RESULTS Analysis of Preference Probabilities

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Perception & Psychophysics 1994, 56(2), 163-172

Upright versus upside-down faces:

How interface attractiveness varies with orientation

K A R L - H E I N Z B A U M L

Universitat Regensburg, Regensburg, Germany

A c h o i c e experiment is reported i n w h i c h a l l pairs and triples o f faces from a set o f eight moderately attractive faces were presented, both upright a n d upside d o w n , to 103 subjects. In each orientation, the subjects had to select the face that appeared more (pairs) or most (triples) attractive to them. F o r each orientation, the preference probabilities that arose from the pair and triple comparisons c o u l d be described by the B T L rule (Luce, 1959). Thus, each face w a s represented by t w o scores, one reflecting its attractiveness i n the upright orientation and the other reflecting its attractiveness i n the inverted orientation. Orientation affected the preference probabilities. Qualitatively, score ratios between faces decreased from upright to inverted orientation, suggesting that the faces became less discriminable by inversion. Quantitatively, the effect of inversion c o u l d be described by a simple rule that assumes a face's t w o attractiveness scores to be affinely related across orientations. This result indicates that inversion affected a l l faces about equally. The present findings are discussed w i t h respect to faces' first- and second-order relational properties, a distinction empha- sized i n current theories o f face perception. They suggest that the processing o f first- a n d second- order relational properties is impaired by inversion to roughly the same degree.

R e c o g n i t i o n o f faces is disrupted by inversion to a far greater extent than is recognition o f other classes o f v i - sual objects, such as houses, airplanes, or landscapes. In the literature, this phenomenon has been referred to as the face-inversion effect. It was first demonstrated by Y i n (1969). Subsequent studies have replicated this effect under quite different experimental conditions, a n d i n this way have demonstrated the very general and robust nature o f the phenomenon (see Valentine, 1988, for a review).

O r i g i n a l l y , the inversion effect was interpreted as e v i - dence for s p e c i a l i z e d face-recognition processes i n v i - sual i n f o r m a t i o n processing ( Y i n , 1969, 1970). T h e n other approaches were proposed i n order to account for the inversion effect without presuming face-specific processes ( D i a m o n d & Carey, 1986; G o l d s t e i n & C h a n c e , 1980; R o c k , 1973). T h e most influential o f these approaches is that o f D i a m o n d and Carey. These researchers proposed a d i s t i n c t i o n between two types o f spatial i n - formation that underlie the processing o f v i s u a l objects:

first-order relational a n d second-order relational properties. W h i l e first-order relational properties refer to i n - formation about the spatial relationships a m o n g parts o f an object, second-order relational properties refer to i n - formation about the spatial configuration between the

The author's thanks are extended to Hede Helfrich-Holter, Jim Tanaka, and T i m Valentine for their comments on an earlier draft o f this manuscript, and also to Armin Hartinger and Maria Schnelzer for their help in the experimental work. The author's mailing address is In- stitut fur Psychologie, Universitat Regensburg, 93053 Regensburg, Germany (e-mail: heinz@rpss3.psychologie.uni-regensburg.de).

parts o f an object, o n the one hand, and the prototypical spatial c o n f i g u r a t i o n o f its parts, o n the other ( D i a m o n d

& Carey, 1986; Tanaka & Farah, 1991). D i a m o n d and C a r e y hypothesized that inversion was particularly sensitive to the processing o f second-order relational properties w h i l e it d i d not affect the processing o f first-order relational properties. T h e y attributed the inversion effect to the use o f second-order relational properties that are important for, although not unique to, face r e c o g n i t i o n .¹ Indeed, the results o f several studies supported the v i e w that inversion affected the processing o f second-order relational properties ( D i a m o n d & Carey, 1986; M a r u - y a m a & E n d o , 1984; Sergent, 1984; T h o m p s o n , 1980;

Y o u n g , H e l l a w e l l , & Hay, 1987). O n the other hand, none o f these studies demonstrated that inversion d i d not affect first-order relational properties to the same degree (Rhodes, B r a k e , & A t k i n s o n , 1993; Tanaka & Farah, 1991; Valentine, 1988).

Recently, two studies reported experimental results that were interpreted as evidence against the hypothesis that second-order relational properties were responsible for the inversion effect. In a mental rotation experiment, Valentine and B r u c e (1988) found response-time patterns for rotated faces w h i c h were s i m i l a r to those that Shep- ard and Metzler (1971) found for rotated three-dimensional b l o c k drawings. T h e response time o f same-different judgments increased linearly as a function o f rotation angle w h e n the second o f a pair o f faces was rotated away from the v e r t i c a l . Valentine a n d B r u c e argued that this result d i d not support the idea that m a t c h i n g two u p - right faces i n v o l v e d a process that was qualitatively dif-

163 C o p y r i g h t 1994 P s y c h o n o m i c S o c i e t y

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ferent from that used to match one upright and one i n - verted face. Instead, not o n l y first-order relational but also second-order relational properties s h o u l d have been extracted from a face when it was presented upside d o w n . Tanaka and Farah (1991) e x a m i n e d the hypothesis that second-order relational properties were disrupted by inversion w h i l e i n v e r s i o n d i d no h a r m to first-order relational properties i n a dot-pattern experiment. T h e y c o m - pared the effects o f inversion on the i d e n t i f i c a t i o n o f dot patterns that differed i n the extent to w h i c h they required the e n c o d i n g o f second-order relational properties. T h e y found that both first-order relational and second-order relational properties were affected by i n v e r s i o n . Specif- ically, the i d e n t i f i c a t i o n o f dot patterns that required more e n c o d i n g o f second-order relational properties was not more vulnerable to i n v e r s i o n than was i d e n t i f i - cation o f dot patterns that m a i n l y required e n c o d i n g o f first-order relational properties.

A l t h o u g h the results o f Valentine and B r u c e (1988) and Tanaka and Farah (1991) are consistent w i t h the v i e w that inversion affects faces' first-order relational and second-order relational properties to the same degree, their results provide o n l y loose support for this view.

First, Valentine and B r u c e ' s (1988) linearity f i n d i n g suggests that the rotation o f a face i n the v e r t i c a l induces a very regular change i n the p r o c e s s i n g o f its relational properties. T h i s finding, however, cannot exclude the pos- s i b i l i t y that it may be m a i n l y the processing o f second- order relational properties that is affected by rotation.

