
META Game Theory: A Holonomic Approach to Decision Making
Formulae
by Dallas F. Bell,
Jr.
Abstract: META game theory is the
Manifold Equation of Theological
Asymmetry. It combines the primary and secondary variables, factors,
and elements or subsets of systematic political science, theology,
epistemology, psychology, sociology, and eschatology. Within these
academic disciplines emerges a dynamic system. Through the singularity of
theological belief, the epistemological vector is created. That vector
produces the parametrics of decision making for individual behavior
and subsequent societal behavior based on the eschatological magnitude
set forth in the chosen theological singularity. This provides the
min max or area of the function where both individual and nationstate
decisionmaking behavior can be predicted stochastically. In this domain
behavioral arcs are plotted threedimensionally. The arcs combine to form
waves. The x axis records the time, and the y axis annotates behavior in
relation to compliance with or defection from the anchor of natural law.
The I and IV quadrants of the z plane registers the problemsolving
ability in reference to the ability to invent tools and use them to
manipulate the environment in the achievement of the common hierarchical
needs; survival, economic security, love and affection, status and
selfesteem, and selfactualization. The dynamic and stochastic
decisionmaking behavior formulae for individuals and nationstates
are presented. This holonomic approach should enhance the forecasting
abilities of decisionmaking analysts from all scientific fields.
1. Introduction
The holonomic approach to decisionmaking formulae must first include
an understanding of systematic political science—Manifold
Equation
of Theological Asymmetry (META) game theory. It basically projects
that a theological singularity must be chosen from either an infinite
God or not. If it is the latter, a finite god who complies with
some natural law or finite gods who comply with few natural laws
must then be chosen. These three options are used to synthesize
input from senses into the rationale for what is considered good
and evil. Those three epistemological vectors set the min max for
behavior in achieving the common individual needs. In ascending
order, the parametric needs are survival, economic security, love
and affection, status and selfesteem, and selfactualization.
The process of pursuing needs causes the formation of groups that
have similar need levels and the same theological singularity.
The corresponding individual need level creates a parametric societal
level of either a First, Second, or Third World political system.
Each system has an eschatological magnitude based on the original
chosen theological singularity.
Additionally, factors and variables exist that must be included in
this analysis. To prevent confusion in the meaning of terms, symbols
in equations unique to systematic political science are in red font.
The subject of natural laws has been introduced briefly. Natural laws
are the anchors of META game theory. Other game theory scenarios
may choose a correct outcome by accident since they are posed on how
players may react to each other without regard to an anchor formed
from cooperating with or defecting from a natural law through the
epistemological vector of a chosen theological singularity.
Finite beings are composed of atoms that compose the molecules of
deoxyribonucleic acid (DNA). Natural Law of this Physical dimension
(NLP) is the dynamic mechanism that provides the order for existence
concerning mass, energy, and velocity. All matter is subject
to those natural laws and the violation of which by individuals
produces inefficiency in achieving needs and hastens physical death
(e.g. gravity, heat, and cold). Law must have authority attested
to by negative sanctions for violations, a justice component, and
positive rewards for compliance, a benevolent or love component.
The second aspect of law is the Natural Laws of the Freewill (NLF).
This dimension provides the dynamic mechanism for decisionmaking
order and is equally real as and important as the NLP dimension.
Steven Pinker has pointed out that children are born with the ability
to recognize verbs and nouns. We also know that children recognize
truth at birth and only later reject it. If adequately modeled
parentally, a common behavior for a child is to avoid eye contact
and gulp when confronted with the truth that exposes their lie.
Thomas Aquinas observed that truth is selfevident and known to all.
It is axiomatic that
two plus two equals four. This can be demonstrated by holding up two
fingers on the right hand and two
fingers on the left hand. A conscious effort must be strategically
made to deny that four digits are being held up and to choose an untrue
sum that is other than four. The stress resulting from the cognitive
dissonance of being confronted with a lie will be physical manifested.
William Blackstone and John Locke believed that good comes from
God's laws and bad from rejecting those laws. That view is opposed
to John Stuart Mill's belief that whatever behavior makes one
happy is good. Thus, a child knows at birth by mean and extremes of
concepts like love and justice etc. that there must be an infinite
God of love whom they justly trust until they choose otherwise.
At a point in all childhood experiences, specific questions of purpose
arise that address past, present, and future realities. This is when
the authority/standard of the infinite God is consciously chosen or
rejected by freewill for a belief in a finite god or gods, resulting
in loss of efficacy in achieving needs and hastens physical death.
The epistemological vector from that chosen faith becomes the
substance of things hoped for and will calibrate the behavioral
boundaries for achieving individual needs unless a conversion is
made to another theology.
