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- 1. PANORAMA SOCIOECONÓMICO AÑO 24, N° 33, p. 66-74 (Julio - Diciembre 2006) INVESTIGACIÓN / RESEARCHMathematical Modelling of Human Motivation: A VectorHypothesisModelación matemática de la motivación humana: una hipótesis vectorialIvan Kotlíarov^^C.Sc. (in Econometrics), B.Sc. (in Human Resource Management), Saint-Petersburg University of Economics and Engineering, Russia.E-mail: lrpg@mail.ru ABSTRACT. The present article gives a list of axioms needed for building up a mathennatical theory of human motivation. A mathematical model of labour motivation is proposed. Motivation is represented as a resulting vector of partial motivation generated by specific groups of needs. Vrooms model is included in the proposed model as Instant motivation. Theoretical correlations between the quantity of funds dedicated to motivate employees and the intensity of motivation factors and between the level of motivation and the level of productivity are proposed. Key words: Motivation, vector, needs. RESUMEN. Este artículo presenta un conjunto de axiomas necesarios para construir una teoria matemática sobre la motivación humana. Se propone un modelo matemático de moti- vación del trabajo. La motivación es representada como un vector resultante de la motivación parcial generada por grupos específicos de necesidades. En el modelo propuesto se incluye el modelo de Vroom como motivación instantánea. Se proponen las correlaciones teóricas entre la cantidad de recursos dedicados para motivar a los empleados y la intensidad de los factores de motivación y entre el nivel de motivación y el nivel de productividad. Palabras clave: Motivación, vector, necesidades. (Recibido: 30 de agosto de 2006. Aceptado: 30 de octubre de 2006)66
- 2. Mathematical Modeiiing of Human iVIotivation: A Vector hypothesis Ivan Kotliarov INTRODUCTION all of them contain - either explicitly or, more often, implicitly - a set of basic rules (hereinafter referred toEffective control of an economical phenomenon as axioms; some of these axioms have beenrequires a mathematical model able to provide a formulated earlier, some should be reformulated fromreliable qualitative description of this phenomenon and implicit indications, some are given here for the firstto ensure quantitative forecasts of its characteristics. time - I will indicate it below for each axiom). It isOur understanding of the nature of human motivation logical to use these axioms as a basis for adid gradually improve over the years (we have now mathematical theory of work motivation (I omit themany more or less consistent theories giving adequate detailed overview of motivation theories in order todescriptions of motivation processes), but a good spare time; a good description from the managementsmathematical model of work motivation is not point of view can be found in [Mescon, Albert, Khedouriavailable. Actually the only example of mathematical 1992]; psychological overview is given in [Njin 2000]).approach towards this problem is Victor Vrooms These axioms are the following (it is worth mentioningmodel [Vroom 1995], but it is rather qualitative than that the complete set of axioms is given for the firstmathematical in the proper meaning of this word, as time; none of existing theories of human motivationit limits itself to only one formula: operates with this list, they just use - explicitly or implicitly - some of them): M = RBW where 1. Human beings have needs that they want to M - motivation; satisfy. Its a common place in most psychological R - employees expectations that his/her and marketing theories. efforts will lead to necessary results; 2. Human motivation (understood as a persons B - expectations that the results will lead to state that defines degree and orientation of activity the expected remuneration; of a person in a given situation) is determined by W - expected value of the remuneration. human needs. All content theories of human motivation include this stipulation as a basicAll other theories existing in this field: Maslows hypothesis, while process theories include ithierarchy of needs [Maslow 1970], Herzbergs two- implicitly (see above, for example, for Vroomsfactors theory [Herzberg, Mausner, Snyderman 1959], model: motivation depends on the value of theMcClelland model [McClelland 1961] - do not offer remuneration, but value of a good is a function ofany quantitative methods for modeling motivation, they its utility, that is, of its capacity to satisfy humanexplore the psychological aspect of motivation but do needs).not use mathematics at all. It is easy to conclude for the axioms 1 and 2 that the satisfied needs have no influence on humanIt is obvious that absence of mathematical tools in motivation. It is very important to remember thatthis field of human resources management is needs that are not actually satisfied, but whoseabsolutely unacceptable nowadays and I will try to fill satisfaction is perceived by a person asin this gap in the present paper. guaranteed (in other words, needs whose satisfaction is seen by a person as guaranteed to DEFINITIONS AND AXIOMS a such degree that he or she perceives them as satisfied, despite the fact that they actually areFirst of all, it is necessary to give a clear and precise not) do not have influence on human motivationdefinition of motivation. Motivation of a human being either. For example, in economically developedis a temporal and dynamic psychological state that countries (like EU), needs belonging to lowerdetermines his/her involvement in an action levels of Maslows pyramid generally have no[Motivation 7; Motivation 8]. Motivation is sometimes influence on human motivation [Mescon, Albert,referred to as process [Motivation 8] thus leading to Khedouri 1992] because of peoples confidenceconfusion between 2 aspects of this concept: in their present and future situation thanks tomotivation as the psychological state of a person who relatively high salaries, good social securityis doing something and motivation as a process of systems and powerful trade unions. However, anyencouraging a person to do something (the latter is of these low-level needs in any moment may bebetter referred to as motivating). Motivation will be actually unsatisfied.considered in this article as a state. 3. Human needs can be divided into separate moreA thorough analysis of motivation theories shows that or less homogenous groups, each one of these 67
