-tion question was found with the discovery that much integration follows a general cognitive algebra.

Figure 1.1. Information integration diagram. Chain of three operators, V – I – A, leads from observable stimulus field, {S}, to observable response, R. Valuation operator, V, transforms stimuli, S, into subjective representations, ψ. Integration operator, I, transforms subjective field, {ψ}, into internal response, ρ. Action operator, A, transforms internal response, ρ, into observable response, R. (After N. H. Anderson, Foundations of information integration theory, 1981a.) INTEGRATION DIAGRAM The Integration Diagram of Figure 1.1 sets out the problems posed by the two axioms. Physical stimuli, SA and SB, impinge on the person and

6 Chapter 1

are transmuted into goal-oriented, psychological values, ψA and ψB, by the valuation operator, V. These psychological values are integrated to construct a unified response, ρ, by the integration operator, I. Finally, this internal response is externalized by the action operator, A, to be-come the observable response, R. The Axiom of Purposiveness is represented in the Integration Dia-gram by GOAL, which influences all three operations. Most important is valuation, which constructs goal-relevant subjective values (ψA and ψB) within the internal, psychological world. The Axiom of Purposiveness entails a functional conception of psychological measurement. The psychological value of any stimulus informer depends on operative goals. The same stimulus may have dif-ferent values relative to different goals. Measurement of functional, goal-specific values is essential for psychological science. Such measurement is possible with the three algebraic laws. INFORMATION INTEGRATION THEORY Information Integration Theory (IIT) rests on three concepts.

1. Integration Graphs. An integration graph shows conjoint action of two or more variables, illustrated in Figure 1.2 below. Pattern in the observable response of an integration graph is a key to nonobservable cognitive processes by which the variables are valuated and integrated.

2. Functional Measurement. Observable responses may be biased— R being a distorted image of underlying response, ρ. How to avoid such bias and obtain true measurement of underlying response had baffled psychologists for over a century. Functional measurement theory can eliminate such response biases. Then the observable pattern visible in an integration graph will be a faithful image of pattern in unobservable cognition.

3. Algebraic Laws. Each of the three laws corresponds to specific patterns in an integration graph. Most useful is the parallelism pattern, which corresponds to an adding-type law, as in Figure 1.2 below. Exper-imental studies by many investigators have revealed these algebraic laws in almost every area of human psychology. These algebraic laws are a base for moral theory. They can be espe-cially useful because the same laws found with young children also ap-pear at older ages and in other cultures. These laws are general; moral theory can thus be unified with general cognition, especially person science, social attitudes, development, learning, and judgment–decision.

MORAL ALGEBRA 7

BLAME HYPOTHESIS To illustrate the problems posed by the Integration Diagram, consider the hypothesis that blame for a harmful act is the sum of two values, the intent behind the act and the harm it caused: Blame = Intent + Harm. (1a) This is more properly rewritten in psychological terms of the foregoing Integration Diagram as ρBlame = ψIntent + ψHarm. (1b) An experimental test could manipulate Intent of a rock throwing child (e.g., malice, carelessness) and Harm (e.g., bruised shin, black eye) as in Figure 1.2 below. To test this blame hypothesis, somehow we must measure all three terms in Equation 1b to see if they add up. Can this really be possible? All three terms are subjective values, not directly observable. Some ψ values are not even conscious. To establish the blame hypothesis, we need to develop a science of the internal world. This is possible with the three laws of information integration. SCIENCE OF THE INTERNAL WORLD Science of the internal, psychological world is the theme of Information Integration theory. This theme appears in Equation 1b: all three terms, ρBlame, ψIntent, and ψHarm, are internal to the person—unobservable. To establish this blame equation, we need some way to measure these three unobservables. This might seem impossible. An obvious approach would ask the person to give numbers to repre-sent each of the three terms and see if they add up. This direct attack failed. Other attempts also failed, even for simple sensations such as loudness or heaviness, despite dedicated efforts beginning in 1860. An alternative conceptual approach was adopted in IIT. Exact tests of the blame hypothesis thus became possible. Remarkably, the blame hypothesis has done well in demanding tests in many countries. Indeed, the mind has been found to exhibit a general cognitive algebra. This theory is actually simple, although it requires a new way of thinking.

