Rational Reconstruction ofJustice Reasoning modelled by an Overlapping-Waves-Model

Rational reconstructions of justice reasoning modelled by an Overlapping-Waves-Model
Kohlberg’s stages of moral development in their final form perhaps died with Kohlberg (Schrader, 2015). They held sway longer, but in the end, followed the earlier fall of the Piagetian Stages.
However, the often presumed empirical inadequacy should not be the final verdict. Stage should have been construed as rational reconstructions, but seldom were. Moreover, empirical predictions following from the theory were unrealistic to begin with. This relates to the fact that sophisticated analysis techniques and appropriate models were seldom applied due to lack of such techniques and models.
Kohlberg’s notions of stage and progress have been criticized on many grounds, the most ironic ground being that these ideas are old fashioned (sort of old stage) and we should move to more modern approaches (initially that was relativism, nowadays this would perhaps be intuitionism).
My claim is that if we understand moral development as a form of rational reconstruction (and acknowledge that we -as a field- should still work on how this is operationalized best), a hierarchy of progressive stages makes much sense. Moreover, I have a new model for this kind of development making it possible to connect them again to empirical research results.
A Latent Developmental Dimension
Moral development can be construed as movement along a Latent Developmental Dimension (LDD) and moral competence characterizes the position of an individual along this LDD. This individual trajectory can be mapped to a measurement scale that consists of discrete markers because we need some manner to track the progress or the lack of progress. These markers are the stages of development. The more developed one is, the more stages are passed through and the higher the stage reached will be.
Regarding moral development, reaching a higher age, or the passing of more time (collecting more experience), does not guarantee development. This implies that large individual differences can be found. Hence, age and time are not perfectly related to the LDD: the correlation is generally modest to low.
Nevertheless, moral competence development presupposes very general learning processes in the individual. Learning is taken here not in the sense of being a result of direct instruction, but in the broader sense of making sense of one’s experiences in life.
Therefore, we must assume dynamic processes at work here. These are processes that build on the previous states to change themselves, thus self-referential, but also based on exchanges with the environment, and characterized by temporary stable equilibria. Such developmentally relevant learning may lead to increasingly higher-order organization of thought.
Stages as Markers
As long as stages are seen as the static markers along this developmental scale, and not as property of actual individuals, they are a very helpful construct.
Stages, in this sense, are static descriptions of a qualitative kind. Each stage itself can be characterized as a set of ideas and strategies (manners of thinking) that forms a structured whole. This structure is relatively closed. Several such stages together may constitute a pattern of stages. The relationships between stages within this stage pattern can be described in a way that is often referred to as logical and sometimes even hierarchical.
To unpack this idea of a hierarchical sequence requires an analysis that uses the idea of a Rational Reconstruction in terms of Habermas, the idea of Reflective Abstraction in terms of Piaget, or Dialectics in the sense of Hegel. I am also indebted to the model of hierarchical complexity by Michael Commons.
On the one hand the stages are believed to be (hierarchically) related, on the other hand, the stages are known to be (qualitative) different. The idea that stages are qualitative different is a consequence of the idea that each stage is a reorganized version of the previous stage, but beyond simple recognition. The core ideas of the next stage can’t be expressed in terms of the ideas that characterize the previous stage. This irreducibility is an almost defining characteristic of stage in the Piagetian stage notion.
We also know that we can approach and see the world in many ways, that is, we humans have a rich variety of cognitive resources to deal with the world. These cognitive resources, though very diverse, are not unrelated to each other; they are building blocks in complex structures. If we want to classify these cognitive resources,
It makes sense to look for different levels of complexity in them with an inherent hierarchical order.
For moral development this requires an optimal point of departure, in normative sense, to describe by looking back, how the transition from the previous stage to the present one can be seen as a learning process (Habermas, 1981). This cannot be done in prospect, other than by making the actual transition yourself, and you do not know, in the moment, whether you actually succeeded. So in looking back and reflecting on earlier held believes and perspective, we might come to the conclusion that these views were not so much wrong in an empirical factual sense, but wrong in the sense of inadequate, incomplete, one-sided, not-generalizable, etc. And should be replaced by a view broader, more inclusive, acceptable to more participants, more generally applicable. For the lower stages it is not so difficult to see what that implies: Selman’s social perspectives: theory from so long ago, illustrate nicely: from egocentric to dyadic to group level considerations constitutes such a sequence.
Reflecting abstraction can perhaps be interpreted also as looking for the (implicit) reasons for success of actions from the previous stage (Piaget, 1974/1978, 2004/2006). This interpretation is consistent with Piaget’s suggestion that finding reasons means fitting the facts into a structural framework where necessary relations are (or could be) distinguished from actual and possible relations, which in turn implies a balance between the affirmations and negations involved. In trying to find the reasons behind success, there is a refocusing on the activity itself (or the relevant operations, etc.). Both processes, that of purely endogenous constructions made by the epistemic subject and that of compensation for disturbances from outside, are integrated by Piaget into his equilibration account. According to this theory, novelty and improvement are joint characteristics of development, neither of which is sufficient by itself to explain change; that is, the two processes when taken in isolation are not sufficient.
Briefly: we want to find a common core in the learning processes of a community of persons, in hindsight that is, in terms of the reflection steps underlying the transition in going to the next meta-level. Each new level is supposed to constitutes a meta-level compared to each previous level in an iterative fashion. Note that steps need not occur, or perhaps only taken by a minority, and we can mistakenly think we made such a step, while later on we have take it back, the more so when our own processes are involved.
We can only find and define levels in such a fashion if they have really have had the chance to develop in an actual community of persons. That is why I like to say that Development is a latent construct. This means we cannot see it directly, it is more than just change, it is more than just the concrete, it concerns more than just an individual, and it is more than just something determined by age. But it pertains to both form and time requiring a complex representation.
Integration
Fortunately, a sort of integrated model of development is possible. I considered two different designations of (moral)development:
1) Development seen as a sort of learning process of an individual as a self-organizing process.
2) Development seen as something defined by a rational reconstruction of the implied hierarchical complexity sequence.
Combining this idea of a self-organizing process with this idea of hierarchical complexity leads to conceiving a process with states that build on the previous to create something more general and abstract, and in that sense more advanced: Dynamic Categorical Development.
I am now going to sketch, very briefly, a model for such development. It will present, even more briefly, a three dimensional, rotatable, interactive visualization of the model at the end. This model can even be used as a statistical model to analyze real longitudinal data.
Let us assume that the inclination to use a certain stage X rises with progression along the developmental scale, reaches its height, and then decreases (when this stage is passed through). Focusing on stage-use and group comparisons makes it possible to compare the multitude of stages along one and the same dimension. But at the same time in the model cultural, contextual, and individual differences and influences can be easily accommodated.
This means that to model development properly we need both a time and a complexity level dimension in the model, without conflating them. The novel way to do this is to create a model with two separate dimensions underlying developmental change and one outcome dimension that represents the likelihood of responding. So we need a 3-dimensional representation.
Time refers to a process which implies changes for an entity. This is the chronological temporal dimension of development. Time can be measured from years to milliseconds between measurement points. But time elapsing does not imply or guarantee development: development takes time but the reverse need not hold.
Complexity level refers to logical hierarchical dimension and requires a measurement scale and is related to learning in a more abstract sense. It concerns change that leads to more encompassing structures which incorporate the lower structure as (modified) substructure in a new higher structure. Learning in the sense that leads to generalizations. We can only define this dimension by its markers (= the stages). But we can still presume an underlying continuous dimension. At least it can be a methodological trick, at best it is represents something like attractor-states in a dynamic growth process.
Use refers to the likelihood of responding in accordance with one of the complexity levels. This can be illustrated with the Overlapping Waves model introduced by Siegler (1996) as a metaphor to illustrate the typical pattern of a sequence of increasing and decreasing use of strategies during development in many cognitive tasks (see Figure 1).
With a three-dimensional version of the Overlapping Waves model both uses can be combined.

