Conflict: a foundational mathematical approach
Gordon Burt
Open University, UK
Travel: a foundational, mathematical approach
If you kept travelling west from here where would
you get to?
1 The physical universe:
a foundational mathematical approach
2 The social universe:
a foundational mathematical approach
3 A proposal and an invitation:
3.1 Modelling Social Conflict:
a degree programme
3.2 An Introduction to the Modelling of Conflict:
the First Level Course
3.3 Mathematical Political Science:
one of the Second Level Courses
4 Fundamental debates
5 The elusiveness of truth: Kierkegaard and Bohr
1 The physical universe:
a foundational mathematical approach …
… ‘a properly grounded theory’
BREAK 2
‘properly grounded theory’,
‘laws of nature’,
‘fundamental laws’,
‘underlying principles
that govern the behaviour of our universe’
What do these phrases mean to you?
2 The social universe:
a foundational mathematical approach
modelling social conflict
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applied mathematical social science
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mathematical social science
applied social scienc
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mathematical science;
social science; social practic
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mathematics
science
society practice
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theory
evidence
reality
a moral concern about conflict
Mathematical social science exists!
Mathematical Social Sciences
Journal of Mathematical Psychology
Journal of Mathematical Sociology
Journal of Theoretical Politics
[economics journals]
[regional science journals]
Artificial Intelligence
Journal of Conflict Resolution
Conflict Management and Peace Science
BREAK 3
a substantial academic literature exists
on mathematical social science
and on modelling social conflict.
Is this a literature you are familiar with? Yes / No
What are your thoughts
about mathematical social science?
Is it a literature you approve of? Yes / No
3 A proposal and an invitation:
3.1 Modelling Social Conflict:
a degree programme
3.2 An Introduction to the Modelling of Conflict:
the First Level Course
3.3 Mathematical Political Science:
one of the Second Level Courses
A proposed programme in Modelling Social Conflict
1 Reflections on social issues & mathematical modelling
2 Social design, social welfare and social choice
3 Experience, language, logic and artificial intelligence*
4 Mathematical psychology*
5 Mathematical sociology*
6 Mathematical political science*
7 Mathematical economics*
8 International relations and conflict resolution*
9 Theory, evidence and practice
Seminars and online resources at:
http://iet-staff.open.ac.uk/g.j.burt/MSConline.htm
Review
Travel: a foundational, mathematical approach
Nicholson: rigorously developed international theory
The physical world:
properly grounded theory … underlying principles
The social world: foundational, mathematical approach
Conceptual pyramid:
applied mathematical social science, modelling conflict
Journals: a substantial literature on social modelling
Modelling social conflict: a degree programme
Modelling social conflict: the ten main topics
Modelling social conflict: ten main snapshots
Unit 1 Reflections on conflict and on modelling
‘My sister Mollie and I fell out
And what do you think it was about?
She liked coffee and I liked tea That was the reason we couldn’t agree.’
Unit 3
Experience, language, logic, artificial intelligence
One possible world
L: My heart leaps up.
R: I behold a rainbow in the sky.
True (1)
True (1)
Unit 4 Mathematical psychology
Signal detection theory
The telephone rings and we hear it. [‘hit’]
The telephone rings but we do not hear it. [‘miss’]
The telephone is not ringing
and we do not think it is ringing. [‘all quiet’]
We think the telephone is ringing but go through
and find it is not ringing. [‘false alarm’]
Unit 5 Mathematical sociology
Individuals and situations …
Where you are in society affects who you are?
Who you are affects where you are in society?
closest friend in shop
closest friend outside shop
total
handmen linotypers total
64 (60%) 71 (49%) 135
42
73
115
106
144
250
the workplace affects the friendship?
the friendship affects the workplace?
is the effect due to individuals or to situations?
Unit 6 Mathematical political science
A proposal: build a path
Social rule: majority wins
You support the proposal.
(1) The proposal wins by two votes to one
your vote had power.
success is due to power.
(2) The proposal wins by three votes to zero.
your vote did not matter
success is not due to power (luck).
(3) The proposal is defeated: failure.