- 3. PANORAMA SOCIOECONÓMICO AÑO 24, N° 33, p. 66-74 (Julio - Diciembre 2006) groups contributing to the general motivation The axiom 7 also means that each group of (generating a partial motivation). I will refer to needs can be satisfied by specific goods, these groups of needs as to motivation factors. typical for this group only. It means that goods An indication to this axiom first appeared in (material, non-material or abstract) that satisfy content theories with their divisions of needs; needs from a certain group of needs cannot however, to the best of my knowledge, neither satisfy needs from other groups (need in this axiom, nor the concept of partial motivation security cannot be satisfied by a hamburger, have not been proposed before. creative needs cannot be satisfied by purchase4. In general, the number of groups of needs of trousers). I would like to highlight that this is influencing a persons behaviour in the moment t true in general - in some specific cases goods is superior to 0. Mathematically it can be can satisfy different needs. An obvious example expressed as follows: if N is the number of is money that can be used for purchase of separate groups of needs, N>0, and if n is the virtually all goods for all types of needs. A number of groups of needs determining an "Rolls-Royce" is not simply a car (that satisfies individuals behaviour in the moment t, then. transport needs) - it can also satisfy ones needs in prestige and luxury. But in general 0<n<N different needs are satisfied by different goods. We can conclude thereof that different needs This axiom has not been formulated explicitly make people act differently in order to achieve before, however some hints can be found in the different goals (we can see a clear connection literature. between the axiom 6 and the axiom 7). Indirect The axiom 4 leads us to the conclusion that the indications to this axiom can be found in the general (total) motivation is equal to 0 in only one literature. case: when all partial motivations are equal to 0, 8. Contributions of all groups of needs (motivation or, in other words, if one or several (k, k<n) partial factors) into total motivation are described by the motivations are equal to 0, the total motivation same mathematical functions (I could have said will nevertheless be different from 0. Mathematical instead that the psychological mechanism of corollary to this conclusion is that we cannot correlation between a need and the motivation is calculate total motivation multiplying partial the same for all types of needs). We can draw motivations. this conclusion from the fact that no motivation5. Every group of needs can be described by two theories - either content or process - supposes characteristics - intensity and importance. a specificity of any group of needs, motivation Intensity is the quantity of goods required to satisfy mechanisms are described the same way for all this need. Importance is the priority of a certain groups of needs. This axiom is proposed here for group of needs over other groups. These the first time. characteristics can be expressed in quantitative 9. There are no universal constants describing from, and. Therefore, it is possible to build up a motivation, that is, we cannot calculate motivation quantitative theory of motivation. The concept of theoretically, not using empirical data. This importance dates back to Maslows hierarchy of statement is made here for the first time. needs and it is clear that the concept of need includes the concept of intensity; however, this All these principles should be respected in a theory of statement has not been made explicitly before. motivation. If we do not take into account any one of6. The general motivation directly depends on groups them, the theory will be over-simplistic or simply of needs (motivation factors) - that is, if the intensity incorrect. and/or the importance of a given group of needs is growing, the overall motivation will grow too. This MATHEMATICAL MODEL OF WORK axiom is proposed here for the first time. MOTIVATION7. Groups of needs are independent from each other, in other words, there is generally no correlation A practical model of motivation should: between changes of importance/intensity of Give a correct description of group of needs different groups of needs. This statement is (motivation factors) determining human implicitly made in content theories. It means that behaviour; the overall motivation of a person can be Explain (adequately enough) the mechanism of described by an additive function. correlation between motivation factors and human68
