Informational Techniques Decision-MakingConcordia

Dr. Niculae V. MIHAITA, Cybernetics, Statistics and EconomicInformatics Department,

University of Economics at the Academy of Economic Studies inBucharest, ROMANIA

PhD Candidate, Pericle NEGESCU, Academy of Economic Studies inBucharest ROMANIA

And CEO at the Romanian Company of Radio (Societatea Romana deRadiodifuziune);

E-mail: Niculae.Mihaita@csie.ase.ro; niculae_mihaita@yahoo.com E-mail: pericle.negescu@gmail.com

Abstract

The purpose of this paper is to illustrate some simple algebraicand informational statistics techniques helpingConcordia/consensus between CEOs in probabilistic situationemerging from the process of Decision-Making. The first part isshaped as a more personal or colloquial approach using the Second-Order Cybernetic concept of Observer INSIDE the black/grey BOX ofthe process he studied. The component shows that the uncertaintiescreated by the mystery of the decision-making depend by the doubtscreated by those chosen to decide and no-one else. It illustrateshow combination of simple quantitative methods reveals hiddenscenarios and deals with true and false money assignments. It iswritten like a play, and like a mathematical riddle. Utility forthis approach is made for better understanding of what is next tocome in the second part of the paper. The paper content also hasresults and comments of an original algorithm of factorialexperiments and Informational Statistics combination, adding moreinformation to find Concordia.

Keywords: Neg-entropy, Statistics of Onicescu, Second-order Cybernetics, Semiotics

Introduction

Identifying the different interpretations or gaps, and filling them with bridges of knowledge, seems as the best approach to raise consciousness and offer specialists a way of stepping out oftheir paradigms or black/grey boxes. It allows them to talk about more familiar subjects, as like information technology versus artificial intelligence, and/or the notions of Concepts, Terms andParadigms as used in this Project.

The Inverse Matrix Advices and Second-Order CyberneticApproach

I am an econometrician and in cybernetic terms I am an Observer,Experimenter and Interpreter using feedbefore, feedforward andfeedback information for decision making. OBSERVER. I observe (feedbefore), around one of the Casino Royaletables several players at a last hand before the fifteen minutesof relaxation. Mainly two groups are of interest to me. The firstgroup was formed by three of my friends, excellent cards players,and the trio named as ABC. In this moment, two from their group inwhich I am interested, A, B and C are cashless. At this table oneis permitted to borrow money from a friend and he can also giveyou some advices during the game.Sometimes, even my friends asked for small amounts of money toplay with other Casino’ guests. Now, the Casino staff announcesfifteen minutes relaxation. In this playing moment A, B and C(remember that two of them are cashless) could select the playerand the adviser. Now, I am an Experimenter. I love my friends but hate to losemoney because I am a risk avoiding fellow. My friends are aroundme and ask for a sum of money they need to continue. I said thatmy limit for any of them is around $500,000.The first player is addressing me (feedforward): -see, we don’tknow what A, B and C decided to play and what adviser he takesbeside. Look here: If A is assisted by B, or B is helped by C, Ipromise to double your borrowed money; if A it is helped by C, Ireturn the money to you (positive feedback).The second player whispered: I return nothing (negative feedback)if A is helped by B (A&B) but I will double your money in anyother combination case.

The third friend put a big smile: if A&B, I shall multiply yourmoney by four and twice for A&C but nothing if B is helped by C(B&C).EXPERIMENTER. Knowing little about the game, players history asbehaviors’ tips but remembering (feedbefore) finance concepts myway of thinking is following: (1) compute the inverse payoffsMatrix and listen to columns add advices (2) compute the purevalues, values that pay one monetary unit (m.u.) in case of it isrealized the combination (state) for which it was created at theend of a determined period and zero if the combination is notrealized. The sum of pure values is less than 1 so the differencesare the gains.(Copeland, Weston, 1988).

Table 1. Players and combinative actions, given advices from theinverse MATRIX

Players

A&B A&C B&C Sum Inverse

Matrix 3 x 3 matrix

First 1 1/2 1 $0.5 mil 1 / 2 - 1 / 1 / 4Secon 0 1 1 $0.5 mil -1 1 1 / 2Third 2 1 0 $0.5 mil 1 0 - 1 / 2

Total $1.5 mil 1st 2nd 3rd

As I put in the vision earlier, my wish (feedforward) is to helpmy friends without losing money, no matter what combination ismade so I’ll pay all the unknown states (combinations) givingnearly the same amount of money to each of my friends.