All NLF natural laws for finite beings with freewill fall into two
core categories. First are those that direct behavior regarding the
infinite or holy God: one, there should not be any other gods; two,
do not make images of those gods; three, do not take God's name
in vain; four, keep His day holy. The second category includes the
last six laws that direct behavior toward others, which are necessary
for a societal Q1 trust quotient. Law number five is for children to
honor parents; six, not to take innocent human life; seven, not to be
unfaithful to your spouse; eight, not to take the property of others;
nine, not to lie; ten, not to desire the possessions of others.
Those are negatively stated with the acknowledgment that their
truth is foreknown by all humans. This is to say, for example,
that we know from birth to be truthful and the laws only reinforce
compliance with what we know is efficient.
It has been said that if the infinite God of grace upon whose
shoulders the government rests is chosen, He will be loved and
the neighbor will be treated as one would like to be treated.
This highest or allencompassing law indicates compliance with or
rejection of the other laws. Those laws provide the basic anchors
for plotting decisionmaking behavior. Technically, if a violation
of such laws is thought, brain activity occurs, and behavior has taken
place. But mapping can take place only if the thought is acted upon.
Conversely, a thought to conform to a law does not mean that behavior
will be compliant. Then neither is it possible for finite humans
to comply with all natural laws in thought or deed. If a thought
is entertained long enough, it will be acted on. When any law is
violated, the min of infinite or righteous perfection is exceeded,
and all law is technically violated. Obviously, then, all finite
beings fall below this infinite threshold, but the plots here are
concerned with compliance or violations as they are seen to occur.
2. Individual DecisionMaking Formulae
2.1 Dynamic (Macro) Equation
Solve for the sum of individual behavioral possibilities.
The y axis, I and IV quadrants, equal the plots from either 1, a subset
of 2, a subset of 3, a subset of , 4, a subset of 5, of the parametric B,
behavioral levels, achieved from a B1, B2, or B3 behavioral track, which
equals to or is less than the corresponding epistemological rationality of
R1, R2, or R3 vector of NLP, known natural laws of the physical dimension
and NLF plus the subsets of known natural laws of the freewill dimension.
The R1, R2, and R3 vectors are a subset of the corresponding theological
singularities of belief of T1, min 0 max 1 lim to infinite compliance NL,
natural laws, or T2, min 1 max 0, or T3, min 2 lim to physical death
from noncompliance with natural law using FA, fuzzy analysis. The T1,
T2, and T3 course is verified with LSA (latent semantic analysis) of the
T belief and its subset of eschatological magnitudes of the corresponding
E1, E2, and E3 beliefs.
And
The x axis equals min 0, which is the birth year and max of 140 years
or time of death that plot
time gradients in years or generations where a generation is 20 years.
And
The z, I and IV quadrants, equal the usually static plot of I,
intelligence of lo, lower problemsolving ability min 0 max 95,
av, average problemsolving ability, min 96 max 139, and gi, gifted
problemsolving ability min 140 max less than 300.
And
Then the xy plots are joined to the plot on the z plane. Those plots
are joined to other xy and z plots by interpolation.
Therefore, the area of the function is extended to indicate the sum of
possible changes in behavior considering the gravitational pull toward the
T track of the societal majority, P1, and specifically known STI (stimuli)
and the need levels achieved and to be achieved by O, probability of
occurrence; O1, 90% to absolute certainty, O2, 75% to 89% certainty,
and O3 50% to 74% certainty. The min max of the x axis is extended by
past time patterns considering the corresponding S category or average
tolerance to moderate persistent stress; S1, 15 to 30 years for T1, S2,
7 1/2 to 15 years for T2, and S3, 3 1/2 to 7 1/2 years for T3. The min max
of the y axis is extended by past compliance with or rejection of NL,
all known natural laws. The z plot usually remains unchanged.
Given that all factors and variables of SPS, systematic political science
and DS, deception strategies have also been considered, the xy and z
predictive plots conclude the dynamic formula input.
Thus, the dynamic individual decisionmaking equation of META game theory
is completed.
2.2 Stochastic (Micro) Equation
Solve for the sum of individual behavioral probabilities.
The y axis shifts the same dynamic plots from the I and IV quadrants to
the respective II and III quadrants, which form the H, history. The I
and IV quadrants now plot the specific compliance or noncompliance with
NL, all known natural laws.
And
The x axis shifts the same dynamic plots from the I and IV quadrants
to the II and III quadrants of a min 0 of the date of the last need
level achieved and a max of the birth date in negative years and less
than 140 years. The I and IV quadrants now plot time in days, weeks,
or months with a min 0 and max of the date the next B need level is
achieved.