8 Chapter 1

COGNITIVE ALGEBRA Many judgments of everyday life have been found to exhibit one of three mathematical laws: averaging, adding, and multiplying. The blame law of Equation 1a is one example, illustrated empirically in Figure 1.2 and in Figure 3.1. A few other examples are listed here. The blame law may be extended to include apology (Chapter 3): Blame = Intent + Harm − Apology. Apology was found to be a powerful process for social healing. Gratitude for a beneficial act performed with specified intent: Gratitude = Intent + Benefit (Figure 7.4). Badness of failure to fulfill an obligation: Badness = Obligation strength − Extenuation (Figure 7.3). Judgment of deserved reward for specified contribution: Deserving = Contribution + Need (Figure 5.3). Multiplication laws are also frequent as with Expected Performance:

Performance = Motivation × Ability (Figure 5.5, Anderson, 1996a).

Expected value of a chance event of specified probability and value: Expected value = Probability × Value. This equation holds in mathematical probability theory; the long-standing conjecture was whether it also held in the mind with subjective values of event value and probability. The answer is yes, as was finally shown with functional measurement (Anderson, 1981a, Figure 1.13). This multiplication law for Subjective Expected Value is appropriate for taking account of uncertain future events in moral judgment–decision. These and diverse other such equations have been extensively veri-fied by many investigators over the last half century. These equations appear in children as young as 4 years of age and over the life-span. They appear in diverse cultures, even with nonliterate persons. These equations represent innate abilities—general cognitive algebra. As they stand, of course, the foregoing equations are merely verbal conjectures. To transmute them into genuine cognitive algebra depended on development of capabilities for true psychological measurement. Doing this turned out to be relatively simple, although it required con-ceptual reorganization embodied in the following parallelism theorem.

MORAL ALGEBRA 9

PARALLELISM THEOREM Although the idea of moral algebra is age-old, it could not be established without capability for true psychological measurement, illustrated with the blame hypothesis of Equation 1b. The parallelism theorem offers a remarkably simple way to resolve this measurement crux. INTEGRATION GRAPHS An integration graph shows the response to two (or more) variables jointly manipulated. The pattern in such a graph can reveal the law that governs the integration of the separate variables into a unified response. This is illustrated with the adding-type law in Figure 1.2. Additive Law. Parallelism pattern supports an adding-type integration. The integration graph of Figure 1.2 shows hypothetical blame judgments of two real persons, F. W. and A. S., in an Intent × Harm integration de-sign. Their task was to judge blame deserved by a story child who threw a rock that harmed another child. Harm is varied across three levels listed on the horizontal: bruised shin, bloody nose, and black eye. The intent of the harmdoer is varied across the three levels listed by the three curves: intent to harm, intent to scare, and carelessness. Note that each point on this integration graph represents a different story child, unrelat-ed to the others except through the common task situation. Parallelism of Figure 1.2 supports the additive law of Equations 1. The scare curve lies a constant distance above the careless curve—scare adds a constant amount of blame, regardless of amount of harm. Every pair of curves shows a similar additive pattern. Parallelism is direct evidence for an adding-type law. Value Measurement. Parallelism pattern can go further to reveal per-sonal values of each person. Figure 1.2 shows that F. W. considers bloody nose and black eye equally bad; both points have the same eleva-tion on his topmost curve. The same appears in each lower curve. A. S., in contrast, considers black eye much worse; this point is much higher than bloody nose on each of the three curves. Perhaps she considered that a rock that caused a black eye could easily have put out the eye. Second, F. W. considers intent to scare substantially less blamable than intent to harm, but substantially more blamable than carelessness. This is shown by the relative elevations of these three curves. A. S., in

10 Chapter 1

Figure 1.2. Parallelism analysis illustrated with hypothetical data. The three curves in each integration graph represent blame for bad deeds of story children specified by an Intent × Harm design. Intent is listed as the curve parameter, Harm on the horizontal. Parallelism reveals an adding-type model: Blame = Intent + Harm. Different shapes of the graphs reflect different personal values of Intent and Harm. (After Anderson, 1990.) contrast, considers intent to scare only slightly more blamable than care-lessness whereas intent to harm is much more blamable than either. These personal values are measured by the integration graph. Thus, the top curve for A.S. in Figure 1.2 yields her personal values for the three amounts of harm. And—by virtue of the parallelism—these same relative values reappear in each lower curve. The same holds for F. W. These values are functional; these values functioned in each person’s blaming process. Empirical applications are given in Chapter 3. PARALLELISM THEOREM The graphical reasoning of the previous section is formalized with the parallelism theorem. Consider a two-variable, row × column integration design like that of Figure 1.2. Denote the row stimuli by SAj and the column stimuli by SBk. Two premises are needed: Premise 1: Additive integration: ρjk = ψAj + ψBk. Premise 2: Linear response: Rjk = ρjk.

