Bell-Conflict

CONFLICT IN GRIDS

The notion that people have inconsistencies in their thinking is neither new nor confined to personal construct theory. Daniel Kahneman was awarded the Nobel Prize for Economics in 2002 for his psychological research showing that people were not rational decision makers. Interestingly Kahneman’s PhD (see Kahneman, 1963) was based on the semantic differential, a technique producing data not wholly dissimilar to that of the repertory grid technique. The personal construct theory of George Kelly (1955/91) allowed for such inconsistencies in construing through the Fragmentation Corollary.

Subsequently constructivists have been interested in construct systems where there are inconsistencies (Honess, 1982), contradictions (Krauthauser, Bassler, and Potratz, 1994), or conflict (Slade and Sheehan, 1979) among the components of the construct system. While these terms have been used interchangeably [we could also consider it as ambiguity in construing], ‘conflict’ has been the most widely used term, and will be used here. There have been two distinct approaches to the measurement of conflict in repertory grid data.

In the first and better known approach Slade and Sheehan (1979) adapted Lauterbach’s use of Heider’s (1946) balance theory where three concepts are assigned positive or negative valances, and balanced triads of concepts have either a pattern of all positive valences or a pattern of one positive and two negative valences (Lauterbach, 1975). Slade and Sheehan proposed using triads of the signs of correlations among three constructs in a similar fashion. Winter (1983) however found the percentage of imbalance triads of constructs to be highly correlated with measures of cognitive complexity.

One issue arising from this measure is the level of correlation at which a triad is designated as ‘balanced’ or ‘imbalanced’. If all correlations are used, whatever their size, then correlations of 0.01 and -0.02 and -0.03 will be said to be balanced. But those correlations most would agree are very likely to be not significantly different from zero, and should therefore not be taken into account as suggesting any relationship. Bassler, Krauthauser, and Hoffman (1992) have suggested a modification to the procedure which would take account of the size of the correlations. In a subsequent empirical evaluation of 140 grids from psychiatric patients, Krauthauser, Bassler, and Potratz (1994) found that large numbers of imbalanced triads were rare, and that the presence of imbalanced triads was affected by the number of constructs (more constructs led to more imbalanced triads) and the number of elements (fewer elements led to more imbalanced triads). Monolithic construing was also associated with more imbalanced triads.

Another measure of conflict or ambivalence that could be used with specific kinds of grids in which figures were seen as both elements and constructs was suggested by Fransella and Crisp (1971)

A NEW APPROACH TO CONFLICT / INCONSISTENCY

The present approach combines aspects of both these approaches; assessing triads for balance, but forming triads from both elements and constructs. The genesis of this idea lies in Lauterbach’s original example. (I like parties, I don’t like depression, but alas I associate parties with depression).These concepts can be interpreted as one element (‘I’) and two constructs, going to parties or not and depressing or not.

Here we adopt the position that Conflict/Inconsistency/Contradictions will exist in a grid where either of the following two conditions hold:
1. An element is at the same time similar or close to two constructs which are themselves different or distant.
2. An element is similar or close to one construct’s pole and at the same time is different to or distant from another construct’s pole, where the two construct poles are similar or close.

This can be operationalised in the following way.
1. Define relationships between constructs and elements, and among constructs, as distances.
2. Let the rating of an element on a construct be the distance between that element and the construct. The rating will designate one pole as the basis of the distance, it is immaterial which pole it is, since reversing the construct ratings will change all three distances and the relationship among them is preserved.
3. Let the distance between constructs be determined by the average distance determined from all other elements.
4. We then define the presence of conflict as the presence of a ‘triangular inequality’. That is, in any three distances defined on three points (one element and two constructs) the longest distance must not exceed the sum of the two smaller distances (in such a case the distances cannot form a triangle). Consider the eight elements rated on three constructs in Table 1 below.

Table 1. Illustrative Grid Data

	A	B	C	D	E	F	G	X
warm	3	4	4	7	6	7	4	1	cold
kind	3	5	4	7	7	6	2	6	cruel
harsh	5	3	1	1	1	2	7	1	gentle
7	< Ratings >								1

Element X is both cold and kind and cold and gentle. The distances between the constructs are shown in Table 2.

Table 2. Construct Euclidean Distances

kind vs cruel	5.7
harsh vs gentle	10.4	12.4
	warm vs cold	kind vs cruel

The sum of the distances from X to warm vs cold and kind vs cruel is 1 + 6 = 7, but the distance from warm vs cold to kind vs cruel is only 5.7. The triangular inequality is not satisfied and there is conflict. Also the sum of the distances from X to warm vs cold and harsh vs gentle is 1 + 1 = 2, but the distance from warm vs cold to harsh vs gentle is 10.4. Again the triangular inequality is not satisfied and there is conflict.