And
The z plane's axis plotted from the dynamic I data usually remains
unchanged.
And
Then each xy plot is joined parallel to the plot on the z plane by
interpolation.
Therefore, the new plots in the I and IV quadrants of the xy plane create
a Barc, behavioral arc. The min max of that Barc and the min max of the
II and III quadrants form the area of the function to be extended to
indicate where the sum of probable behavior change is likely to occur
in relation to compliance with or rejection of NL, known natural laws
expressed in the affirmative as either a Barc1, O1 of T1 arc momentum;
Barc2, O1 of T2 arc momentum; or Barc3, O1 of T3 arc momentum, given
that the same information and analysis techniques used in the dynamic
model have been considered.
Thus, the stochastic individual decisionmaking equation of META game
theory is completed.
3. NationState DecisionMaking Formulae
3.1 Dynamic (Macro) Equation
Solve for the sum of nationstate behavioral possibilities.
The y axis, I and IV quadrants, equal the plots from either 1,
an element of 2, an element of 3, an element of 4, an element of 5,
of the parametric W, behavioral levels, which are derived from the
polarization of individuals with the same T1, T2, or T3 singularity
of beliefs, corresponding R1, R2, or R3 vectors of rationality, in
achieving the same B1, B2, or B3 parametric track of 1, 2, 3, 4, or 5
levels of individual behavior. They form either a P1, 51% or more, P2,
more than 24% and less than 49%, or P3, more than 2% and less than 24%,
group with a T1, min 0 max 1 lim to infinite utopic compliance with known
NL, natural laws, or T2, min 1 max 0, or T3, min 2 max 1 lin societal
collapse from noncompliance with natural law and can be categorized using
FA, fuzzy analysis. Each of those demographics influence the four societal
institutions of Fa, family, Ch, church, Bu, business, and Go, government
to form and support a corresponding 1W, First World, 2W, Second World,
or 3W, Third World political system. They can be identified with tools
such as polling using LSA, latent semantic analysis of the T belief
and its subset of eschatological magnitudes of corresponding E1, E2,
and E3 beliefs.
The 1W1 has a P1 of T1, a P2 of T2 and a P3 of T3; the 1W2 has a P1 of
T1, P2 of T2 and a P3 of T3, with Q1 trust all are equal under the law,
C1, and free, F1, to pursue their needs productively at 75% to 100%
average capacity, A1; the 1W3 experiences a min max shift to a P1 of
T2, a P2 of T1, and a P3 of T3 , and now don't trust Q2, two tiers
of legal classes C2, and average productive capacity of 50% to 74%, A2;
the 1W4 min max shifts to a P1 of T2, P1 of T2, and a P3 of T1 , and F2
with a O1 of M2, projection of power; the last level 1W5 shifts the min
max to a P1 of T3, a P2 of T2, and a P3 of T1, now with three tiers of
legal classes C3, fear Q3, slavery F3, and average productive capacity
of less than 50%, A3 ending the cycle with a ST, societal transition,
either of STr, rational transition to another 1W system by STrr,
reformation of the L2, or higher level of crisis/change affecting 50%
to 74% of the population, to a T1 belief; or a Strw transition to a 1W
system by victory in a war for independence over T2 and T3 opposition.
The second transition option of STir, irrational transition leads to a
2W or 3W system by either STird, dominated by another society with T2 or
T3 beliefs; or STirr, revolution resulting in military victories over
other T beliefs; or STirc, catastrophic crisis from famine, disease,
war, etc., leading to the extinction of societal structures and mass
migration to other societies.
The 2W1 has a P1 of T2, a P2 of T3, and a P3 of T1, with two tiers of
legal classes, C2, the elite
ruling class has F1 freedom to pursue needs with Q1 confidence but the
worker class is F2,
Q3, and A2. The 2W2 has a min max shift of the P1 to a T3, the P2 to T2,
and P3 is T1, now is C3, Q3, F3, and A3. The 2W3, 2W4, and 2W5 levels
are not collectively achievable because of
noncompliance with natural laws—lim. The ST options are the same as
for a 1W system.
The 3W1 has a P1 of T3, a P2 of T2, and a P3 of T1., with three tiers
of legal classes, the elite has F1 freedom to pursue needs with Q2
confidence but the worker class is F2, Q3, and A3 and the slave class
is F3, Q3, and A3. Noncompliance with natural law prevents a 3W2, 3W3,
3W4, or a 3W5 level being collectively achieved—lim. The ST options
are the same as for the 1W system.
And
The x axis of 1W, 2W, and 3W systems equal min 0 max end of the cycle
plots of time in years or generations.