You could see the sum in the table 1 above the same amount ofmoney for each. Now I compute the inverse Matrix and put theresults. Remember that you can have a Unit matrix (1 on maindiagonal and 0 in any other cell of it) by multiplying the matrixwith his Inverse. By summing on column is obtained (1, 1, 1).

INTERPRETER. In the above case, the last three columns of table 1,needs interpretations. If its happening the combination A&B,consider half of first friend promises, wipe half of the secondand pay money for a quarter of the third friend promises; if A&Cexists, sell the promises of the first, consider the second playerpromises and take into account half of the third. If B&C happens,

consider the promises of the first, ignore the second’s promisesand sell half of the third.

Not knowing the circumstances, the entropy is maximum for me (1/3chances for each combination), so I look again at these InverseMatrix advices: in relation to the first payer I must buy half,sell all and buy all; so I decide to buy a half (0.5 -1 + 1 =0.5). For the second player I also buy half such as (-0.5 + 1 + 0)= 0.5, and a quarter from third player promises’ (¼ + ½ - ½ = ¼).Table 2 shows some results.

Table 2. Players and cumulative actions following the advices fromthe inverse MATRIX

Cumuli

A&B A&C B&C Pure value

If A&B IF A&C If B&C

First 0.5 0.25 0.5 0.125 $1 mil $0.5 $1 milSecon 0 0.5 0.5 0.250 0 $1 mil $1mil Third 0.5 0.25 0 0.250 $2 mil $1 mil 0Total 1 1 1 0.625 $3 mil $2.5 $2 mil

The inverse Matrix multiplied with column vector of money Ihelped, gives the pure values. The risky combination was B&C but Imanage to retrieve my money entirely, on average $2.5 mil versus1.5 and that means 60% more for me.

In conformity with some portfolio theory, for 25 cents I could winone dollar if A&C or B&C happen but nil for other combination(see, in table 2, the pure value column). The most attractivecombination is A&B, when the win could be seven times more, andfor 12.5 cents payment is $10. The probabilities, as we know wereone third for each combination. By buying this portfolio, for 62.5cents, the revenue is $10 no matter the unknown states of thecombination.

I not remember telling you that all my friends are semioticiansand I see myself as cybernetician. They know everything aboutsigns: road signs, pub signs and star signs (‘visual signs’),drawings, paintings and photographs (the art), words, sounds and

‘body language’ (all these things have something). They said thateverybody ‘reads the signs’ only if they are aware of.

The recreation pause is finishing. Now, at work! We still don’tknow about ABC combination. O! Alas! I forgot to tell you that Iam still in play. Question 1: Who wins currently? Ha, ha! Possibleanswer: we did not know, the entropy is still higher!

O, again! Earlier I said to my friends that my limit for any ofthem it is around $500,000. Around, means around not three timesmore. Because I need all my friends to be satisfied, and still Iam not a rich man, I pay attention again to the Inverse Matrixadvices that suggests a Total (Table 3), proportioned with(.5, .5, and .25) breaking up my $500.000 into two hundredthousand dollars for player 1 and player 2 and one hundredthousand dollars. Same payoff or promises, but the rented moneyvector is (200000, 200000, and 100000).

Let see the experiment in table 3.

Table 3. Players and cumulative actions following the advices from the inverse MATRIXCumuli

1st 2nd 3rd Pure value

If A&B IF A&C If B&C

A&B ½ - 1/2 1/4 0.025 $0.4 $0.2 $0.4 milA&C -1 1 1/2 0.050 0 $0.4 $0.4 mil B&C 1 0 - 0.150 $0.4 $0.2 0Total ½ 1/2 1/4 0.225 $0.8 $.8 mil $0.8 mil

I invest $0.5 mil and receive $0.8 mil no mater of otherscombination. No bad at all, 60% more.The application with and important NOTE