Person F.W. Person A.S.

MORAL ALGEBRA 11

Premise 1 says that the response to the stimulus combination {SAj, SBk} in row j, column k of the integration design is the sum of their subjective ψ values. Linear response in Premise 2 means that the observable re-sponse, Rjk, is a faithful measure of unobservable response, ρjk (Note 1). Granted these two premises, two conclusions follow: Conclusion 1: The integration graph will exhibit parallelism.

Conclusion 2: Mean response in each row (column) of the integra-tion graph measures the true value of ψAj (ψBk).

BENEFITS OF PARALLELISM The parallelism theorem exemplifies the functional measurement logic:

measurement is derivative from empirical law. Pattern in an empirical integration graph can diagnose underlying pro-cess. The long-standing dual cruxes of psychological measurement—of response and of stimuli—can be solved with a pattern of parallelism. These and other benefits of parallelism are itemized next. 1. Additive Integration. Since the two premises predict parallelism, observed parallelism supports both premises, additivity in particular. Of course, no single experiment goes very far by itself. Confidence only builds up from a group of interrelated experiments. 2. True Response Measurement. Premise 2 (linear response) is critical. Premise 1 (additivity) refers to unobservable addition; ρ = ψA + ψB. Could you look inside the head of F. W. or A. S., you would see a paral-lel integration graph. For this unobservable pattern to appear in the observable integration graph, you must use a linear response measure. Conversely, observed parallelism supports Premise 2 of response linearity, that the observed R is a true measure of the unobservable ρ (see Note 1). True response measurement had been unsuccessfully pursued by numerous investigators for over a century. Actualizing this goal depend-ed on development of experimental procedures to eliminate certain re-sponse biases in the rating method, making it a true linear scale (Method of Functional Rating, Chapter 6). Most important, actualizing this goal depended on empirical reality of algebraic law (Note 2). 3. True Stimulus Measurement. An almost magic property of parallel-ism theory is that only the response need be measured. This is enough to test additivity. Prior stimulus measures of ψA and ψB are not needed.

12 Chapter 1

No less magical, true measures of ψA and ψB are available from the integration graph. This stimulus measurement follows from Conclusion 2, already illustrated in the discussion of Figure 1.2. This measurement capability is a godsend; stimulus values may not even be conscious. 4. Meaning Invariance. Observed parallelism goes further to shed new light on the flow of information processing. Parallelism implies that the stimulus informers do not interact to change one another’s values during the valuation processing. Each SA adds the same fixed amount, ψA, regardless of SB—contrary to strong introspectionist claims. 5. Cognitive Unitization. Complex stimulus fields can be treated as cognitive units by virtue of the parallelism theorem. Unitization, together with functional measurement, allows exact measurement of effects of complex stimulus fields (see Analytic Context Theory, Chapter 7). Unitization, which follows from the Axiom of Purposiveness and an algebraic law, is invaluable for cognitive theory. The valuation operation of a complex stimulus field may be unknowably complex, much of it not conscious. Yet all your complex processing is reduced to a single num-ber in the algebraic law—which can be exactly measured. Unitization is a fundamental property of information processing. It would seem hard to pin down without an algebraic law. Once estab-lished, however, unitization may be hypothesized to hold more generally in situations that do not follow any simple integration rule.

THREE INTEGRATION MODELS Three algebraic models of information integration have done well across most areas of human psychology: addition, multiplication, and averag-ing. Each implies specific diagnostic patterns in an integration graph as just illustrated with parallelism analysis for adding-type models. Tech-nical issues are discussed in Chapter 6, but the following overview should suffice to understand the empirical chapters that follow. ADDITION Parallelism theory gives a simple analysis of addition models. It is logi-cally possible, of course, that parallelism could be produced by some different model (see Chapter 6, Note 10). In fact, the averaging model with equal weights does yield parallelism (see below). Mathematically, the averaging model with equal weights is additive. Psychologically,