For instance, linearity may result from the fact that an i n - creasing rotation i n the v e r t i c a l does not affect first- order relational properties but has a linear impact o n the processing o f second-order relational properties. Sec- ond, Tanaka and Farah's (1991) result stems from experiments i n w h i c h dot patterns were used. In order to generalize their result to situations i n v o l v i n g faces, the processing o f first- and second-order relational properties s h o u l d r e m a i n the same for h i g h l y a r t i f i c i a l dot patterns and photographs o f real faces. However, the e m - p i r i c a l soundness o f this presupposition, though c r u c i a l , is not guaranteed. T h e processing o f relational properties i n d u c e d by a r t i f i c i a l stimulus sets may w e l l be different from that i n d u c e d by realistic facial s t i m u l i (e.g., Valentine, 1988). T h e present study presents an alternative approach to testing the hypothesis o f whether the i n f o r m a t i o n processed from upright and inverted faces is the same. T h i s approach is different from the ones used by Valentine and B r u c e , or Tanaka and Farah, and may be more c o n c l u s i v e on the issue.

The approach relies on the a p p l i c a t i o n o f a choice par- a d i g m where preference p r o b a b i l i t i e s are separately measured o n sets o f faces i n the upright and the inverted orientations. T h e point to be e m p h a s i z e d is that the way preferences between faces are affected by orientation may tell us something about the way i n w h i c h the processing o f facial properties changes from upright to u p s i d e - d o w n orientation. C o n s i d e r a set o f faces w i t h given preferences on them i n terms of, say, their perceived attractiveness. Suppose that the perceived attrac-

tiveness o f a face depends o n both its first-order relational and its second-order relational properties (see below). Suppose n o w that we can account for the effect o f orientation o n the preferences by assuming that i n - version affects a l l faces—that is, their perceived attractiveness—in the same way. S i n c e faces w i l l vary i n terms o f the c o n t r i b u t i o n o f first- and second-order relational properties to their overall attractiveness, this account suggested that inversion has the same effects on faces' first- and second-order relational properties. For instance, i f inversion affected o n l y faces' second-order relational properties, inversion w o u l d have a stronger impact o n faces w i t h a higher c o n t r i b u t i o n o f second- order relational properties on attractiveness than o n faces w i t h a lower contribution o f second-order relational properties; inversion w o u l d affect the faces differently.

B a s e d o n this argument, the degree o f a face-orientation interaction may indicate the extent to w h i c h inversion i n - duces a change i n the processing o f face properties.

F i n d i n g a substantial face-orientation interaction therefore suggests that i n f o r m a t i o n processed from upright and inverted faces is different; f i n d i n g no substantial i n - teraction suggests that the i n f o r m a t i o n processed is the same.

To b r i n g this approach to some direct experimental a p p l i c a t i o n , two issues must be s p e c i f i e d . First, a facial attribute must be chosen that relies both on faces' first- order relational properties and o n faces' second-order relational properties. S e c o n d , an adequate method must be chosen to reveal the degree o f the face-orientation interaction. There is g o o d e m p i r i c a l evidence i n d i c a t i n g that the perceived attractiveness o f a face is based on both its first-order relational and its second-order relational properties. Several researchers ( L a n g l o i s & R o g g - man, 1990; Perrett, M a y , & Y o s h i k a w a , 1994) hypothesized that the attractiveness o f a face is a function o f its closeness, or deviation, from a facial prototype and thus is a function o f its second-order relational properties. In fact, these researchers reported experimental results i n support o f their hypotheses. These hypotheses, however, can serve as o n l y rough approximations ( A l l e y & C u n - n i n g h a m , 1991) that leave r o o m for an additional role o f first-order relational properties to affect a face's attractiveness. Indeed, results from the studies o f M e e r d i n k , G a r b i n , and L e g e r (1990) and C u n n i n g h a m , Barbee, and P i k e (1990) indicate that not only second-order relational properties but also first-order relational properties have an impact o n the perceived attractiveness o f a face.

To reveal the degree o f a face-orientation interaction, I deduced a theoretical scale from the preference proba- b i l i t i e s , separately for the two orientations. Indeed, i f preference probabilities i n the two orientations f u l f i l l certain regularities (see Suppes, K r a n t z , L u c e , & T v e r - sky, 1989), they can be used to infer two theoretical scales o f perceived attractiveness. In this case, each face can be represented by two scores, one score reflecting the per- c e i v e d attractiveness o f a face i n the upright orientation and the other reflecting its perceived attractiveness i n the inverted orientation. O n the basis o f these two scales, I

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compared a face's two scores across orientations. T h e present study searches for a face-independent rule that relates the faces' two scores for the two orientations. It is argued that the extent to w h i c h such a rule can account for the change i n the faces' scores reveals the extent to w h i c h inversion affected faces' first-order relational and second-order relational properties to the same degree i n the present experiment.

METHOD

Subjects

The subjects were 103 psychology students at the University o f Regensburg. They were tested individually and were given credit for f u l f i l l i n g degree requirements.

Materials

Eight frontal-view photographs o f stimulus faces o f moderate attractiveness were used. The pictures were a l l o f males between the ages o f 21 and 26 years, and a l l were very similar i n terms o f hair length and shadows. They wore no eyeglasses, beards, or mus- taches, and the expression on their faces was neutral. A l l faces were unknown to the subjects. The pictures were copied i n d i v i d - ually onto monochrome slides, and copies were made at two different orientations, upright and upside-down.

Apparatus

The slides were presented using a K o d a k Carousel S - R A 2500 projector that was controlled by a computer. The slides were presented on a blank w a l l , i n front o f w h i c h the subject sat at a dis- tance o f about 2 m . E a c h face subtended about 8° o f visual angle.

The subject indicated his or her response by using push buttons, and the response was recorded by the computer.

Design and Procedure

A l l 8!/(2!6!) = 28 different pairs and a l l 8!/(3!5!) = 56 different triples o f faces were presented to each subject, in both upright and inverted orientations. The pairs and triples were either presented first in the upright orientation and then, about 1 week later, in the inverted orientation, or vice versa. Fifty-two subjects started with the upright orientation, and the remaining 51 subjects started with the inverted orientation. For each orientation, the presentation o f the pairs preceded the presentation o f the triples.

