An Application of Monte Carlo Method to Computer Simulation of Decision

Making Processes in Society

- Theoretical Foundation of the Method -- Theoretical Foundation of the Method -

Satoru Ozawa and Sarkar Barbaq Quarmal Graduate School of Science and Engineering

Ibaraki University

Hitachi 316-8511, Japan

ozawa@mx.ibaraki.ac.jp

1) Unit 1: Explosion, roof blown off (12 March, 2011)2) Unit 2: Explosion (15 March), Contaminated water in underground trench, possible leak from suppression chamber3) Unit 3: Explosion, most of concrete building destroyed (14 March), Possible plutonium leak4) Unit 4: Fire (15 March), Water level in spent fuel pools partly restored5) Multiple trenches: probable source of contaminated water, partly underground, leaked stopped (6 April)

Fukushima NPP Accident 11March2011

Before the accident (11March 2011) In Japan, 23% of electricity power supply depended on NPP.

The government was trying to increase the ratio up to 30% because of Global Warming Problem. This was supported by most of Japanese.

Just after the accident

All of the NPP have been shut down. The previous government decided Zero-NPP within 30years. This was not supported in the general election (16 Dec 2012).

Today Most of the NPP still being stopped. The new government

has not yet decided future energy plan. Question is “Do we depend on NPP for electric power supply?”.

We are not interesting in the conclusion of the problem, but how they conclude is our study. “Computer Simulation of Decision Making Processes in Society”

Elements of this work• Artificial society modeling to simulate decision making

dynamics in society• Knowledge function to characterize people’s knowledge• Simulation of thinking process based on linkage model

in cognitive psychology• Method to guess knowledge function• Monte Carlo computer simulation

An artificial society modeling describes processes of knowledge-based decision making in society on a given problem.

Note: Real society as a whole is too much complicated. We are going to model society regarding one given problem.

The problem is expressed in a form of a question, for example, “Do you accept NPP to produce electricity?”

Artificial Society

Agent

Knowledge

Character

Agent

Knowledge

Character

Agent

Knowledge

Character

Agent

Knowledge

Character

Agent

Knowledge

Character

Channels

Message

“Do you accept NPP to produce electricity?”

Artificial Society Model• ARTIFICIAL SOCIETY is made of a set of AGENTS.

• The AGENTS represent groups of similar character people in society regarding a given PROBLEM

• Each AGENT has a certain KNOWLEDGE regarding the PROBLEM.

• Each AGENT makes a DECISION of the PROBLEM based on the KNOWLEDGE.

• Each AGENT has an individual CHARACTER in DESION MAKING.

• There are CHANNELS between AGENTS.

• AGENTS produce MESSAGES and send them through the CHANNELS.

• AGENTS change their KNOWLEDGE as the results of MESSAGE exchanges.

Artificial Society

Agent

Knowledge

Character

Agent

Knowledge

Character

Agent

Knowledge

Character

Agent

Knowledge

Character

Agent

Knowledge

Character

Channels

Message

Looks like physical systems with interactions!

Definition of Knowledge Function

Parameter, xis called“preferential parameter”

Knowledge Function is not observable just like wave function in quantum mechanics

Quite natural to assume that such function exists and satisfactorily describes a state of brain regarding the given problem

Elemental processes of knowledge modification in artificial society model

Thinking Process (Decision Making) : Linkage Model of Cognitive Psychology

Which knowledge come up : nondeterministicIt depends also on state of mind (sad or happy) and personal character (optimistic or non-optimistic) : Emotional Factor

Question: Do you accept NPP?

Basic Assumption: Principle of equal a-priori probability (Each element of knowledge has equal probability of coming up into mind)

Which knowledge come up into mind is stochastic in nature (Neglect Emotional Factor: Rational Thinking)

Various types of thinking• Thoughtful rational thinking : Number of

elements of knowledge coming up into mind is large. Principle of equal a-priori probability is OK.

• Emotional thinking: Principle of equal a-priori probability does not work. (For example, negative idea more easily coming up in depressed state of mind). Weighing factor (Emotional factor) is needed.

• Panic thinking : Only few extreme knowledge coming up into mind.

We restrict ourselves for the rational thinking

Let us describe it in terms of mathematics : Algorithm

Algorithm (Step 0) : Selection of Channel

• Each channel has a band width.• One channel is randomly selected with taking into the channel

width, i.e., the channel width parameter

is the weighing parameter. This work is easily carried out by using random number generator.