MORAL ALGEBRA 13

however, adding and averaging differ in fundamental ways, one of which is discussed under Opposite Effects below. MULTIPLICATION The multiplication model may be illustrated with the classic hypothesis: Subjective Expected Value = Subjective Probability × Subjective Value. In this model, Subjective Probability refers to felt likelihood of some uncertain event of felt Subjective Value. This model is basic in judg-ment–decision theory and has also been conjectured in many other fields of psychology, including moral judgment. It is needed to take account of the uncertain likelihood and personal value of many goals. These Probability × Value conjectures remained verbal conjectures; capability for true measurement of Subjective Expected Value was lack-ing. This measurement roadblock was overcome with the linear fan theo-rem of functional measurement theory (Anderson & Shanteau, 1970; see Figure 10.1, p. 319 in Anderson, 1996a). The diagnostic pattern of a multiplication model is a linear fan, that is, a diverging fan of straight lines in the integration graph (see Chapter 6). Such linear fans have been observed in many areas, even with young children (e.g., Anderson, 1980; Schlottmann, 2001; Shanteau, et al., 2007). AVERAGING Averaging has been by far the most common integration process in em-pirical studies. Most tasks that were expected to exhibit strict addition have instead exhibited averaging. Three variants of the averaging model require comment. Averaging Model With Equal Weights. The averaging model for two variables with equal weighting may be written

!

" =#A $Aj + #B $Bk

#A + #B

. (2)

Here ψAj and ψBk denote polarity values of stimulus informers SAj and SBk, as in the Integration Diagram of Figure 1.1. Their importance weights are denoted ωA and ωB.

14 Chapter 1

The numerator of Equation 2 is the weighted sum of stimulus values. This weighted sum is converted to an average by dividing by the sum of weights in the denominator (Note 3). In Equation 2, all ψAj have equal weight, ωA, and similarly all ψBk have equal weight, ωB. With equal weights, the sum of weights in the denominator of Equation 2 is constant; hence it may be absorbed into the unit of the response scale. With equal weights, therefore, the averaging model obeys the parallelism theorem. With equal weights, accordingly, all the benefits listed above for the parallelism theorem apply. The simplicity of parallelism analysis and its several benefits suggest using experimental procedures conducive to equal weighting. Most important would be to equalize amount of infor-mation across different SAj and similarly across different SBk. Averaging Model With Unequal Weights. Equal weights will not al-ways obtain. If SA1 contains more information than SA2, the importance weight for the former will be larger. In Equation 2, ωA would have to be replaced by ωAj, ωB by ωBk. Parallelism theory does not apply; unequal weights cause systematic nonparallelism (Notes 4 and 5). Unequal weights was a blessing in disguise for it allowed simple analysis of what seemed intractable phenomena. Most striking, it pre-dicted opposite effects—adding a positive stimulus informer may in-crease or decrease the response; this might seem to rule out any algebraic model (see below). It made possible measurement of importance weight (ω) separate from value polarity (ψ), a stumbling block for the many previous attempts. Moreover, it showed that previous theories of psycho-logical measurement were conceptually deficient (see Psychological Measurement Theory, Chapter 6). Decision Averaging Model. One special case of unequal weight averag-ing has general interest. To illustrate, suppose a total amount T is to be shared between persons A and B, who have made contributions meas-ured by ωA and ωB. Without going into detail (Anderson, 1981a, p. 66), the averaging model of Equation 2 implies that A’s fair share is

!

"A

"A + "B

T. (3)

In words, A and B should be rewarded in proportion to their relative contributions. This decision averaging model has done well in fairness theory (Chapter 2).

MORAL ALGEBRA 15

The decision averaging model has the same form as a basic Bayesian model. But whereas Bayesian theory applies only to probability, the decision averaging model applies generally, as with fair shares.

EXPERIMENTAL EVIDENCE

Information Integration Theory has done well in almost every field of human psychology. Some difficult problems had to be resolved, but little of this is needed to read this book. For completeness, however, four sub-stantive problems will be briefly noted (see Twelve Theoretical Issues, pp. 54-68, in Anderson, 2008, Note 6 below; more detailed discussion is given in Chapters 2-4 in Anderson, 1981a). A task of person cognition was used in much of this early work. Par-ticipants receive a list of personality trait adjectives that describe a per-son; they judge that person on likableness, a response that facilitates equal weighting and hence parallelism (see Notes 4 and 7). MEANING INVARIANCE Meaning invariance, benefit 4 of the parallelism theorem, has been and sometimes remains unbelievable. To introspection, it seems compelling-ly clear that trait adjectives in a person description interact to change one another’s meanings. Some writers still adhere to this introspective change-of-meaning hypothesis despite repeated disproof with parallelism analysis. A different objection is that a given stimulus may have different val-ues in different contexts. This is not actually an objection; the context may influence the GOAL for the valuation operation in the Integration Diagram. Hence the context will also influence the value. Thus, the trait happy-go-lucky could be positive in a picnic companion but negative in a research assistant (Anderson, 1968a, pp. 232ff). Within either role, how-ever, traits would have fixed value, as may be shown with parallelism analysis. Verbal reports can be priceless clues about conscious and noncon-scious cognition. They can be obstinately wrong, however, as with the disbelief in meaning invariance (Note 8). The psychological laws provide a validity criterion for verbal reports. These laws can adjudicate phenomenological claims, as with the change-of-meaning hypothesis. More important, such validity criteria can help develop Science of Phenomenology (Chapter 7).