NOTE.The NEXT three pages is based on an already paper accepted byIBIMA reviewers for the 18th IBIMA Conference held in Istanbul,Turkey, Informational Statistics in Cybernetics, Semiotics’Concepts in Management. First of all, the OBSERVER which is inside an decision-roomcollect all the data, signs and create a system of attitudes as

members speak, talk, converse, tell, chat, verbalize, articulate,have a word, address OR listen, pay attention, take note,eavesdrop, listen in, snoop. As an EXPERIMENTER, he launched aQuest for finding first (AB, AC, BC) and second orderrelationships (ABC) where A, B and C are three members indifferent departments around the council table with microphones’buttons pushed for speak/listen alternatives. As feedforwardinformation he made assumptions, supposition, statements,postulations, hypothesis, guesses, develop theories, imagine anafter or will be conjecture.

Described in the paper announced above he used experimentalstatistics plans as factorial experiments for 162 interventions,in frequencies and the codes used for simple or combinedinteractions.

The EXPERIMENTER knows that ALL systems have an internal model of themselves embodying their responses to environmental perturbationthat could be approximated by computed entropies.

Table 4. Percents Statistical instrumentation and conditionedentropies possibilities

Dept Dept. B, B1 B2 Grand ComputedC A Speak listen Total Row Entropies

Speak Speak 2 10 12 E(B /A1C1)=0.44 C1 Listen

A24 45 49 E(B /A2C1)=0.70

TOTAL Speak 6 55 61 E(B /C1) = 0.65Listen Speak 10 24 34 E(B /A1C2)=0.17 C2 Listen 47 20 67 E(B /A2C2)=0.16TOTAL Listen 57 44 101 E(B /C2) = 0.02Grand Total 63 99 No=162 E(B) = 0.05

E(B/A1C1)=IF(A1B1=0,"0",IF(A1B2=0,"0",((2)*((p(B1/A1C1)^2+p(B2/A1C1)^2)-1)))= = (2)*((2/12) ^2+ (20/12) ^)-1 = 0.44 or for the last line atTable 4: = 2*(63/162) ^2+ (99/162) ^2 -1 = 0.05 in conformity with theANNEX.

In above formula, the integer 2 is the value needed for comparableresults in the interval [0, 1] where MAXIMUM is equal to ONE forunequal percents greater than 95%/5% for two states and the zerofor 50%/50% probability. It is the reflection in mirror ofENTROPY.The Adjusted Informational Energy, Ea(X) for N number of statesand the values obtained in the interval [0, 1] come from [E(X) –Emin]/[Emax - Emin] where Emax is MAXIMUM ONE and Emin is equal to1/N.

What we are looking for? Consensus, harmony!. For example theEXPERIMENTER composes with the last results equations shown asthat in the paper named above, Informational Statistics inCybernetics, Semiotics’ Concepts in Management: : - transinformation as informational gain Δ, given by variable X

to variable Y, Δ(Y/X) = H (Y) – H (Y/X) = H (before) - H (after X action)

=E (Y/X) - E(X) = E (after X action)-E (before).Δ (B/A) + Δ (C/A) + interact (BC) = Δ (A/BC)

Δ (A/B) + Δ (C/B) + interact (AC) = Δ (B/AC)

Δ (B/C) + Δ (C/C) + interact (AB) = Δ (C/AB).

Any decision-making is looking for the knowledge received afterthe meeting from speaking/listening activities. The EXPERIMENTERassembles the given/receiving information (surprise, changes, andnovelties) as:

Table 5/a. Information and combinative actions on diagonal fromENTROPIES

Out/In

B&C A&C A&B In percents

Inverse

Matrix 3 x 3 matrix

A 9 2 2 5 0.114 - - 0.006B 2 25 17 5 - 0.077 - 0.054C 2 17 24 5 - - 0.081

Total 13 44 43 15 0.103 0.018 0.021

Main diagonal contains the informational gain obtained frominteraction of B&C over A, A&C over B and A&B over C. Lines in the

first 3x3 matrix shows how much informational gain is given by A,B and respectively C. Table 5/b. Pure values, given advices from the inverse MATRIX for

ConcordiaDept. Pure

v.invM % advice A B C

A 0.51 0.10 0.728 10.9 19.66 4.37 4.37B 0.08 0.01 0.127 1.9 0.76 9.52 6.47C 0.10 0.02 0.145 2.2 0.87 7.40 10.45

Total 0.70 0.14 1 15 21.29 21.29 21.29

The methodology is following the Casino example. For the firstcolumn in Table 5/b, pure securities (values) it is recommendedCopeland and Weston, pg.111. The advice of the inverse matrixexists in the second column, and it is the last vector of the 3x 3inverse matrixes as Total and here as its transpose. By amplifyingthe importance of A and by tempering B and C the Concordia isobtained.