A n experimental session consisted o f two parts, the presentation o f the pairs and the presentation o f the triples. A t the beginning o f each experimental session, a l l pairs and a l l triples were mixed ran- domly, as were a pair's two faces and a triple's three faces. The two (three) slides o f a pair (triple) were presented successively with a presentation time o f 2 sec for each slide. The presentation o f the single slides was interrupted by a 1 -sec blank field. After the presentation o f a pair or triple o f faces, the subject immediately se- lected w h i c h o f the two or three faces he or she preferred in terms o f attractiveness by pressing one o f two (pair comparison) or one o f three (triple comparison) buttons. F o l l o w i n g a 2-sec blank field, the next pair or triple o f faces was presented.

Data Analysis

For each o f the two orientations, a subject's pair comparisons gave rise to a 2 8 X 2 matrix, a subject's triple comparisons gave rise to a 5 6 X 3 matrix. E a c h cell o f the pair (triple) comparison matrix was coded as 1 or 0, depending on whether a face was preferred (1) or not (0) in a pair (triple) comparison. These two matrices represented a subject's preferences with respect to the presented faces. The pair (triple) comparison matrices were summed over subjects to result i n one pair (triple) comparison matrix for each orientation.

These matrices represented the data o f the experiment. To for- mulate a statistical model o f these preferences, the sequence o f choices o f a pair's first or second face was viewed as a sequence o f B e r n o u l l i trials with underlying parameter pab, representing the probability that, for a pair (a,b), face a is preferred over face b. The relative frequency with w h i c h face a is chosen from the pair (a,b) is taken as an estimate o f p^ab. Similarly, the sequence o f choices o f a triple's first, second, and third face was viewed as a sequence o f trials with underlying parameters pa;bc and pb;ac, representing the probabilities that, for a triple o f faces (tf,6,c), face a is preferred over faces b and c, and face b is preferred over faces a and c.

A g a i n , relative frequencies serve as estimates for the probabilities (see Suppes et al., 1989). Based on this statistical model, an orientation's preferences were described by 140 ( 2 8 X 1 + 5 6 X 2 ) free parameters.

In order to infer a simple theoretical scale o f attractiveness w h i c h w i l l give a parsimonious account for an orientation's whole set o f preference probabilities, some restrictions on the preference probabilities must be fulfilled. The B r a d l e y - T e r r y - L u c e rule (Bradley & Terry, 1952; L u c e , 1959; Suppes et a l . , 1989; i n the following referred to as the B T L rule) was fitted to an orientation's two matrices. T h i s rule sets strong restrictions on the relationship between pair and triple preferences. It demands the f o l l o w i n g property, called the constant-ratio property, to be true for all triples o f faces (a,b,c):

Pab _ Pa,be Pba Pb;ac

where p^ab stands for the probability that given the pair (a,b) face a is preferred over face b, and pa;bc stands for the probability that given the triple (a,b,c) face a is preferred over faces b and c. This property, i n effect, asserts that the strength o f preference o f the triple's face a over the triple's face b is unaffected by the other available alternative, the triple's face c.

If the constant-ratio property is satisfied, each face a can be as- sociated with a numerical value v(a), so that the preference probabilities for a pair o f faces (a,b) are determined by the rule = v(a)/[v(a) + v(b)] and the preference probabilities for a triple o f faces (a,b,c) are determined by the rule pa b c = v(a)/[v(a)+v(6) + v(c)]. These numerical values are unique up to scalar transformations. Thus, only the numerical value o f one face can be chosen freely. For the eight face stimuli employed i n the present experiment, the B T L rule therefore results i n only seven free parameters to describe an orientation's 140 independent data ob- servations.

A likelihood-ratio test (cf. L i n d g r e n , 1976) was used to deter- mine whether the rule fitted an orientation's data. G i v e n the data, the likelihood o f the B T L rule ( L B T L ) was compared with the likelihood o f the statistical model (Z,s) by using the property that the term - 2 1 n IB T L/ Ls is approximately chi-square distributed.

The parameters o f the B T L rule were estimated by using the iter- ative search procedure P R A X I S (Gegenfurtner, 1992).

RESULTS Analysis of Preference Probabilities

Table 1 shows the estimated preference probabilities (relative frequencies) for the pair comparisons, both for the upright and the inverted orientations. T h e A p p e n d i x shows the estimated preference probabilities for the triple comparisons. T h e preference probabilities v a r i e d over a large range o f values, suggesting considerable dif- ferences between faces w i t h respect to their perceived attractiveness. T h i s pattern o f results h e l d for both o r i -

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Table 1

Pair Comparison Matrices for the Two Orientations, Upright and Inverted F2

^5 Fi F*

Upright Orientation

— 0.515 0.709 0.728 0.583 0.689 0.252 0.961

Ft 0.485 — 0.757 0.660 0.612 0.670 0.340 0.922

f] 0.291 0.243 — 0.437 0.408 0.408 0.146 0.854

F, 0.272 0.340 0.563 — 0.437 0.447 0.194 0.913

F5 0.417 0.388 0.592 0.563 — 0.524 0.243 0.961

^6 0.311 0.330 0.592 0.553 0.476 — 0.214 0.913

Fi 0.748 0.660 0.854 0.806 0.757 0.786 ^— 0.913

FH 0.039 0.078 0.146 0.087 0.039 0.087 0.087 _—

Inverted Orientation

— 0.476 0.689 0.602 0.621 0.641 0.262 0.816

F-> 0.524 — 0.670 0.573 0.592 0.680 0.291 0.845

F) 0.311 0.330 — 0.544 0.398 0.456 0.243 0.748

F⁴ 0.398 0.427 0.456 — 0.456 0.476 0.155 0.757

Fs 0.379 0.408 0.602 0.544 — 0.447 0.184 0.835

F<> 0.359 0.320 0.544 0.524 0.553 — 0.282 0.728

Fn 0.738 0.709 0.757 0.845 0.816 0.718 — 0.913

F8 0.184 0.155 0.252 0.243 0.165 0.272 0.087 —

Note—Each cell represents the estimated probability that one o f a pair of faces is preferred over the other (F„ = face number n).

entations. To test whether an orientation's preferences differed reliably from indifferent choices, I c o m p a r e d , for each orientation, the (perfect) fit o f the statistical m o d e l that describes the 140 independent preference probabilities (see M e t h o d section) w i t h the fit o f a statistical m o d e l that restricts a l l preference probabilities to 1/2 (pairs) or 1/3 (triples). T h e l i k e l i h o o d - r a t i o tests were conducted w i t h 140 df. T h e ^²( 1 4 0 ) values o f 3,575.605 (p < .0001) for the upright orientation and 2,474.733 (p < .0001) for the inverted orientation d e m - onstrate that preferences differed reliably from indifferent choices.