• Thus, a channel from Ai to Aj is decided.

And, two agents are also decided in this step.

Algorithm (Step 1) : Decision making • Select N memories randomly with equal

probability from all the memories of agent, Ai. Then, we have a set of preferential parameters,

for .

• Calculate the mean value

and the mean square deviation,

• Produce a decision function, which is assumed to be a normalized Gaussian type, .

jix , Nj ...,1

N

jjiji x

Nxx

1,,

1

N

jjijiji xx

Nxx

1

2,

2,,

1

2

2)(

)( xx

i eAxD

Algorithm (Step 2) : Message making

• Multiply a psychological factor (authority factor),

to the decision function and add it to the knowledge function to produce a message function,

Here, the suffix i, j means the message transfer from Ai to Aj .

• Then, normalize .

jiC ,

)()()( ,, xMxDCxM iijiji

jiM ,

Algorithm (Step 3) : Knowledge Modification

• Multiply a psychological factor (authority factor, or reliability factor) to the message function and add it to the knowledge function to produce a new knowledge function,

• Then, normalize .

)()()( ,,_ xKxMCxK jjijiNewj

)(_ xK Newj

• Multiply an aging factor, to

Here, is an parameter of aging.

• Add it to the knowledge function to produce an aged knowledge function,

• Then, normalize, .

Algorithm (Step 4) : Aging of Received Knowledge

t

e

),(, txM ji

),(),(),( , txKtxMettxK jji

t

j

),( ttxK j

Let us Produce Knowledge FunctionsPreliminary Study (1) : One Agent Model - How the parameter relates to D(x) -K

2.0K 8.0K

How the parameter N relates to fluctuation of D(x)

10N

30N

2.0K 8.0K

Careless Thinking

Thoughtful Thinking

Sta

ndar

d de

viat

ion

of th

e fl

uctu

atio

n of

pea

k po

siti

on o

f D

(x)

K

N

Careless Thinking

Thoughtful Thinking

Preliminary Study (2) - How to guess knowledge function -

Question: Do you accept NPP?

Free description related to the question Examination by keyword analysis method knowledge function

Definition of Knowledge Function

Parameter, xis called“preferential parameter”

Examples of Computer Simulation

Question in the case of Bangladesh : Do you accept NPP to produce electricity?

Official namePeople’s Republic of Bangladesh

GovernmentUnitary parliamentary democracy

Gross national income per capita

$700

National Urban Rural

Population 150

million38

million112

million

Adult literacy 58% 68% 54%

Newspaper readers 40% 50% 36%

Mobile phone users 66% 94% 53%

The Internet users 3.7% 10%

1.6%

Bangladesh Society

ToFrom

GP GOV MM SNM

GP - - 1 2.5

GOV - - 1.5 -

MM 3 3 - 3

SNM 3.5 - 3.5 -

Number of messages sent by agents per year

ASM for Bangladesh Society

Knowledge Functions of Bangladeshi Agents determined by KAM: Initial Data

Examples of Computer Simulation

(A) at present (B) after 2 years

(C) after 4 years (D) after 6 years

20N

Time Variation of Center of Knowledge Function

20N1

0)( dxxfxxc

Ensemble Averaged Time Variation of Center of Knowledge Function

What would happen if SNM is 5 times stronger?

Summary (1)• Theoretical formulation of Artificial Society Modeling to study

decision making processes in society is explained. • This model enables to study time variation of knowledge function of

agents for a short period.• Computer simulations, taking an example of Bangladeshi society,

have been carried out under the conditions of thoughtful rational thinking ,

• Even if the thoughtful rational thinking, the results unexpectedly contain fluctuations and an ensemble average is needed to have meaningful results.

,1,1,20 ,, jiji CCN

Summary (2)

• This method can be applied any problem of decision making in any society (even on globe), if the needed data are obtainable.

• One problem is that the model does not include the God’s will. When and where disasters happen is only determined by the God.

Cf. Idea of Japanese people on NPP is dramatically changed after 11 March 2011

• For this reason, it is not recommended to use the model for the simulations of long time span.

Two kinds of Thinking

• Logical Thinking : Thinking in conscious part of brain

• Instinct Thinking : Thinking in non-conscious part of brain

“Knowledge coming into mind” should be understood as “Knowledge contributed to decision making both in Logical Thinking and Instinct Thinking”