Table 6/a. Information and combinative actions on diagonal fromINFOENERGIES

Out/In

B&C A&C A&B In percents

Inverse

Matrix 3 x 3 matrix

A 11 3 2 5 0.092 - 0B 2 30 20 5 - 0.062 - 0.042C 2 20 29 5 - - 0.063

Total 15 53 51 15 0.085 0.011 0.021

Table 6/b. Pure values, given advices from the inverse MATRIX forConcordia

Dept. Purev.

invM % advice A B C

A 0.41 0.08 0.727 10.9 24.00 6.545 4.364B 0.08 0.01 0.091 1.4 0.545 8.182 5.454C 0.08 0.02 0.182 2.7 1.091 10.909 15.818

Total 0.58 0.11 1 15 25.636 25.636 25.636

Approximately same results using computation shown in figure 1annexed where θ is the E (before) and I the conditionedinformation. The difference is coded Δ, the informational gain.

Table 7/a. Information and combinative actions on diagonal fromINFOCHANEL

Out/In

B&C A&C A&B In percents

Inverse

Matrix 3 x 3 matrix

A 36.1 10.6 9 5 0.032 - 0.003B 34.5 85.8 80.5 5 - 0.096 - 0.091C 25.8 76.8 82.7 5 0.015 - 0.095

Total 96.4 173. 172.2 15 0.020 0.002 0.007

Table 7 shows results obtained by using the informational channelcapacity illustrated from lines no.46 up to 53 in the synopticfigure 1 and explained as quantity of subtle information received.The better is the conditioning the bigger the channel capacity oftransmitting information.

Table 7/b. Pure values, given advices from the inverse MATRIX forConcordia

Dept. Purev.

invM % advice A B C

A 0.14 0.02 0.667 10.005 72.2 21.2 18.0B - 0.00 0.080 1.202 8.3 20.6 19.4C 0.11 0.00 0.253 3.793 19.6 58.3 62.7

Total 0.15 0.02 1 15 100.1 100.1 100.1

Column coded % in tables’ 5-7 b, could be obtained with matrixalgebra of minimum variance portfolio as shown in Copeland andWeston, pg.871. This constrained optimization problem can besolved by the method of the Lagrange multiplier.

But it is as much as necessary with the quantitative approach. What about qualitativeapproach of Concordia. Let’s imagine one pebble over a surface of water. If x is theheight where the pebble is and y is the mass of it, then when the pebble touch the watera resonance of circles happens over the surface of the water. If the pebble is thrown overthe surface of a lake with still water, a number of x (x1, x2,..xn), a vector of heights and ofy let’s say speed (y1, y2…yn) creates circles when the pebble touches the surface of thelake in a different resonance and interaction.

The dog near you barked. Maybe it hears the sounds made by the hits over water, andsome others from the environment spoiling the harmony. The person throwing thepebble is the experimenter, observer and interpreter. The dog near him is another

observer and interpreter of sounds, signs, changes in nature, well-disposed ordisagreeing with what it knows.Now, the heavy rain began. Millions of small pebbles of water hitting the water, sounds, thunders, lights. A live symphony begins and what harmony .Next time we use and observe following terms. Uncertainty, doubt, indecision, hesitation, vagueness, ambiguity, insecurity, improbability, confidence (antonym)

Ambiguity, vagueness, uncertainty, haziness, doubt, indistinctness, certainty (antonym),

Assessment, Appraisal, evaluation, estimation, measurement, judgment, review, consideration, opinion

Assess, tax, charge, review, levy, evaluate, fine, judge, appraise

Attitude, approach, outlook, manner, stance, position, feelings, thoughts, mind-set