A first v i s u a l c o m p a r i s o n o f the preference p r o b a b i l - ities across orientations (see Table 1 and the A p p e n d i x ) suggests that the probabilities were fairly stable across orientations. However, some tendency showed up for the preferences to be closer to indifferent choices i n the i n - verted orientation than i n the upright orientation. For i n - stance, 19 o f the 28 independent preference probabilities for pairs were less close to indifference (p = 1/2) w h e n the faces were presented upright than w h e n they were presented u p s i d e - d o w n . To test whether the preference probabilities c o u l d be assumed to be constant across o r i - entations, I c o m p a r e d the (perfect) fit o f a j o i n t statistical m o d e l that d e s c r i b e d the two o r i e n t a t i o n s ' 280 ( 2 X 1 4 0 ) i n d e p e n d e n t preference p r o b a b i l i t i e s (see M e t h o d section) w i t h the fit o f a statistical m o d e l that restricted the p r o b a b i l i t i e s to b e i n g constant across o r i - entations. T h e *2( 1 4 0 ) value o f 184.763 (p = .007) d e m - onstrates that preferences v a r i e d reliably across orientations. T h u s , both faces and orientation had a reliable effect on the preferences.

Quality of Fit of the BTL Rule

To get a more detailed insight into how faces and o r i - entation affect preferences, a more p a r s i m o n i o u s ac-

count for an orientation's w h o l e data set is useful. For each orientation, I e x a m i n e d whether the preferences c o u l d be fitted by the B T L rule. I f this rule fitted the data w e l l , each face c o u l d be represented by one positive real-valued score that reflected its perceived attractiveness for the particular orientation. T h e B T L rule was s i - multaneously fitted to an orientation's pair and triple c o m p a r i s o n matrices. For each orientation, the B T L rule has seven free parameters to describe the 140 independent preference probabilities. The ^²( 1 3 3 ) values o f 8 6 . 4 2 9 (p = .999) for the u p r i g h t o r i e n t a t i o n a n d 103.208 (p = .974) for the inverted orientation d e m o n - strate an excellent fit o f the rule to the data. T h u s , for each orientation, the effect o f the faces on the preference probabilities can be described by the B T L rule.

In the top panel o f F i g u r e 1, the preference p r o b a b i l - ities measured i n the two orientations w i t h the predictions o f these probabilities when u s i n g the B T L rule ("two i n d i v i d u a l B T L rules") are compared. The data are merged over the two orientations. I f the B T L rule h e l d perfectly, a l l 280 data points w o u l d fall on the diagonal line. A s suggested by the above l i k e l i h o o d - r a t i o tests, the B T L rule fits the data w e l l . A s a result, each face is represented by its two B T L scores as described below.

Analysis of BTL Scores

I c o m p a r e d the scores o f the faces across orientations.

Figure 2 provides bar charts o f the faces' scores, separately for each orientation. Because the B T L rule fitted the data w e l l , an effect o f orientation on the B T L scores that was qualitatively s i m i l a r to the one found for the preference probabilities w o u l d be expected. Indeed, the scores o f the faces show a considerable stability across orientations. T h e order o f the faces' scores is hardly affected by inversion, and furthermore the score ratios between faces do not change in a major way across orien-

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T W O INDIVIDUAL BTL-RULES

1 . 0 0 -

P-

p r e d 0.75

0.50

0.25

0.00 -r 1 1 1 1

0.00 0.25 0.50 0.75 1.00 P - m e a s

ONE C O M M O N B T L - R U L E

0.00 0^25 0.50 0.75 L 0 0 P - m e a s

B T L - R U L E + A F F I N E RULE

l . O O n

0 . 7 5 -

p r e d ° '50

0.25

0.00

0.00 0.25 0.50 0.75 P - m e a s

1.00

Figure 1. Scatterplot of measured preference probabilities (P-meas) versus predicted preference probabilities (P-pred) when using differ- ently restricted rules to fit the data. The top panel shows the quality of fit of a joint B T L rule where a face's two parameters are free to vary across orientations (7+7=14 parameters). The middle panel shows the quality of fit of a joint B T L rule where a face's two parameters are re- stricted to not vary with orientation (7 parameters). The bottom panel, finally, shows the quality of the fit of a joint B T L rule where a face's two parameters are restricted to being aflfinery related across orienta- tions (7+1 = 8 parameters). The data are merged over the two orien- tations (upright orientation •, inverted orientation °). If the rules ac- counted perfectly for the variation in the preference probabilities, each panel's 280 data points would fall on the diagonal line.

tations. Despite this stability, there is some tendency for the score ratios between faces to be reduced by inversion. I e x a m i n e d whether orientation had a reliable effect o n the score ratios, that is, whether the assumption that v^{u p}(a)/v^Up(6) = v^{i n v}(a)/v^{i n v}(Z?) holds for all pairs (a,b) had to be rejected statistically. Because the two scales v^{u p} and vinv are unique only up to scalar transformations (see M e t h o d section), this question is equivalent to testing whether the two scores o f a face can be assumed to be constant across orientations. I fitted a j o i n t B T L rule to the preference matrices o f the two orientations where the two scores o f a face are restricted to not v a r y i n g w i t h orientation. T h e fit o f this rule to data was compared w i t h the fit o f a j o i n t B T L rule where the two scores o f a face were free to vary w i t h orientation. The #²( 7 ) value o f 112.284 (p < .001) rejects the hypothesis that score ratios are constant across orientations. T h u s , the effect o f orientation found i n the preference probabilities is also reflected i n the B T L scores.

T h e m i d d l e panel o f Figure 1 depicts the c o m p a r i s o n o f the preference probabilities measured i n the two o r i - entations w i t h the predictions o f these probabilities w h e n using a j o i n t B T L rule where the two scores o f a face do not vary w i t h orientation ("one c o m m o n B T L rule").