And
The z plane's I and IV quadrants plot by hundred thousands, ten
millions, or billions the I, intelligence min max of lo, av, and gi
demographics of either I1, 85% to 90 % av, 5% to 7% gi, 5% to 7% lo;
or I2, less than 85% av, more than 7 1/2 % gi, less than 5% lo; or I3,
less than 85% av, less than 5% gi, more than 7 1/2 % lo.
And
Then the xy plots are joined to the plot on the z plane. They are joined
to other xy and z plots by interpolation.
Therefore, the area of the function is extended to indicate the sum of
possible O1, O2, or O3 changes in behavior considering the gravitational
pull of geographical neighboring nationstates, G2, with the same T track
or, G3, with a different T track; the supply of natural resources, N1,
requiring 10% or less on imports, N2, requiring 11% to 30% on imports
or, N3, requiring more than 30% on imports; and specific STI, stimuli.
The min max of the x axis is extended by past time patterns considering
the corresponding S category of S1, S2, or S3. The min max of the y axis
is extended by past compliance with or rejection of NL, natural laws,
and the corresponding level of 1W, 2W, or 3W system template of P1, P2,
and P3 based T demographics. The z plane is also projected with special
interest to the L factor involving immigration and migration.
Given that all factors and variables of SPS and DS deception strategies
have been considered, the predictive xy and z plots conclude the dynamic
formula input.
Thus, the dynamic nationstate decisionmaking equation of META game
theory is completed.
3.2 Stochastic (Micro) Equation
Solve for the sum of micro nationstate behavioral probabilities.
The y axis shifts the dynamic plots from the I and IV quadrants to
the respective II and III quadrants that form the H, history, and may
include more than one cycle. The I and IV quadrants now plot the specific
compliance or noncompliance with NL between societal levels.
And
The x axis shifts the same dynamic plots from the I and IV quadrants to
the II and III quadrants
with a min 0 of the date the last level was achieved and a max when
the cycle(s) began in negative years or generations and less than
1,000 years. The I and IV quadrants now plot time in
days, weeks, or months with a min 0 and a max of the date the next W
level is achieved.
And
The z plane plots in quadrants I and IV the same I data as in the
dynamic model.
And
Then each xy is joined parallel to the plot on the z plane by
interpolation.
Therefore, the new plots of the I and IV quadrants on the xy plane
create a Warc, behavioral arc. The min max of that Warc and the min
max of the II and III quadrants form the area of the function to be
extended to indicate the sum of probable behavior change is likely to
occur in relation to compliance with or rejection of NL, natural laws
expressed in the affirmative as either a Warc1, O1 of T1 arc momentum;
Warc2, O1 of T2 arc momentum; or Warc3, O1 of T3 arc momentum, given
that the same information and analysis techniques used in the dynamic
model have been considered.
Thus, the stochastic nationstate decisionmaking equation of META game
theory is completed.
4.Conclusion
The dynamic and stochastic formula template of both the individual and
nationstate decisionmaking models reflect a topographical equation
with asymmetrical theology—META game theory. A global formula is
constructed in the same manner as the nationstate template where
as all P1, P2 and P3 groups combine worldwide from each 1W, 2W, and
3W system to create a global 1W, 2W, or 3W world dynamic model and
stochastic model expressed in the affirmative as either a global arc,
GLarc1, O1 of T1 arc
momentum; GLarc2, O1 of T2 arc momentum; or GLarc3, O1 of T3 arc momentum.
Forecasting accuracy at all levels lies in the skill of the analyst
to use these tools in applying data.
Obviously, only the infinite God has the infinite data necessary to
predict behavior perfectly. It is not the
nature of those with free will to be epistemological nihilists, so
man is likely to continue to study decision making for prudence sake.
Hopefully, the holonomic approach presented will be of assistance to
this worthwhile strategy.
References
Aquinas, S. T. Treatise on Law (Summa Theological Questions).
Washington, D. C.:
Regnery Publishing, Inc., 1990.
Bell, Dallas F., Jr., Anthropological Mapping in Socionatural
Systems—META Game Theory. 2005.
Bell, Dallas F., Jr., How Theology Dictates Political Systems.
Presented at the conference hosted by Mid
America Baptist Theological Seminary in Memphis, TN, 2002.
Bell, Dallas F., Jr., The Primary and Secondary Precursors to Mathematical
Formulations in Dynamic
Games. Presented at the New 2004 Economic Windows conference hosted
by the Department of
Economics and Statistics at the University of Salerno, IT, 2004.
Mill, J. S. On Liberty and Utilitarianism. New York: Bantam Books,
1993.
Pinker, Steven. The Language Instinct: How the Mind Creates Language.
William Morrow. 1994.
ALL RIGHTS RESERVED (2005) Dallas F. Bell, Jr.