Wrought, shaped, bent, fashioned, twisted, formed, created, produced, wreak

Rough, (smooth), uneven, coarse, bumpy, irregular, jagged, violent, forceful

Negation, (reinforcement), cancellation, reversal, contradiction, denial, repudiation, exclusion, refusal

Yes, all right, okay, sure, why not?, no problem, of course, agreed, fair enough

Affirmation, confirmation, assertion, pronouncement, avowal, declaration, statement, announcement, verification

Retain, keep, keep hold of, hold on to, hold, hang on to, preserve, maintain, save

Convey, express, communicate, suggest, put across, put into words,get across, pass on, transmit Meaning, sense, connotation, denotation,import, gist, significance, importance, implication

Illusory, deceptive, false, illusive, misleading, not real, erroneous, real (antonym),

Hidden, concealed, out of sight, unseen, secreted, veiled, buried, unknown, secret, Spurious, false, bogus, fake, forged, counterfeit, imitation, specious, unauthentic,

Quest, mission, expedition, pursuit, search, hunt, seek, chase, pursue,

Chaos, disorder, confusion, bedlam, anarchy, pandemonium, commotion, disarray, turmoil,

Conclusion

The Purpose of this paper was to find at least one answer at thequestion: is Information Theory needed for decision making lookingfor consensus (agreement, accord, harmony, compromise, consent)?It is used a new approach by applying algebraic and PortofolioAnalysis, quantitative methods, cybernetics and semioticsparadigms and concepts. Among Shannon’s Entropy whom is added tothe suspicions created about this kind of approach conditioned bythose of Chaos Theory we imagined a new methodology based onOnicescu Informational Statistics looking for Concordia.

Organizational theory is in general unable to create any degree ofcoherence in the field due to the plurality of its unconnected andunrelated models (Suddaby et al., 2008; Scherer, 1998). This hasresulted in the search for alternative approaches. The problem is,to find new approaches, one has to move outside the traditionalfield, and other related fields operate with different andincommensurable paradigms (Burrell and Morgan, 1998).

Two promising areas are cybernetics (the study of control andcommunications) and semiotics (the study of signs and theirrelated processes and signification, especially within the contextof communication), and there is often a perceived connectionbetween them (Brier, 2008). In my own work, I have built on thecommonality that exists between cybernetics and semiotics, throughprocesses of communication. Such a synergistic approach is notcommon.

The reason is that the distinct paradigms that operate within thedifferent fields are by their very nature incommensurable, and onehas to create a new paradigm from elementary propositions thatencapsulate the desirable elements that are extracted from thecollective of paradigms. This is not always seen as an appropriateway forward to the traditional holders of those paradigms, whichtend to be constrained by the boundaries that they create for

themselves, and therefore are blind to alternative perspectivesunless they are couched in their own specific terms of reference.

The task in this project is to figure out how to communicate theirtruth through case studies.  If we have the possibility to engagewith groups long enough, they will teach us what ideas theyrespond to.  By engaging with several specialists in parallel, weshall encounter some successes and some failures.  We need to usea variety of ways of describing what we are doing. A combinationof academic and practitioner voices would probably be mostpersuasive.

For example a partial solution given by Brier Soren (2008) aboutInformation-Semiotics paradigm: „The information paradigm is based on anobjective, quantitative information concept and works with algorithmic models ofperception, cognition, and communication. Semiotics, in contrast, is based in humanlanguage’s meaningful communication and is phenomenological as well as dependenton a theory of meaning.”

The contribution of cybernetics to management and semiotics atmarketing cannot be neglected because the language of marketingmanagement as the most books of the well known Philip Kotler isjust filled with the concepts and terms taken from semiotics andcybernetics. Small arches for cultural bridges: Noise: anythingfrom the environment that does not exceed the everyday level ofclamor and do not alert any single or multiple sensationrequesting recognition. Reflexive as term: refers to the presenceof a relationship between an entity and itself. One can, writesKauffman be aware of one's thoughts. (2010) Sign: anything thatcan be recognized, calls, signals, shapes, drawings, human beings as“signs for ourselves”.