A g a i n the data are merged over orientations. A s suggested by the above l i k e l i h o o d - r a t i o test, the fit o f this j o i n t B T L rule is somewhat worse than the fit o f a j o i n t B T L rule where the two scores o f a face are free to vary w i t h orientation ("two i n d i v i d u a l B T L rules," top panel).

A l t h o u g h the difference i n fit is not large, the deteriora- tion is significant. A s a result, a face cannot be represented by the same B T L score for the two orientations.

A rule is needed to describe h o w a face's two scores are related across orientations.

A c c o r d i n g l y , I tested a simple rule to describe the effect o f orientation o n the faces' scores. T h i s rule assumes that the two scores o f a face are affinely related across orientations, that is, vi n v( a ) = vup(a)+k for each face a, where k is a real-valued parameter that does not depend on the faces. Equivalently, across orientations the score ratios between faces are related by the equa- tion v^{i n v}(a)/v^{i n v}(Z>) = [ v^{u p}( f l ) + * ] / [ v^{u p}( f t ) + * ] . T h i s rule has two interesting properties. First, the affine relationship includes the assumption that inversion affects a l l faces equally. T h u s , no interaction is supposed to occur between faces and orientation. T h e w h o l e effect o f o r i - entation is reduced to parameter k. S e c o n d , the sign o f k determines h o w preferences are affected by inversion. I f k is positive, preferences are less close to indifferent choices i n the upright orientation than they are i n the i n - verted orientation, a result suggested above b y v i s u a l analyses o f the preference probabilities and the score ratios. O n the other hand, i f k is negative, preferences are more close to indifferent choices i n the upright orientation than they are i n the inverted orientation. k=0 is equivalent to an invariance o f score ratios and preferences across orientations, a hypothesis already rejected above.

To examine whether this rule describes the effect o f inversion for the present data, I tested whether the pref-

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o u u o u o u o

Figure 2. Bar charts showing the attractiveness scores of faces for the two orientations. The scores were estimated by fitting the B T L rule individually to an orientation's preference matrices. For each orien- tation, the face scores were fixed by assigning Face 1 a scale value of 1.

erence matrices o f the two orientations c o u l d be fitted by a j o i n t B T L rule where the two scores o f a face were restricted to being affinely related through parameter k.

S i m i l a r l y , I c o m p a r e d the fit o f this j o i n t B T L rule w i t h the fit o f a j o i n t B T L rule where the two scores o f a face were free to vary w i t h orientation. T h e ^²( 6 ) value o f 7.241 (p = .299) supports the hypothesis that a face's two scores are affinely related across orientations. T h u s , the introduction o f the rotation parameter k reduces the c h i - square value by more than 100 points, demonstrating that k plays an essential role i n fitting the data. T h i s holds true even though I found the value o f k to be fairly s m a l l (&=.135). T h e fact that k is positive indicates that preferences are indeed less close to indifferent choices

in the upright orientation than they are i n the inverted orientation.

T h e bottom panel o f Figure 1 depicts the c o m p a r i s o n o f the preference probabilities measured i n the two o r i - entations w i t h the predictions o f these probabilities w h e n using a j o i n t B T L rule where the two scores o f a face are affinely related across orientations ( " B T L rule + affine r u l e " ) . A g a i n , the data are merged over orientations. A s suggested by the above l i k e l i h o o d - r a t i o test, the data are w e l l fitted. In fact, a v i s u a l c o m p a r i s o n w i t h the fit o f a j o i n t B T L rule where the two scores o f a face are free to vary w i t h orientation ("two i n d i v i d u a l B T L rules," top panel) demonstrates that the more restrictive, 8-parameter m o d e l provides a fit to the data that is equal to that o f the less restrictive, 14-parameter m o d e l . In this sense, the data are consistent w i t h the hypothesis that the faces' two parameters are affinely related across o r i e n - tations. In addition, the figure v i s u a l i z e s that the 8- parameter m o d e l provides a somewhat better fit to the data than does the 7-parameter m o d e l where the two scores o f a face are restricted to not vary w i t h orientation ("one c o m m o n B T L rule," m i d d l e panel).

These analyses show that the reliable effects o f faces and inversion on the preference probabilities can be described i n a simple way by assuming, first, that each o r i - entation's preference probabilities f o l l o w a B T L rule, and second, on the basis o f this idea, that a face's two B T L scores are affinely related across orientations. B y using these two rules, the 280 measured preference probabilities can be described by o n l y eight parameters.

Seven o f these eight parameters reflect the effect o f faces;

the eighth parameter reflects the effect o f orientation i n the present data sets.

DISCUSSION

Preferences between faces were measured w i t h regard to the perceived attractiveness o f the faces. T h i s was done w i t h the faces presented upright and w i t h the same faces presented upside d o w n . Inversion affected the preferences. Qualitatively, the preferences between faces became more close to indifferent choices when the faces were presented upside d o w n than when they were presented i n the upright orientation. T h i s indicates that the faces became less d i s c r i m i n a b l e when inverted, suggest- i n g an i m p a i r m e n t i n the processing o f facial properties for this orientation. Quantitatively, the effect o f inversion c o u l d be described by a s i m p l e rule that assumes the two attractiveness scores o f a face to be affinely related across orientations. A t the core o f this rule is the assumption that inversion affects a l l faces equally w i t h no substantial interaction between the faces' perceived attractiveness and their orientation. It was argued above that the degree o f a face-orientation interaction reflects the extent to w h i c h i n f o r m a t i o n processed from upright and upside- d o w n faces differs. T h e result that the effect o f inversion in this study can be described equally for the single faces demonstrates a negligible amount o f face-orientation i n -

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teraction, suggesting that about the same information is processed from upright and upside-down faces.