16 Chapter 1

COMPLEX PROCESSING A specific objection to meaning invariance was that the personality adjective task may suffer from superficial processing. More complex processing, it is argued, would yield meaning changes that would produce deviations from parallelism. To test this hypothesis, one group of participants was instructed to write a paragraph describing the person in their own words before they rated likableness. They are thus forced to interrelate the trait adjectives. Their integration graphs, however, still showed parallelism. Indeed, these graphs were virtually identical to those of the no-paragraph comparison group (Anderson, 1981a, pp. 168f). OPPOSITE EFFECTS The same stimulus may have opposite effects, additive or subtractive. Such opposite effects might seem to rule out any algebraic model. In fact, opposite effects is predicted by averaging theory: adding a medium stimulus will average up a low stimulus, average down a high stimulus (e.g., Figures 4.2 and Figure 5.2). Such opposite effects have given extensive support to averaging theory. Besides the two cited figures, the numerous examples include attitudes towards U. S. presidents (Figure 6.1), judgments of persons described by personality traits (Anderson, 1981a, Figure 1.20, p. 59), females’ judgments of prospective dates (Lampel & Anderson, 1968), adjective–predicate language integration (Anderson, 1996, Figure 12.4, p. 406), divorced women’s judgments of marriage satisfaction (Ander-son, 1996a, Figure 5.12, p. 178), and children’s judgments of probability (Schlottman, 2000). HALO THEORY Suppose you are given a set of personality traits that describe a person, make some integrated judgment of the person, such as likableness, and then judge the value of one specified trait of that person. This judgment will be closer to the overall judgment of the person than if it had been judged alone (Anderson & Lampel, 1965). This effect might well seem solid proof of change of meaning. Instead, it is a halo effect; the integrated judgment of the whole reacts back on the subsequent judgment of the part. These two different inter-pretations imply different flow of information processing, shown in

MORAL ALGEBRA 17

Figure 4.2, page 113 of Anderson (1996a) together with experimental evidence. Integration theory thus allows experimental analysis of halo effects, which have been a concern in business and industry but whose analysis has been hobbled by reliance on correlation analysis. PSYCHOLOGICAL LAWS Can psychology aspire to true laws like those in natural science? This question was considered by the philosopher Silverberg (2003). He gave cogent, detailed evaluation of experimental evidence on Information Integration Theory and concluded (p. 299):

N. H. Anderson and his colleagues’ achievements are relevant . . . to much dis-cussion in philosophy of cognitive science. For example, there has been much controversy whether there can be a science of ordinary psychology, that is, of higher cognition and propositional attitudes, that would bear comparison with the sorts of developments that have been achieved in the natural sciences. There has been much controversy as to whether such a psychological science would contain laws. N. H. Anderson’s work presents strong grounds for affirmative answers to these questions.

MORAL ALGEBRA

Moral algebra rests on solid empirical ground. Moral algebra is opera-tive by 4 years of age and continues throughout the life span. Moral al-gebra has cross-cultural generality, even with nonliterate persons. Moral algebra offers powerful methods for studying social–moral cognition. A brief overview of issues covered in later empirical chapters is given here. FAIRNESS AND EQUITY The social maxim of fairness and justice—people should get what they deserve—seems universal. But how do we judge what people deserve? Systematic attempts to uncover algebraic rules of fairness and justice began in the 1960s but were roadblocked by lack of capability for true psychological measurement of deserving. Functional measurement theory revealed exact algebraic laws in several such tasks (Chapter 2). This moral algebra led to a new conceptual framework. Unfairness, previously submerged under fairness ideals, was recognized as a basic social motivation. Unfairness also follows algebraic laws.

