An inbvited talk at the Workshop on Coherence -Based Approaches to Decision-Making, Cognition and Communication, Berlin July 2016 Human cognition can be usefully understood as a primarily social set of abilities - its survival benefit is from our ability to social organise and hence inhabit a variety of niches. From this point of view any ability makes more sense when put into a social context. This includes our innate ability to judge candidate beliefs in terms of their coherency with our existing beliefs and goals. However studying cognition in its social context implies high complexity, for this reason I describe an agent-based model of coherency based belief within a dynamic network of individuals. Here beliefs might be copied (or discarded) by an individual based upon the change in coherence it causes with its other beliefs, but also that an individual will change their social connections based upon the the coherence of their beliefs with those they socially interact with.

1. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Social and Cognitive Coherence
Bruce Edmonds
Centre for Policy Modelling
Manchester Metropolitan University

2. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
The Tethered Goat
People can ‘wander’ a little way from where they
start (in terms of their beliefs) but not very far!

3. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
The Road to Brexit (opinion polls) – a
collective shift in opinion
-15
-10
-5
0
5
10
15
20
25
24/09/2011 11/04/2012 28/10/2012 16/05/2013 02/12/2013 20/06/2014 06/01/2015 25/07/2015 10/02/2016 28/08/2016
Remain-Leave(%)
Date

4. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Lada Adamic's analysis of US political
bloggers of the 2004 presidential election

5. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Social Intelligence Hypothesis
• Kummer, H., Daston, L., Gigerenzer, G. and Silk, J. (1997)
• The crucial evolutionary advantages that human
intelligence gives are due to the social abilities it
allows
• Explains specific abilities such as imitation,
language, social norm instinct, lying, alliances,
gossip, politics etc.
• Social intelligence is not a result of general
intelligence, but at the core of human intelligence,
“general” intelligence is a side-effect of social
intelligence (in particular language and the ability
to learn and remember complex beliefs)

6. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
An Evolutionary Perspective
Social intelligence implies that:
• Groups of humans can develop their own
(sub)cultures of knowledge, technologies, norms
etc. (Boyd and Richerson 1985)
• These allow the group with their culture to inhabit
a variety of ecological niches (e.g. the Kalahari,
Polynesia) (Reader 1980)
• Thus humans, as a species, are able to survive
catastrophes that effect different niches in
different ways (specialisation)

7. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Implications of SIH
• That different complex “cultures” of knowledge,
skill, habit etc. are significant
• An important part of those cultures is how to
socially organise, behave, coordinate etc.
• That these will relate as a complete “package”
to a significant extent
• Human cognition is (at least partly) evolved to
make this group survival work
• Including the capacity of maintaining a
complex set of beliefs that are coherent with
others in the group, whilst retaining flexibility

8. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Social Embedding
• Granovetter (1985)
• Contrasts with the under- and over-socialised
models of behaviour
• That the particular patterns of social interactions
between individuals matter
• In other words, only looking at individual
behaviour or aggregate behaviour misses crucial
aspects
• To understand the behaviour of individuals one
has to understand the complex detail and
dynamics of the interactions between them
• Agent-based simulation does this, few other
formal techniques do

9. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Context of the Simulation Models
Presented Today
• Dissatisfied with representing beliefs at “opinions”
as a point on a continuous scale, since this
confuses a measured effect with an underlying
mechanism
• Wish for some link to the ‘logic’ of beliefs
• Wish to combine something of a cognitive model
with social process of influence
• This is quite abstract at the moment, much
simpler than my usual style of model!
• I am looking for suitable data to enable its
assessment and further development

10. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Explanatory Coherence
• Thagard (1989) etc.
• A network in which beliefs are nodes, with
different relationships (the arcs) of consonance
and dissonance between them
• Leading to a selection of a belief set with more
internal coherency (according to the dissonance
and consonance relations)
• Can be seen as an internal fitness function on the
belief set (but its very possible that individuals
have different functions)
• The idea of the presented model is to add a social
contagion and network change processes to this

11. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Opinions from Beliefs
• The idea is that a belief may be adopted by an
actor from another with whom they are connected,
if by doing so it increases the coherency of their
set of beliefs
• Thus the adoption process depends on the
current belief set of the receiving agent
• Belief revision here is done in a similar basis,
beliefs are dropped depending on whether this
increases internal coherence
• Opinions can be recovered in a number of ways,
e.g. a weighted sum of belief presence

12. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Model Basics
• Fixed network of nodes and arcs
• There are, n, different beliefs {A, B, ....} circulating
• Each node, i, has a (possibly empty) set of these
“beliefs” that it holds
• There is a fixed “coherency” function from
possible sets of beliefs to [-1, 1]
• Beliefs are randomly initialised at the start
• Beliefs are copied along links or dropped by
nodes according to the change in coherency that
these result in

13. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Coherency Function
• A generalisation of pairwise (in)coherence
• Gives a measure of the extent to which
different sets of beliefs are coherent
• Assumes a background of shared beliefs
• Thus {A}0.5 and {B}{0.7} but {A, B}-0.4
if beliefs A and B are mutually inconsistent
• Different coherency functions will be applicable
to different sets of ‘foreground’ candidate
beliefs and backgrounds of shared beliefs
• The probability of gaining a new belief from
another or dropping an existing belief in this
model is dependent on whether it increases or
decreases the coherency of the belief set

14. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Belief Change Processes
Each iteration the following occurs:
• Copying: each arc is selected; a belief at the
source randomly selected; then copied to
destination with a probability related to the change
in coherency it would cause
• Dropping: each node is selected; a random belief
is selected and then dropped with a probability
related to the change in coherency it would cause
• -11 change has probability of 1
• 1-1 change has probability of 0
• There are different ways of doing this mapping

15. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Illustration – Belief Change
A
B
C
A
B
Copying
C
C
Dropping
A

16. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Scaling of Impact of Coherence
• There are a variety of ways to map a change in
coherence to a probability (of the change)
0
1
1-1
0
1
1-1
difference in coherence
difference in coherence
probabilityprobability
A ‘weak’ mapping –
probably changes to
increase coherence
A ‘strong’ mapping –
almost certainly only
changes to increase
coherence

17. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Network Change Processes
Each iteration the following occurs for each agent:
• Link Drop: with a probability: if a belief copy was
rejected by the recipient, then drop that in-link.
• New Links: with another probability, create a new
random link with a random other (with a friend of a
friend if possible, otherwise any)
In order to maintain the average link density I added
the following ‘cludge’: If there are too many links (as
set by arcs-per-node) increase the rate of link drop,
if there are not enough, reduce the rate of link drop.

18. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Illustration – Network Change
A
B
C
A
B
Rejected Copy
Random New
Links

19. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
A Particular Example
• 20% of agents (stars) are such that the ‘yellow’ beliefs
are attractive and the ‘blue’ ones unattractive (due to
coherence with background beliefs), they are also
‘strong minded’ in the sense that they only change
their mind if it increases their coherence
• 80% of agents (circles) are such that the ‘blue’ beliefs
are attractive and the ‘yellow’ ones unattractive, they
are also ‘weak minded’ in the sense that they only
have a tendency to change their mind if it increases
their coherence (more probabilistic in their belief
change)
• Both change their links (or not) similarly and both are
agnostic with respect to the ‘red’ belief

20. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
The Run Variants
• 10 runs of each variant
Runs with
• no belief change and no link change
• with belief change only
• with link change only
• with both belief and link change
(there is some random chance of changing beliefs)
Output shown in terms of:
• Animations
• Average results over the 10 runs for each option

21. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Animations
• Atomic beliefs: yellow, red, blue
• Agents shown in colours
indicating the mixture of
beliefs held (or if none, grey)
• Links are relationships such
that the beliefs of one might
be adopted by the other
• Star nodes or triangle nodes
are minorities
• Circle nodes are of the
majority

22. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Average Opinion at End
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
"drop & add" "none" " bel ch & drop &
add"
"bel ch"
AverageOpinion

23. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
With and without changing links and
beliefs (average over 10 runs)
-0.1
0
0.1
0.2
0.3
0.4
0.5
1 101 201 301 401 501 601 701 801 901 1001
AverageOpinion
Time
Change links
Change nothing
Change beliefs and links
Change beliefs

24. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Proportion of same kinds linked together
0.5
0.6
0.7
0.8
0.9
1
"drop & add" "none" " bel ch & drop &
add"
"bel ch"

25. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Towards a ‘Brexit’ example
3 groups: floaters, yellows and blues
1. 70% Floaters, (circles) towards either yellow or
blue (but not both) beliefs, weak scaling function
2. 10% Yellows, (stars) are for yellow and against
blue with a strong scaling function
3. 20% Blues (triangles) are for blue and against
yellow, with a medium scaling function
Groups start separate (to allow for self-
reinforcement), with random beliefs, but then both
network and beliefs co-develop

26. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Distribution of Final Average Opinions
(1000 runs)
0
50
100
150
200
250 -1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
NumberofRuns
Final Average Opinion

27. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Example run 1
Yellow connects
with floaters first,
followed by the
blues, these
polarise the
floaters, which
then separate off
into two groups,
which then slowly
convert the
floaters to their
own colours
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 100 200 300 400 500 600 700 800 900 1000

28. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Example run 2
both integrate
and polarise
floaters, then a
period of islands
(blue more), then
some yellow
mutate in blue
island, which
then spreads
pulls apart, then
yellow integrates
into other and
converts more -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400 500 600 700 800 900 1000

29. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Example run 3
‘Westminster
bubble’ of blues
and yellows
separate from
floaters forms,
seperately
floaters flip each
other back and
forth but in a
random walk
which happens to
end with more
yellow -0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 100 200 300 400 500 600 700 800 900 1000

30. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Example run 4
Both connect
with floaters, but
blues more
intimately,
yellows always
on the peripheral,
yellow connects
again and again,
but does not ever
gain enough
influence to
convert many
floaters -0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 100 200 300 400 500 600 700 800 900 1000

31. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
(At least) two clusters of results
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.4 0.5 0.6 0.7 0.8 0.9 1
DiversityofLinkedBeliefs
Homogeneity of Types Linked
Same
kinds
linked but
with a
greater
variety of
beliefs
linked
Different kinds linked
within same group
with a lower variety of
beliefs

32. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
Suggested Issues/Hypotheses
There are ‘competing’ processes of:
• Social influence (suggestion) vs. internal coherence
with existing set of beliefs
• Social influence vs. social linking
– An ‘extreme’ group may be good at convincing another
group when connected but groups tend to disconnect from
those with very different views to themselves
How processes actually happen may matter a lot:
• e.g. what influences people’s change of links – do
people have a ‘whitelist’ of those they are willing to
allow to influence them?
This model does not touch upon the development of
people’s belief structures within their society

33. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
The Complexity of Socio-Cognitive
Coherence
• Much cognition (including belief coherence)
makes more sense in a social setting
• But also the possible social structures are
affected by our cognitive
abilities/limitations/biases
• To understand such phenomena one needs to
see how the cognitive, interactive and social
levels relate to each other
• Just looking at global statistics and hoping to
tease out what is happening will often be
insufficient
• Just looking at individuals outside their real,
messy social contexts will also be insufficient

34. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
A Plea For ‘FAT Data’
• Often we have different kinds of data originating
from different sets of events or people
– a time series about a certain series of events
– an experiment for a particular set of people in a
particular context
– some qualitative research observing people in another
particular situation
– ‘big data’ streams of records of position, urls etc.
• Rather I need lots of data at all levels with
consistent IDs over this data, e.g.: repeated
surveys, interviews, time-series data about the
same people and events!

35. Social and Cognitive Coherence, Bruce Edmonds, Coherence-Based Approaches to Decision Making, Cognition, and Communication, Berlin, July 2016.
The End
Bruce Edmonds: http://bruce.edmonds.name
Centre for Policy Modelling: http://cfpm.org
A version of these slides (without movies) is at:
http://slideshare.com/BruceEdmonds
The simulation is at:
http://openabm.org