It is a w i d e l y h e l d v i e w i n the literature that inversion is particularly disruptive to processing faces' second- order relational properties but that it hardly affects the processing o f faces' first-order relational properties ( D i a m o n d & Carey, 1986). A l t h o u g h the results from a number o f studies were interpreted i n favor o f this view, none o f those studies p r o v i d e d u n e q u i v o c a l evidence for it (e.g., Rhodes et a l . , 1993; Valentine, 1988). M o r e o v e r , the data from two more recent studies were interpreted as evidence for an equal impairment i n the processing o f first- and second-order relational properties (Tanaka &

Farah, 1991; Valentine & B r u c e , 1988). W h i l e the relationship i n these two studies between results and c o n - clusions may still have been tentative i n nature (see introduction), the results from the present study provide more direct evidence for this alternative view. S i n c e the same information seems to have been processed from upright and upside-down faces, it is suggested that first- and second-order relational properties are affected by inversion to roughly the same degree. T h i s f i n d i n g establishes a major challenge to D i a m o n d and Carey's (1986) propo- sition. It indicates that the distinction between faces' first- and second-order relational properties cannot ex- p l a i n w h y recognition o f faces is disrupted by inversion to a far greater extent than is recognition o f other classes o f v i s u a l objects.

M o s t recently, Rhodes et a l . (1993) reported an experiment i n w h i c h they compared the effects o f face i n - version for detecting changes that span the c o n t i n u u m from first- to second-order relational properties. U s i n g this k i n d o f face m a n i p u l a t i o n , they found evidence that second-order relational properties are more sensitive to inversion than first-order relational properties. W h i l e their method has the desirable feature that it addresses the question o f interest very directly, their method depends c r u c i a l l y on the assumption that faces' first- and second-order relational properties can be manipulated independently. A s also outlined by Rhodes et a l . (p. 50), some o f their results suggest that this assumption does not h o l d i n general: first- and second-order relational properties appear to be inherently confounded i n faces.

The degree to w h i c h their findings can challenge the view supported by the present study, that first- and second- order relational properties are equally affected by inversion, therefore remains unclear.

Attractiveness and Fit of BTL Rule

A n orientation's preference matrices c o u l d be w e l l described by the B T L rule, i n d u c i n g a o n e - d i m e n s i o n a l representation o f faces w i t h regard to their perceived attractiveness. A t first, this f i n d i n g might appear to c o n - flict w i t h some current theories o f attractiveness w h i c h suggest several quite different factors as affecting a face's perceived attractiveness, i n c l u d i n g both first- and second-order relational properties ( C u n n i n g h a m , 1986;

C u n n i n g h a m et a l . , 1990; M e e r d i n k et a l . , 1990). H o w -

ever, the two findings do not conflict w i t h each other.

Instead, the B T L representation i m p l i e s o n l y that w h e n two faces are compared w i t h regard to their attractiveness, a l l factors affecting the attractiveness o f a face c o m b i n e into one g l o b a l score that represents the face's overall attractiveness. Indeed, this score can be interpreted as the sum o f the attractiveness values o f the s i n - gle factors that affect the attractiveness o f a face (Sup- pes et a l . , 1989; Tversky, 1972).

T h e present results reveal a s u r p r i s i n g l y g o o d fit o f the B T L rule to orientation data. There are not many data sets i n the literature where choice behavior c o u l d be w e l l described by the B T L rule ( L u c e , 1977). Face attractiveness as investigated i n the present experiment seems to be one o f those. In fact, I replicated the experiment for upright faces for two other sets o f faces, 10 male and 10 female. A g a i n , I used perceived attractiveness as the facial attribute. F o r both the males and the females, the B T L rule led to fits to the data that c o m - pared w e l l w i t h those found i n the present study.

Comparing Faces

⁹

Attractiveness Scores Across Orientations

T h i s study focuses o n interface relationships and the question o f h o w attractiveness ratios between faces vary w i t h orientation. O n the basis o f pair and triple comparisons o f faces o f equal orientation, this question c o u l d be addressed i n a w e l l - f o u n d e d way. In order to include meaningful comparisons o f the two attractiveness scores o f a single face across orientations, however, measurements beyond those reported i n the present study w o u l d be needed. S p e c i f i c a l l y , preferences between faces o f different orientations w o u l d have to be measured. O n the basis o f these additional measurements, a new scale that simultaneously quantified the perceived attractiveness o f the faces i n their upright and their inverted orientations w o u l d have to be developed. C o r r e s p o n d i n g measurements were not conducted i n the present study.

M o r e formally, the fact that the two scores estimated for a face i n this study cannot be compared i n a meaningful way across orientations is a simple consequence o f the fact that the two scales for upright and inverted orientation ( v^{u p}, v^{i n v}) are unique only up to scalar transformations (see M e t h o d section), and that the units o f the two scales can be f i x e d independently from each other. T h u s , whenever the score o f a face is higher i n the upright orientation than i n the inverted orientation—

after two units for the two scales have been chosen—an appropriate change i n the unit o f one o f the two scales can reverse the order. T h e development o f one c o m m o n scale for both orientations, i f successful, w o u l d e l i m i - nate this freedom.

From Inversion to a General Rotation in the Vertical

Inversion o f a face provides only a special case ( 1 8 0 ° ) o f a more general rotation o f a face i n the vertical. In- deed, rotation angles other than 180° are also k n o w n to affect face recognition ( R o c k , 1973), response times

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(Valentine & B r u c e , 1988), and/or e n c o d i n g ( B a u m l , 1992). A s a result, the attractiveness relationships between faces can be expected to be affected not o n l y by inversion but also by other rotation angles.

T h e c h o i c e p a r a d i g m e m p l o y e d i n the present study can be used i n a straightforward way to study h o w other rotation angles affect the relationships between faces.

S p e c i f i c a l l y , i f the affine rule found i n the present study to describe the effect o f inversion h e l d for any rotation angle, the effect o f each rotation angle o n interface relationships c o u l d be represented by just one parameter, k. In this case, the way that parameter k depended on ro- tation angle w o u l d reveal useful i n f o r m a t i o n on how the rotation angle affects the relationships between faces.

O n the basis o f Valentine and B r u c e ' s (1988), or R o c k ' s (1973), or B a u m l ' s (1992) results, a m o n o t o n i c relationship between rotation angle and parameter k may be expected. M o r e s p e c i f i c expectations about the functional form o f the relationship between rotation angle and parameter k, however, are hard to derive from previous studies. In this sense, the question o f how rotation angles other than inversion affect the attractiveness relationships between faces is open to future studies.