1. This simple example is a relatively easy one in which to detect such conflict. However the number of possible conflict situations in a grid is NE * NC * (NC – 1) / 2, where NE is the number of elements and NC is the number of constructs. Thus in this tiny example there are 8 by 3 by 2 divided by 2 equals 24 possible conflict situations. In an ordinary grid, say 10 by 10 there would be 450.

2. We then define overall conflict as the ratio of observed conflict situations to possible conflict situations. The overall conflict may be partitioned to identify proportions of conflict attributable to each element and each construct.

3. Variation in conflict within a grid may also be important. Since it seems likely that there will be a certain degree of error or random conflict in any grid, we could assume that such conflict will be distributed randomly across elements and randomly across constructs. A null hypothesis for these distributions of conflict across elements and constructs is that it they are uniform distributions. If we make such as assumption we can use departures from such a distribution to indicate the presence of systematic rather than error conflict. We could find the average conflict per element by dividing the total conflict by the number of elements and compare this to the actual conflict attributable to each element. These could be combined by summing the ratio of squared discrepancies over the square expected (average) conflict to give a pseudo-chi-square measure. While this could not be tested for significance [1], it could be transformed into a standardized measure, Cramer’s V [2], whose values range from zero - no departure from the expected values, to a maximum of 1.0 which would enable conflict variation to be compared across grids.

There are a number of advantages to this approach. The procedure involves both elements and constructs and can be applied to any repertory grid data, and involves minimal departure from the actual grid data. Element – Construct distances are taken directly from the grid, while the estimation of the between construct grid retains the grid data properties. Unlike correlation approaches there is no data standardization, and as with distances, conflict is invariant over construct pole reversal. The outcome can be interpreted at grid, element, construct, and element by construct level.

AN EXAMPLE

As an example we consider a grid published by Leach, Freshwater, Aldridge, and Sunderland (2001). This was a grid completed prior to therapy with a victim of child sexual abuse. It had fourteen constructs and nine elements, giving a total of 819 potential element-construct conflict situations. In 340 of these situations (42%) conflict was observed. The distribution of conflict by construct and element is shown in Table 3.

Table 3. Percentage of 340 Conflict Instances by Construct and Element

Construct	%	Element	%
assertive vs not assertive	8.1	Child Self	10.9
confident vs unconfident	7.6	Self Now	7.9
does not feel guilty vs feels guilty	9.1	Women in General	1.8
abusive vs not abusive	7.4	Men in General	8.2
frightening vs not frightening	6.5	Father	16.5
untrustworthy vs trustworthy	6.8	Partner	10.3
powerful vs powerless	6.2	Ideal Self	14.7
big headed vs not big headed	6.0	Mother	10.6
independent vs dependent	6.0	Abuser in Childhood	19.1
confusing vs not confusing	6.9
guilty vs not guilty	6.2
cold vs shows feelings	6.0
masculine vs feminine	7.5
interested in sex vs not interested in sex	9.6
	100.0		100.0

Index of Conflict Variation	.109		.309

The index here termed an index of conflict variation is the Cramer’s V coefficient referred to earlier. In can be seen in this grid the variation in conflict across elements is nearly three times as great as across elements. The abuser in childhood figure has the highest level of conflict. Conflict involving any element can be further examined to see which constructs most often are involved in conflict situations with the element and the other constructs. Table 4 shows how the conflict for this figure was distributed across constructs.

Table 4. Distribution of conflict across constructs for Abuser figure

Percentage Conflict	Construct
6.9	assertive vs not assertive
7.7	confident vs unconfident
7.7	does not feel guilty vs feels guilty
6.9	abusive vs not abusive
6.9	frightening vs not frightening
6.9	untrustworthy vs trustworthy
5.4	powerful vs powerless
5.4	big headed vs not big headed
6.2	independent vs dependent
5.4	confusing vs not confusing
6.2	guilty vs not guilty
10.0	cold vs shows feelings
8.5	masculine vs feminine
10.0	interested in sex vs not interested

It can be seen that the conflict for this figure occurs primarily with respect to the constructs cold vs shows feelings and interested in sex vs not interested. Although it was shown earlier that the number of potential conflict situations in a grid is large, when we have identified a particular element involved in more conflict than others, we can examine directly the discrepancies between this element and all pairs of constructs. Table 5 shows these data. There are 91 possible conflict situations and there is no conflict (discrepancy of zero) in 28 (31%) of these situations. In some situations the conflict is minimal (for example the conflict between big headed vs not and independent vs dependent is only 0.1). We can see the conflict is most evident for this figure between constructs cold vs shows feelings and both big headed vs not (3.6) and masculine vs feminine (4.1).