Figure 1. 3D-Overlapping Waves Model

In Figure 1 the X-axis refers to individual differences, the Z-axis to time (measurement occasions = eight weeks in this microgenetic example), and the Y-axis refers to probability of using one of five (example) strategies.

Figure 2. Trajectories (thin grey lines) and snapshot of Response Functions for one participant (heavy black lines)

In Figure 2 estimated (idealized) individual trajectories of development in strategy maturity are shown on the floor plane for a small sample. For one individual, as illustration, the implied category boundaries are also depicted in the Z-plane.


Figure 3. 3D-Overlapping Waves Model for one participant

The more growth, in Figure 3, the more the set of curves for a particular individual turns away from an orientation parallel to the week axis, and the more curvature will result. No growth would result in straight lines for each of the 5 strategies. But also a different starting point (different intercept in the growth model part) can lead to completely different curvatures: imagine the set of curves shifted along the difficulty dimension.
This model solves many problems associated with the old Piagetian stage model.
- Each individual can move through this 3-dimensional space in any way we like: so individual differences can be accommodated in this way. But still beginning point, speed, acceleration, etc. can easily be modeled.
- In actual analysis it is often desirable to assume only linear trajectories as a handy simplification. But this is necessary.
- Deviations from the assumed linear (or more complex) trajectory are allowed, as the model is probabilistic. If the likelihood of using stage 2 (for example) is .50 it is still also possible to use another stage.
- Still, on the group level a clear pattern may emerge
- Stage mixture is possible but now with likelihoods attached to them, and mixture is more likely between stages closer to each other.
- Still the surface representing the stages and their separation remains as characterization of the developmental pattern.