18 Chapter 1

BLAME Blame, ubiquitous in everyday life, follows the basic blame law for a harmful act committed with specified intent: Blame = Intent + Harm. (4) Blame and other negative reactions are basic social tools. They deserve study to decrease their personal aversiveness and increase their social effectiveness. This direction has been pursued in extensions of the blame law to study apology, recompense, and extenuation (Chapter 3). LEGAL PSYCHOLOGY Moral algebra has done fairly well in legal psychology (Chapter 4). Arduous, pioneering work by Ebbesen and Konečni uncovered sharpest contrast between Superior Court judges’ ideals and their practice. In setting bail, for example, judges ideally gave high importance weight to community ties; in practice, they ignored community ties. The cogent work of these two investigators is a powerful argument for conjoint experimental–field investigation in the moral field. A scientific base for the 7–year age limit for responsibility in civil liability was begun by Wilfried Hommers using integration experiments. His method has notable advantages of simplicity and objectivity over prevailing idiosyncratic clinical assessment. Understanding social–moral systems of sociological deviants and criminals would be interesting in its own right and useful for improving social control. Integration experiments have advantages of objectivity and generality lacking in case reports as shown by Etienne Mullet, Yuval Wolf, and their associates. Their approach can reveal personality func-tioning of such individuals. MORAL DEVELOPMENT Moral development has central importance because social morality resides largely in the transitory knowledge systems of individuals who are born, develop, and die. Moral development is thus the foremost problem of moral science. Piagetian Theory. Systematic study of blame was begun in pioneering work by Piaget who concluded that young children have strong cognitive

MORAL ALGEBRA 19

limitations. Given the harm caused by an act and the intent of the actor, they cannot integrate the two. Instead, said Piaget, they center on one or the other and judge on the basis of that one alone. Young children thus have severely limited cogni-tive capabilities, not only in moral cognition but generally in cognition about the external world. Only at Piaget’s stage of formal operations, at 10-12 years of age, would integration laws be possible. An entirely different picture emerged as soon as IIT was applied in the 1970s by Manuel Leon and Colleen Surber Moore. Young children can integrate very nicely—they follow algebraic laws in moral cognition, judgment–decision, and naïve physics. Such integration studies showed that young children have far higher cognitive capabilities than previously realized (Chapters 3 and 5). Moral Stage Theories. Moral theory in developmental psychology has been dominated by stage views that moral development progresses through a succession of distinct stages, each of which involves qualita-tive reorganization of the previous stage. These theories suffer crippling inadequacies, largely a consequence of their reliance on people’s verbal rationalizations for their choices in moral dilemmas (see Moral Stage Theories in Chapter 5). Information Integration Theory. A new base for studying moral de-velopment was provided by finding algebraic moral laws at young ages. These same integration laws appear across the lifespan and in other cul-tures. Moral values differ widely, of course, but the integration laws allow for this. Indeed, these laws can measure values of individuals, a unique idiographic aid for cross-age and cross-cultural analysis.

MORAL SCIENCE A variety of issues in moral theory are discussed in Chapters 7 and 8. One class of issues concerns cognitive processes in moral thought and action. A second class of issues involve the dual, societal–individual functions of moral systems noted above. Moral algebra has shown prom-ise with many such issues, including deserving, forgiveness, gratitude, and conflict/compromise. Social betterment is the most important concern of moral science. Moral systems have improved markedly over the centuries but still leave much to be desired. Further progress requires empirical grounding to which every area of psychology can contribute. Moral science offers an effective base that can unify the now fragmented field of psychology.