Three Final Remarks

First: B y using attractiveness as a facial attribute, the present study provides evidence for the feasibility o f u s i n g a s i m p l e rule to describe the effect o f inversion on the relationships between faces. T o the extent that this rule captures the w h o l e effect o f face inversion, its ade- quacy s h o u l d not depend o n the facial attribute e m - ployed. Indeed, w h e n u s i n g other facial attributes, such as, for instance, distinctiveness or age, the pattern o f results s h o u l d be s i m i l a r to that described above w i t h regard to attractiveness. T h i s expectation constitutes a strong p r e d i c t i o n to be tested i n further experiments.

Second: R e c a l l that this study used photographs o f eight moderately attractive males o f about equal age.

A l t h o u g h these experimental c o n d i t i o n s m i g h t have fa- v o r e d the results obtained i n this study, the faces e m - p l o y e d p r o v i d e d a reasonable test o f the hypothesis that the same i n f o r m a t i o n is processed from upright and i n - verted faces. Indeed, a considerable range o f p e r c e i v e d attractiveness was spanned b y the single faces. T h e attractiveness ratios for pairs o f faces v a r i e d from less than 1.1:1 up to more than 40:1 (cf. F i g u r e 2). Further experiments must show whether the rules found i n the present study w i l l also apply to quite different sets o f fa- c i a l s t i m u l i , i n c l u d i n g those o f males o f v e r y l o w or v e r y h i g h p e r c e i v e d attractiveness, o l d e r males, and females.

Third: T h e s i m p l e rule proposed i n this study to ac- count for the inversion effect l e d to a reasonable de- s c r i p t i o n o f the data sets. D u e to its strong restrictions, however, this rule is a s i m p l i f i c a t i o n . Presumably, some faces do " l o s e " some o f their properties w h e n they are inverted, a phenomenon inconsistent w i t h the idea that i n v e r s i o n affects a l l faces i n the same way. Future studies must show whether frequency a n d size o f these

"losses" are l o w enough to accept the v i e w suggested i n this study, at least as a first-order m o d e l .

R E F E R E N C E S

A L L E Y, T. R., & CUNNINGHAM, M . R. (1991). Averaged faces are at- tractive, but very attractive faces are not average. Psychological Sci- ence, 2, 123-125.

BAUML, K . - H . (1992). Diskriminationslernen bei rotierten Gesichtern:

Eine Markov-Analyse von Kodierungs- und Assoziationsprozessen.

Zeitschrift fur Experimentelle und Angewandte Psychologic 39, 1-17.

BRADLEY, R. A., & TERRY, M . E . (1952). Rank analysis of incomplete block designs. I. The method of pair comparisons. Biometrika, 39, 324-345.

CUNNINGHAM, M . R. (1986). Measuring the physical in physical at- tractiveness: Quasi-experiments on the socio-biology of female facial beauty. Journal of Personality & Social Psychology, 50, 925-935.

C U N N I N G H A M, M . R., B A R B E E , A. P., & P I K E , C. L . (1990). What do women want? Facialmetric assessment o f multiple motives in the perception o f male facial physical attractiveness. Journal of Per- sonality & Social Psychology, 59, 61-72.

DIAMOND, R., & CAREY, S. (1986). Why faces are and are not special:

A n effect of expertise. Journal of Experimental Psychology: Gen- eral, 115, 107-117.

GEGENFURTNER, K . (1992). P R A X I S : Brent's algorithm for function minimization. Behavior Research Methods, Instruments, & Com- puters, 24, 560-564.

GOLDSTEIN, A . G . , & C H A N C E, J. E . (1980). Memory for faces and schema theory. Journal of Psychology, 105, 47-59.

LANGLOIS, J. H . , & ROGGMAN, L . A . (1990). Attractive faces are only average. Psychological Science, 1, 115-121.

LINDGREN, B . W. (1976). Statistical theory (3rd ed.). New York:

Macmillan.

L U C E, R. D. (1959). Individual choice behavior: A theoretical analy- sis. New York: Wiley.

L U C E, R. D. (1977). The choice axiom after twenty years. Journal of Mathematical Psychology, 15, 215-233.

MARUYAMA, K . , & ENDO, M . (1984). Illusory face dislocation effect and configural integration in the inverted face. Tohoku Psycholog- ica Folia, 43, 150-160.

MEERDINK, J. E . , GARBIN, C . P., & L E G E R, D . W. (1990). Cross-gender perceptions o f facial attributes and their relation to attractiveness:

Do we see them differently than they see us? Perception & Psy- chophysics, 48, 227-233.

PERRETT, D. I., M A Y, K. A . , & YOSHIKAWA, S. (1994). Facial shape and judgements o f female attractiveness. Nature, 368, 239-242.

RHODES, G . , B R A K E, S., & ATKINSON, A . P. (1993). What's lost in i n - verted faces? Cognition, 47, 25-57.

ROCK, I. (1973). Orientation and form. New York: Academic Press.

SERGENT, J. (1984). A n investigation into component and configural processes underlying face perception. British Journal of Psychol- ogy, 75, 221 -242.

SHEPARD, R. N . , & M E T Z L E R, J. (1971). Mental rotation o f three- dimensional objects. Science, 171, 701-703.

SUPPES, P., K R A N T Z, D . H . , L U C E, R. D . , & TVERSKY, A . (1989). Foun- dations of measurement (Vol. 2, pp. 383-458). San Diego: Academic Press.

TANAKA, J. W., & FARAH, M . J. (1991). Second-order relational prop- erties and the inversion effect: Testing a theory of face perception.

Perception & Psychophysics, 50, 367-372.

THOMPSON, P (1980). Margaret Thatcher: A new illusion. Perception, 9, 483-484.

TVERSKY, A . (1972). Elimination by aspects: A theory of choice. Psy- chological Review, 79, 281-299.

VALENTINE, T. (1988). Upside-down faces: A review of the effect of in- version upon face recognition. British Journal of Psychology, 79, 471-491.

VALENTINE, T , & BRUCE, V. (1988). Mental rotation o f faces. Mem- ory & Cognition, 16, 556-566.

YIN, R. K . (1969). Looking at upside-down faces. Journal of Experi- mental Psychology, 81, 141-145.

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YIN, R. K . (1970). Face recognition by brain-injured patients: A dis- sociable ability? Neuropsychologic!, 8, 395-402.

YOUNG, A . W . , H E L L A W E L L , D . , & HAY, D . C . (1987). Configurational information in face perception. Perception, 16, 747-759.

