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packages, graphing and visualisation. The whole construction process results in
categories of description that may not have been used for describing the pre-
computational model. This is the so-called idea of emergence, when interactions
among model components specified through pre-computational models at some
level of description give rise to different categories of model descriptions identified
in the executable model at macro levels of observation, expressed through post-
computational models.
As an example consider the culture dissemination model of Axelrod (1997b)
which has a goal of analysing the phenomena of social influence. At a micro-
level of description, a pre-computational model defines: (a) the concept of actors
distributed on a grid; (b) the concept of culture of each actor, specified as a set of five
features; and (c) the interaction mechanisms specified with a bit-flipping schema, in
which the probability of interaction between two actors is set proportionately to the
similarity between two cultures. The executable model is then explored and other
categories of descriptions resulting from the interaction of individual cultures may
be defined. These are associated with macro properties of interest and conditions in
which they form, such as the concepts of regions and zones on the grid. A great deal
of the simulation proposed by Axelrod concerns investigating properties of regions
and zones in the executable model, giving rise to a proposed conceptual, post-
computational model, which expresses traits such as the relation between the size of
a region formed and the number of features per individual culture. These concepts
are interpreted in relation to the target social phenomena of social influence.
We will now situate the role of V&V in the modelling process of social
simulation.

9.2.1 What Does It Mean to Verify a Computational Model?

Computational model verification is defined as checking the adequacy among
conceptual models and computational models (see also Chap. 7 in this volume,
Galán et al. 2017). Consider the lower quadrants of Fig. 9.1. They are concerned
with ensuring that the pre-computational model has been implemented adequately
as an executable computational model, according to the researcher’s intentions in the
parameter range considered, and also that the post-computational model adequately
2
represents the executable model in the parameter range considered. In short, the
three models must correspond to each other adequately, relative to the same target
they are meant to represent.
At this point you might question the meaning of adequately. A minimal definition
could be the following: adequateness means that the inputs, outputs and the
mechanisms post-computationally modelled from the executable computational
model are consistent with the ones specified through the pre-computational models,

2 Verification in the left quadrant of Fig. 9.1 is sometimes known as “internal validation.”