20 Chapter 1

FUNCTIONAL THEORY OF ATTITUDES Moral attitudes are the wellspring of moral thought and action. Parental instruction and discipline of a child depend on both parents’ attitudes about ideal child behavior—and about how to teach each child. These parental attitudes have major influence on children’s learning of moral–social attitudes and behavior. Yet moral theory pays little attention to the mass of work on social attitudes, the major subfield of social psychology. Attitude researchers, in turn, have neglected the advantages and importance of the moral domain for developing functional theory of attitudes. Hand in hand will benefit both (see Functional Theory of Attitudes, Chapter 8). FUNCTIONAL THEORY OF LEARNING AND MEMORY Moral theory requires a functional approach to learning and memory, qualitatively different from conditioned responses and verbal memory that characterize so much current learning theory. What is learned is not stimulus informers but their goal-oriented meanings. The same stimulus may have different meanings relative to different goals as required by Axiom of Purposiveness. Learning itself can be viewed as information integration. The inte-gration laws have made some progress on functional analysis of learning and memory (see Functional Theory of Learning, Chapter 8). FUNCTIONAL THEORY OF JUDGMENT–DECISION Integration models are ubiquitous in the field of judgment–decision, a consequence of the general concern with conjoint effect of two or more variables. This field has been roadblocked, however, owing to lack of capability for true psychological measurement. Instead, the dominant conceptual framework has been normative models of optimal behavior. The three integration laws, in contrast, are psychological. These laws describe reality, not what people optimally should do, but what they actually do do. As one example, the averaging law explains the radically nonnormative “opposite effects” discussed above (see also “Bias” in Chapter 7). These integration laws solve the long-standing problem of true measurement of functional values, essential for psychological theory of judgment–decision. One result was a solution to the much-conjectured crux of Subjective Expected Value noted above.

MORAL ALGEBRA 21

CONFLICT Conflict is ubiquitous in moral thought and action. Conflict between self-interest and other-interest is a major concern of custom and law. Conflict between two other-obligations is also common, as in a woman caught between work and family. Personal conflict between present and future is common, as with the present temptations of the primrose path (see Conflict and Compromise, Chapter 7). Algebraic laws have shown promise with some forms of conflict. The decision averaging law has done well with judgments of fair sharing between two claimants with extensions to unfairness (Chapter 2). MORAL PHILOSOPHY The moral dilemmas beloved of philosophers embody stark conflicts. One would expect them to have given much attention to ways of resolv-ing conflict. Quite the contrary; most strive to deny that moral conflict is morally real, being incongruous with their ideal of universal moral law. About real moral conflicts of real life, they have little to say (see Moral Philosophy, Chapter 7). Some recent philosophers, it should be emphasized, have begun to recognize the importance of empirical considerations, a notable example being Bok’s (1999) wide-ranging discussion of lying. Most, however, remain constricted by belief in the supremacy of verbal reasoning. SOCIAL HEALING Healing processes are needed to ameliorate negative feelings resulting from inequities inevitable in social organization and from selfishness, unfairness, and dishonesty, and maintain working levels of social inter-action. Healing processes such as blame and apology (Chapter 3), expia-tion and retribution (Chapter 4), and forgiveness (Chapter 7) exhibit moral algebra. Exceptional work on societal forgiving has been done by E. Mullet and his colleagues. As one example, Azar and Mullet (2001) showed that willingness to forgive a gunman who had shot a child during the civil wars in Lebanon was a neat additive function of four stimulus variables for all three Muslim sects and all three Christian sects. Forgiveness was substantial—nearly the same for gunmen of the same or opposite religion as the respondent (Algebra of Forgiveness, Figures 7.5 and 7.6).

22 Chapter 1

FAMILY LIFE Family life is a fundamental domain for moral science. Basic compo-nents of our moral knowledge systems develop in infancy and childhood and have been studied by many investigators. Much of our moral thought and action develop and function in family life. The family is a natural laboratory for empirical analysis with para-mount importance. The family provides ample opportunities for many areas of psychology. No area of psychology has greater importance (see Family Life and Personal Design, Chapter 6 in Anderson, 1991c). EDUCATION Elementary schools do valuable work in teaching moral attitudes and moral behavior. This focus dwindles sharply in secondary schools whereas it should be increased. Here are unparalleled opportunities to improve the dual societal–individual functions of our moral systems. Colleges and universities should similarly increase emphasis on now-neglected instruction, not only with adaptive transfer, their proper goal, but surely with marriage and parenting, which are a foundation for society (see Education in Chapter 7). MORAL SCIENCE

Moral considerations operate at every turn of daily life, from simple courtesy to family interaction, in reactions to TV news on local and na-tional politics, and in seeking self-fulfillment. Morality should thus be a central concern in every social science, psychology especially. But although dedicated work has been done by a number of persons, morality is hardly mentioned in the main fields of psychology. From learning to personality, morality is virtually ignored. Within each field, moreover, progress has led to increasing fragmentation, as several writers have complained. Unification of most fields of psychology is possible by focus on the central problem of morality, to which every field can make valuable con-tributions. The three laws of information integration are an effective base for unification discussed in Chapter 8.