N O T E

1. Actually, Diamond and Carey (1986) not only distinguished between objects' first-order relational and second-order relational prop-

erties, but made an additional distinction between these two kinds o f relational properties on the one hand and more isolated features on the other. The crucial point in Diamond and Carey's hypothesis, however, dealt with the special role o f the second-order relational properties in object inversion; their hypothesis did not incorporate any distinction between first-order relational properties and the more isolated features. Thus, for sake of brevity, I use first-order relational properties in this paper as a summary term to refer both to first-order relational properties and to more isolated features.

APPENDIX

T h e triple c o m p a r i s o n matrices for the two orientations, w i t h each c e l l representing the estimated p r o b a b i l i t y that one o f a t r i p l e o f faces is preferred over the other t w o . Face Triple

(a.b.c)

Upright Inverted

Face Triple

(a.b.c) a;bci b,ac c,ab a,bc b;ac c,ab

0.417 0.456 0.126 0.427 0.388 0.184

(FUF2,F4) 0.369 0.466 0.165 0.350 0.398 0.252

( F „ F2, F5) 0.369 0.437 0.194 0.398 0.350 0.252

(F^UF²,F⁶) 0.388 0.447 0.165 0.495 0.340 0.165

(F^X,F².F⁷) 0.165 0.214 0.621 0.184 0.194 0.621

(F^UF².F^S) 0.485 0.485 0.029 0.447 0.437 0.117

(Fx.F3.F4) 0.515 0.223 0.262 0.485 0.223 0.291

(F^},F³,F^S) 0.495 0.243 0.262 0.515 0.194 0.291

0.495 0.214 0.291 0.544 0.223 0.233

(F^UF³,F⁷) 0.204 0.087 0.709 0.223 0.087 0.689

(F^UF^},F,) 0.680 0.291 0.029 0.592 0.291 0.117

(F^hF⁴,F^s) 0.485 0.204 0.311 0.495 0.252 0.252

< F „ F⁴, F⁶) 0.447 0.223 0.330 0.466 0.252 0.282

(F\. F⁴, F⁷) 0.233 0.107 0.660 0.214 0.155 0.631

(F^UF⁴,F^S) 0.689 0.282 0.029 0.592 0.311 0.097

(FUF5,F6) 0.398 0.320 0.282 0.456 0.272 0.272

( F „ F5, F7) 0.214 0.117 0.670 0.233 0.126 0.641

( F „ F5, F8) 0.563 0.408 0.029 0.592 0.330 0.078

( F „ F6, F7) 0.204 0.165 0.631 0.243 0.136 0.621

( F „ F6, F8) 0.592 0.359 0.049 0.602 0.301 0.097

(F\,Fi,F») 0.262 0.709 0.029 0.272 0.699 0.029

(F2.F1.F4) 0.583 0.155 0.262 0.505 0.165 0.330

(F2.F1.Fi) 0.563 0.146 0.291 0.466 0.214 0.320

(F2.Fi.F6) 0.524 0.204 0.272 0.563 0.214 0.223

(F2.F3.F-,) 0 282 0.039 0.680 0.282 0.097 0.621

(F².Fi,F^s) 0.670 0.262 0.068 0.544 0.301 0.155

(F2.F4.Fi) 0.553 0.223 0.223 0.485 0.262 0.252

(F2,F4,F⁶) 0.524 0.233 0.243 0.427 0.311 0.262

(F2.FA.F7) 0.291 0.097 . 0.612 0.291 0.107 0.602

(F²,F⁴,F^S) 0.689 0.301 0.010 0.583 0.340 0.078

(F2.Fi.F1) 0.544 0.282 0.175 0.456 0.320 0.223

(F²,F⁵,F⁷) 0.243 0.126 0.631 0.320 0.097 0.583

(F2.Fs,Fa) 0.641 0.320 0.039 0.544 0.359 0.097

(F2.Ft.Fj) 0.223 0.107 0.670 0.243 0.155 0.602

(Fi.Ft.Ft) 0.650 0.311 0.039 0.553 0.320 0.126

(F2.Ft.Ft) 0.262 0.718 0.019 0.311 0.680 0.010

(F1.F4.Fs) 0.272 0.369 0.359 0.320 0.282 0.398

(Fi.F⁴,F^b) 0.282 0.330 0.388 0.282 0.359 0.359

(F1.F4.Fj) 0.117 0.155 0.728 0.136 0.175 0.689

(F3.F4.Ft) 0.456 0.495 0.049 0.369 0.505 0.126

(F3.F5.F6) 0.214 0.369 0.417 0.214 0.369 0.417

(Fi.Fs.F-,) 0.107 0.155 0.738 0.184 0.146 0.670

(F3.Fi. Ft) 0.417 0.534 0.049 0.369 0.524 0.107

(F„Fb,F7) 0.087 0.184 0.728 0.126 0.233 0.641

(F3.Ft.Ft) 0.369 0.563 0.068 0.408 0.456 0.136

(Fi.F7.Ft) 0.175 0.806 0.019 0.146 0.825 0.029

(F⁴.Fi,F⁶) 0.272 0.350 0.379 0.272 0.330 0.398

( f4, F5, f7) 0.146 0.136 0.718 0.136 0.155 0.709

(F4.Fi. Ft) 0.476 0.456 0.068 0.417 0.466 0.117

(F4.Ft.F-,) 0.107 0.155 0.738 0.136 0.214 0.650

(F4.Ft.Ft) 0.437 0.505 0.058 0.456 0.437 0.107

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A p p e n d i x (Continued) Face Triple

(a,b,c)

Upright Inverted

Face Triple

(a,b,c) a;bci b;ac c;ab a\bc b;ac c\ab

(FA,F7,FB) 0.146 0.825 0.029 0.243 0.728 0.029

( F5, F6, F7) 0.155 0.184 0.660 0.146 0.175 0.680 ( F⁵, F⁶, F⁸) 0.466 0.505 0.029 0.417 0.456 0.126 ( F5, F7, F8) 0.184 0.777 0.039 0.223 0.748 0.029 ( F⁶, F⁷, F⁸) 0.204 0.786 0.010 0.272 0.699 0.029

*Fn = face number n. ia;bc = face a is preferred over faces b and c, and so forth.

(Manuscript received July 1, 1993;

revision accepted for publication January 18, 1994.)