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 programme3.2 An Introduction to the Modelling of Conflict:

the First Level Course3.3 Mathematical Political Science:

one of the Second Level Courses

4 Fundamental debates5 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|

applied mathematical social science| |

mathematical social science applied social science

| | | |mathematical science; social science; social

practice| | | | | |

mathematics science society practice| | | |

theory evidence reality

a moral concern about conflict

Mathematical social science exists!

Mathematical Social Sciences

Journal of Mathematical PsychologyJournal of Mathematical SociologyJournal 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 modelling2 Social design, social welfare and social choice3 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 approachNicholson: rigorously developed international theory

The physical world: properly grounded theory … underlying principlesThe social world: foundational, mathematical approach

Conceptual pyramid: applied mathematical social science, modelling conflictJournals: a substantial literature on social modelling

Modelling social conflict: a degree programmeModelling social conflict: the ten main topicsModelling 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 2 Social design, social welfare and social choice. The mean function and three individual functions

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40 50 60

% of assignments being f or mative

mean

lef t peak

middle peak

right peak

Unit 3 Experience, language, logic, artificial intelligence

One possible world

L: My heart leaps up. True (1)R: I behold a rainbow in the sky. 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?

handmen linotypers totalclosest friend in shop 64 (60%) 71 (49%) 135closest friend outside shop 42 73 115total 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 winsYou support the proposal.

(1) The proposal wins by two votes to oneyour vote had power. success is due to power.

(2) The proposal wins by three votes to zero. your vote did not mattersuccess 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 price t timeb speed of adjustment m proportion of naive traders n proportion of sophisticated tradersx^^ mean opinion amongst the sophisticated tradersx^ 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 modelling2 Social design, social welfare and social choice3 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 approachNicholson: rigorously developed international theory

The physical world: properly grounded theory … underlying principlesThe social world: foundational, mathematical approach

Conceptual pyramid: applied mathematical social science, modelling conflictJournals: a substantial literature on social modelling

Modelling social conflict: a degree programmeModelling social conflict: the ten main topicsModelling 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 true true trueIndividual 2 false true falseIndividual 3 false false true

Majority false true trueno WMD war 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 theorySource: Page, 2008, p. 115

‘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.htmWould 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 ideas:

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