MORAL ALGEBRA 23

NOTES

Note 1. Premise 1 of the parallelism theorem contains an implicit assumption that the stimulus informers have independent effects. Hence observed parallelism supports mean-ing invariance (benefit 4). This independence assumption may need to be implemented with task instructions. In the personality adjective task discussed in the text, the standard instructions state that each adjective that describes the person had been contributed by a different acquaintance who knew the person well. A likely case of nonindependent stimulus informers appears in the study of appro-priateness of amnesty after civil war in Togo (see Note 6 in Chapter 6). Premise 2 of the parallelism theorem is a simplified statement of response linearity. The complete statement is R = c0 + c1ρ, where c0 and c1 are zero and unit constants. For simplicity, these constants are set at 0 and 1, respectively, here and in later chapters. This entails no restriction on the conclusions. Linear is a more appropriate name for what is often called an interval scale; see Chapter 6. Mathematically, the parallelism theorem is simple and proof is omitted here. The real problem is empirical proof. With empirical data, of course, the row and column means are only estimates of the true values of the row and column stimulus informers. Deviations from parallelism may be tested with the interaction term from analysis of variance to obtain a proper test of goodness of fit (Chapter 6). Note 2. Behavioral response measures have proved to be linear in some experiments with humans (e.g., Anderson, 1996a, pp. 327, 401), bar press rate in rats, and peck rate in pigeons (see Anderson, 1996a, p. 104, 2002). Perhaps infrahumans could be trained to use a behavioral form of rating by responding around some location on a line. Stimulus integration is important in infrahumans, as in sensory processing. Perhaps they also fol-low simple laws. Note 3. Equation 2 for the averaging model omits the term ωoIo, which represents the initial impression (prior state). With equal weights, prior state acts as an additive constant and so may be omitted in parallelism analysis (see Prior State, Chapter 6). It must be included, however, to account for the set-size effect and for estimating weight and value with the Average program. Note 4. Unequal weight averaging was troublesome in the early stages of IIT because it produces deviations from parallelism. These deviations could result from nonlinear response, from nonadditive integration, or from both together. Hence there was much uncertainty about what was what, especially because additivity was the prevailing expec-tation and averaging was neither expected nor then considered desirable. This tangle was unsnarled, in part because the averaging model with equal weights is common and yields parallelism, and in part because the procedures initially adopted for the method of functional rating (Chapter 6) were effective in eliminating nonlinear response bias. Most important, experimental manipulation of importance weights successfully predicted deviations from parallelism. Note 5. Qualitative information about unequal weights can be obtained from an inte-gration graph. In the blame experiment of Figure 1.2, suppose more serious harm had

24 Chapter 1

greater weight as well as greater value. Then the curves for intent would be closer to-gether than for less serious harm. Qualitative tests can be simple and useful; see Qualita-tive Tests in Chapter 6.. Note 6. Here are two of the 16 lists of personality trait adjectives used in the very careful experiment of Hendrick and Costantini (1971) to test whether the reliable primacy effect with this task of person cognition resulted from changes of meaning, from inconsistency discounting, or from attention decrement: energetic, vigorous, resourceful, stubborn, dominating, egotistical energetic, vigorous, resourceful, withdrawn, silent, helpless Primacy was assessed by presenting each set in high-low and low-high order. Note that the first and last three adjectives are consistent in the first list, inconsistent in the second. Hence change of meaning and inconsistency discounting predict greater primacy with the second list; attention decrement predicts no difference. Changes of meaning and incon-sistency discounting failed; attention decrement succeeded in this ingenious experiment, one of several by Clyde Hendrick in the early years of IIT. The adjectives and results for all 16 lists are given in Table 3.2, p. 189 of Anderson (1981a). Note 7. Set-Size Effect. A number of investigators took vigorous exception to the averaging model in the early stages of IIT, arguing instead for addition. A seemingly compelling argument for addition is the set-size effect: more stimuli of equal value yield more polarized response. Averaging theory however, gave an exact account of the set-size effect by virtue of the concept of prior state, a belief or attitude that the participant brings to the judgment task that is averaged in with given stimulus information (see Note 3). Note 8. Participants asked to explain their judgments in the personality adjective task typically give plausible, detailed accounts of how one trait adjective modified the mean-ing of another. The observed parallelism reveals the invalidity of these verbal reports. Instead, they appeared to be halo effects (see Halo Theory above). I regret that we have not made systematic study of these verbal reports. Aside from their interest for language cognition, deeper understanding of this difference between introspection and actual cognition would help develop science of phenomenology.