Unit 7 Mathematical economics
A macro-dynamic equation for price
(Lux and Marchesi, 1999)
dp/dt = b[mx^ + n(x^^-p)]
p
t
b
m
n
x^^
x^
price
time
speed of adjustment
proportion of naive traders
proportion of sophisticated traders
mean opinion amongst the sophisticated traders
index, mean optimism/pessimism, naive traders
dp/dt = b[mx^ + n(x^^-p)]
= b’[ wi xi - p]
Unit 8 International relations and conflict resolution
increase in defences = menaces
[1]
increase in own defences = other country’s defences [2]
increase in X defences = Y defences
[3]
increase in Y defences = X defences
[4]
A proposed programme in Modelling Social Conflict
1 Reflections on social issues & mathematical modelling
2 Social design, social welfare and social choice
3 Experience, language, logic and artificial intelligence*
4 Mathematical psychology*
5 Mathematical sociology*
6 Mathematical political science*
7 Mathematical economics*
8 International relations and conflict resolution*
9 Theory, evidence and practice
Seminars and online resources at:
http://iet-staff.open.ac.uk/g.j.burt/MSConline.htm
Review
Travel: a foundational, mathematical approach
Nicholson: rigorously developed international theory
The physical world:
properly grounded theory … underlying principles
The social world: foundational, mathematical approach
Conceptual pyramid:
applied mathematical social science, modelling conflict
Journals: a substantial literature on social modelling
Modelling social conflict: a degree programme
Modelling social conflict: the ten main topics
Modelling social conflict: ten main snapshots
Mathematical Political Science:
one of the proposed Second Level Courses
Please can someone lend me 20,000 Kroner?
Should Denmark have as many votes as the UK?
Does Iraq have WMD?
Is there are a ‘theory of everything’ for the social
universe?
Should Denmark have as many votes as the UK?
a political process within EU
what rules govern the political process?
how did the rules come about?
are the rules good rules?
what criteria are used to judge the rules?
maximise power versus maximise satisfaction?
success = power plus luck
Does Iraq have WMD?
What were your views just prior to the war with Iraq?
Iraq has weapons of mass destruction (WMD).
yes / no?
Military action should be taken against Iraq.
yes /no?
Military action should be taken against Iraq,
if and only if Iraq has WMD.
yes / no?
War? - a discursive dilemma
WMD
war
war iff WMD
Individual 1
Individual 2
Individual 3
true
false
false
true
true
false
true
false
true
Majority
false
no WMD
true
war
true
war
if and only if WMD
Source: Dietrich and List, 2007, p. 392, Table 1
Is there are a ‘theory of everything’ for the social
universe?
Figure 1 Behavioral and environmental assumptions
and model types
Action type
Optimal behav.
Rule-based behav.
Insulated
Decision theory Non-linear optimizn.
Interdependent Game theory
***
***learning models (including evolutionary game theory),
agent-based models and behavioural game theory
‘The approach of this book has its critics, opponents
and detractors.’
(Nicholson, 1992, p. 221)
six basic debates:
knowledge v. practice
theory v. evidence
science-based v. humanities-based
data modelling v. conceptual modelling
rational choice theory
problem-based mathematics v.
foundational mathematics
Your ideas, my ideas,
don’t quite capture the essence of the thing …
… the essence of faith
… the essence of morality
… the essence of reality
… the essence of truth
… the essence of selfhood
fundamental debates about the essence of the thing
‘Your ideas, my ideas, don’t quite capture
the essence of the thing.’
The six fundamental debates
not the slightest attempt … [at] a properly grounded theory
A foundational mathematical approach
‘The [modelling] approach … has its critics, opponents
and detractors.’
Does mathematical social science actually exist?
Is there are a ‘theory of everything’ for the social universe?
The Modelling Social Conflict course / online resource:
http://iet-staff.open.ac.uk/g.j.burt/MSConline.htm
Would your university run a degree programme
in Modelling Social Conflict?
a grand unified theory (GUT)
a theory of everything
different theories for different things
each thing is unique and needs its own unique theory
a foundational mathematical approach
mathematics underpins the understanding of reality;
simple ideas provide foundation for more complex idea
73 73/365 √2 π
2+3i 2+3i+5j+7k;
precisely defined concepts, precisely constructed
statements, logically constructed arguments;
mathematics provides a variety of alternative
mathematical models …
… which mathematical model does the physical
universe conform to?;
spacetime: Aristotle, Galileo, Newton, Einstein