Reasons for building a new series of forums.: Articles and papersawarded recently and illustrated in the attached bibliographyuphold even quantitative methods taken from Corporate Policy byCopeland and Weston just focused on Art (Theatre of the Absurd,Poetry, Paintings) or management through cybernetics/systemsthinking as entities and systems.

It is well known that with the exception of technology sector,human affairs are still mostly has the pattern of Aristotelian-Newtonian-Darwinian paradigm no matter we are thinking ofacademics, professionals or organizations. The knowledge bridgesbetween them are difficult to be build teach us academicians andscientists. Some of them said that trying to get cybernetic papersinto personality or psychology journals or AMR is impossibility.

On the other hand, Second Order Cybernetics and the Semiotics ofC.S.Pierce have a lot in common. The problem is of course thatholders of those paradigms are constrained by the boundaries thatthey create for themselves, and are blind to alternativeperspectives unless they are couched in their own specific terms.

ANNEX. Concepts, terms and paradigms used in this paperCybernetics: “Cybernetique = the art of growing”- A.M. Ampere; “Thescience of control and communication in the animal and themachine”- Norbert Wiener; “The science of effective organization”-Stafford Beer “The art and science of manipulating defensiblemetaphors”- Gordon Pask; “A way of thinking” - Ernst von Glasersfeld;“Should one name one central concept, a first principle, of

cybernetics, it would be circularity”- Heinz von Foerster “The scienceand art of understanding” - Humberto Maturana

Feedback: a regulator process used by an experimenter who needs tobe able to match, interacting in a positive or negative way, withthe number of Object’s states of that which it seeks to control insuch a way that variety absorbs variety attending a planned goalmentioned by feedforward information.Feedbefore: gathering data, information, sign, signals, evensources of knowledge from the External Reality, in a quest forobserving Objects characteristics and/or actionsFeedforward: "a wish", expected desires, statistical hypothesis,expressed as fuzzy or qualitative goal, a bet in a wayantenarrative of Boje is.

Informational energy E(X): when r is the number of states i inwhich X could be, then p (xi) is the probability of X in differentstates and basically is a statistical average measuringconcentration or the order in organization

(1)

Gini’s coefficient or Onicescu’s adjusted Informational energy:

Ea(X) = (r*E(X)-1)/(r – 1). (2) If the values of E(X) exists between [1/r, 1], Ea(X) exists in [0,1].Claude E. Shannon’s entropy:

(3)

measuring uncertainties or disorder in organization; a measure of

the average information content.

References

[1] Boje, David (1991). The storytelling organization: A studyof storytelling performance in an office supply firm.Administrative Science Quarterly, 36: 106-126.[2] Brier Soren, CyberSemiotics, Why Information is Not Enough. P99 .B752008, P115 .B575 2008 The Blackwell guide to research methodsin bilingualism and multilingualism.[3] Copeland, E., Thomas, Weston, J., Fred, Financial Theory andCorporate Policy, page 113, Third Edition, Addison-WesleyPublishing Co., 1988, ISBN 0-201-10648-5. [4] Guiasu, Radu Cornel, Guiasu, Silviu (2010), Diversity Measuresand Coarse-graining in Data Analysis with an Application Involving Plant Species onthe Galapágos Islands, Journal of Systemics, Cybernetics andInformatics, Volume 8-Number 5-Year 2010. ISSN: 1690-4524. [5] Kauffman, Louis H. & Brier, Soren (Ed.) (2010), Peirce andSpencer-Brown: History and Synergies in Cybersemiotics. ImprintAcademic (6.2007) 1 84540 105 0[6] Scherer, A. G., 1998 ‘Pluralism and incommensurability instrategic management and organization theory: A problem insearch of a solution’. Organization, 5: 147-168.[7] Suddaby, R., C., Hardy, Q.N., Huy, 2008 ‘TheoryDevelopment: Where are the New Theories of Organization’ TheAcademy of Management Review, 33(2) 569 – 570Tabbi, Joseph (2002).Cognitive Fictions. University of Minnesota Press. ISBN 0-8166-3557-9 — draws on systems theory and cognitive science to introduceautopoiesis to literary studies.[8]Umpleby, Stuart (2010) http://www.gwu.edu/~umpleby/recent_papers/2010%20JWAS%20Corona%20Thomas.pdf