- 4. Mathematical Modelling of Human Motivation: A Vector hypothesis Ivan Kotliarov behaviour (that is, explain the formation of motivation are oriented in different directions). The fact motivation); that values of different groups of needs are marked Give a quantitative evaluation of human motivation; on different axes means that groups of needs are Provide a correlation between an employees independent from each other (axiom 7). Its worth motivation and an employees productivity. mentioning that radius vectors of partial motivation lie on positive parts of Cartesian axes, as from theFrom the mathematical point of view it is necessary economical point of view it is extremely difficult toto build up a model of motivation that should be as imagine a person having needs with negative intensitygeneral as possible, not limited by specific (however, the model does allow introducing suciicharacteristics of employees interviewed and that needs). The overall motivation is calculated as acould be easily adapted to a concrete situation. Thus, resulting vector of these partial motivations - or, inlet us suppose that human needs are divided into N other words, the overall motivation is itself a vectorgroups - but not specifying what criteria we use to described by a motivation vector. Lets introduce themake this division (it is obvious that according to our following symbols:goals and depending on the concrete situation needscan be divided in groups in different ways). m. - value of the i-th motivation factor (a scalar valué);The contradiction between the practical requirement M. - value of the motivation generated byto provide descriptions of groups of needs and of the i-th motivation factor. Its value is equal to m, but itmechanism of their influence on human motivation is a vector; and the mathematical decision not to specify number M -overall value of motivation (resultingof groups of needs and criteria used for subdivision motivation, is also a vector). Its absolute value is equal(this decision is due to the necessity to make our (in an N-dimension coordinate system):theory as general as possible) - this contradiction in ÍÑ reality does not exist. It can be easily solved thanks M = J 2 w.^ (1)to the following conclusions: a company may andshould divide needs into groups according to its goals(I will propose below my own scheme of possible The vector formula of the resulting motivation (thedivision), and, according to the axiom 8 above, the formula of the motivation vector) is:mechanism of influence of needs on human behaviouris the same, therefore, we can describe the M = 2 M. (2)mechanism for any group of needs using mathematicaltools and then we will simply apply this model to other The motivation vector in the chosen coordinate systemgroups of needs). is written as M (m,, m^,..., m^^).Representing motivation as a vector in the space Interestingly enough, this vector approach seems toof needs not respect the corollary to the axiom 4: indeed, it is quite easy to imagine a mathematical situation, whenIf we use a physical analogy, we can describe the all vectors of partial motivation are different from 0motivation as a force that incites people to act in a and are oriented in space the way the total motivationcertain way. Force is physics is a vector and therefore is brought to 0.has not only a quantitative measure but also adirection. We supposed above that a man acts under But this approach just takes into account the absoluteinfluence of N groups of needs. I will mark the absolute value of motivation factors (their intensity) - but notvalue (the intensity of motivation factors) of these their importance. In order to introduce their importanceneeds on axes of a Cartesian coordinate system x^x^x^^. into the model I will take correction coefficients varyingEach motivation factor will generate a partial from 0 to 1. The final formula for calculation of absolutemotivation - that is a radius vector of a point value of motivation (after introduction of correctioncorresponding to the intensity of a motivation factor. coefficients) is:This passage from scalar representation to vector onereflects the fact that different motivation factors make (3)people act in different ways (needs of a certain groupcannot be satisfied by goods satisfying needs from a^ - coefficients reflecting the importance ofother groups - corollary to axiom 7; vectors of partial a corresponding group of needs for an employee. 69
- 5. PANOFÎAMA SOCIOECONÓMICO AÑO 24, N° 33, p. 66-74 (Julio - Diciembre 2006)From the economical point of view the formula 3 is the formula 3). It reflects the fact that different needsmuch more precise in describing human motivation lead people to different actions (as reflected by(as it taies into account the axiom 4), but it does not divergence of vectors of partial motivation), while thecorrespond to the mathematical logic of presenting overall motivation is a compromise between differentmotivation as a vector in a Cartesian system of partiai motivations.coordinates. However, this seeming inconsistency canbe easily solved, as intensity of motivation factors can Group motivation and ideai motivation vectorbe marked on axes of a rectilinear- but not Cartesian- system of coordinates, that is (m,, m^, ..., m j . are Overall motivation of a group of peopie (grouprectilinear, but not Cartesian coordinates. The passage motivation) is equal to the vector sum of motivationsfrom rectilinear to Cartesian coordinates is made of all members of the group. A company is interestedaccording to the foiiowing formula: in having maximum individual and group motivation of its employees. The absolute value will be maximal X,.= m. cos (p., (4) if all individual motivation vectors lie on the same line. It is possibie to check if this condition is respected by X. - the i-th Cartesian coordinate; calculating the angle between these vectors. As their ni. - the i-th rectilinear coordinate; coordinates are known, the angle can be found 0i- angle between the corresponding axes through their scalar product.of the Cartesian and the rectiiinear systems ofcoordinates. I will below show this caiculation for 2 employees, butIt is absoluteiy obvious thereof that this method can be easiiy generaiized for n employees. q).. (5) M, M^ - motivation vectors of the first and the second a. = employee (their absolute values are M, M^The formula 4 takes into account only one projection respectively). Their coordinates in the N-dimensionof a rectiiinear axis - h o w e v e r , in order to be Cartesian motivation space are:mathematically correct, the formula should inciudeprojection on all N axes. But this fact does not ^X,^...,V) (6)contradict the logic of the model, as, supposing thatdifferent groups of needs are independent, we cannot It is important thatconnect one partiai vector with different axes. Thisphenomenon helps to understand the limits of this I I I (7)model and to propose ways for its deveiopment. ß - angie between motivation vectors:Therefore, ail multipiicators from the formula 3 have ^1 y 1 y 2a clear mathematical, economicai and psychoiogicai ß = a r c e o s /-i (8)meaning.This model is developed on a basis of presentation The angie ß is a measure of divergence of motivationthe motivation as a vector in an N-dimension space. vectors of different employees, that is, a measure ofThis N-dimension space can be defined as motivation qualitative difference of their needs (a measure ofspace (or space of needs) in which the motivation quantitative difference is the difference of theirvector iies. The number N corresponds to the number absoiute vaiues).of groups needs are divided to. This number is definedby researchers and managers goals and it is possible In order to effectively manage a group of employeesto study space with different N whiie studying it is very important to have a good idea about the groupmotivation, it is necessary to mention that the number motivation. Each Cartesian coordinate of the groupof groups of needs and criteria used for division have motivation vector M^ is caiculated according to theno influence on the model structure. following formula:As vectors of partial motivations iies on axes of a ^ =2 2 x/ = 2 2 w/ cos cpj, (9)Cartesian system of coordinate, the absolute value ofthe overall motivation wiil be inferior to the sum of K - number of employees in the group.vaiues of vectors of partiai motivation (according to The formula of average motivation:70
- 6. Mathematical Modelling of Human Motivation: A Vector hypothesis Ivan Kotliarov M= lM, (10) definition of the angle could be the fact that the n employees productivity reaches 100% when the KThe passing from individual and group motivation to convergence between their expectations of theaverage motivation is very important: it gives the ma- company and the company expectations of employeesnager a possibility to evaluate influence of different reaches 60%. [Solomanidin, Solomanidina 2005]].changes of values of motivation factors on motivationof an average employees without diving into analysis As indicated above, the precise set of groups of needsof all individual vectors. But this average approach should be defined according to the studys tasks -gets closer to the real situation when motivation different goals require different distribution of needs.profiles of different employees get closer to each other However, in general it might be logical to divide needs(in other words, when divergence between their into 3 major groups: material consumptive (related tomotivation vectors gets smaller). Motivation profile satisfaction of material - physiological and social -stands here for a list of intensities and importances of needs), non-material consumptive (related with needsmotivation factors of an employee. in respect, in good relations with colleagues, in good social climate at work) and creative (relative with need It is possible to set up for every position within every to realize ones potential).department of company an ideal motivation vector,that is, the motivation vector of an ideal employee who Vector model of work motivation and Vrooms for-completely shares the companys goals, mission and mulaexpectations (importances of motivation factors for thecompany and for this employee are equal) and who I noted in the very beginning of this article that it theis perfectly happy with values of motivation factors only example of application of mathematical tools tooffered by the company (the intensities are equal too). motivation analysis was Vrooms formula. It would beThe Cartesian coordinates of such vector are: logical to try to include it in the present model of motivation. M (a, m, a^-m^,..., a / mj ), (11) The proposed model of motivation is a long-term model - it is supposed that employees motivation a - ideal (perfectly corresponding to the profiles remain unchanged during a relatively longcompanys expectations) importance of the i-th period of time. It describes general aspirations of anmotivation factor; employee but provides no information about his/her m. - ideal (perfectly corresponding to the reaction to a concrete task. However, in practice itcompanys budget limitations) intensity of the i-th might be important to forecast employees behaviourmotivation factor. not only in long and middle term, but also in short term, even better - in a concrete moment. This goalThe correspondence of motivation vectors of newly could be reached thanks to the notion of instanthired employees to the ideal vectors defined for their motivation that is understood as the probability thatpositions will help to ensure the maximal convergence the employee will perform necessary actions in orderbetween the companys and the employees interests to fulfill the task he/she is in charge of. The formula is:and to avoid motivation losses during the passing fromindividual motivation to group motivation. Mp=LSCP (12)Of course, the full convergence of companys Mp - instant motivation (motivation inexpectations and employees interests is an utopia, probabilistic form);therefore the company should define the maximal L - measure of how the task is hard toacceptable angle ß_^^ between the motivation vector perform;of an employee and the ideal motivation vector defined S - self-reliance of the employee, his/herfor his position. After that the company can defined belief in his/her forces and potential;the corporate solid angle Q^^, within wich all employees C - belief of the employee in justice andmotivation vectors should" be located and which is honesty of the person responsible for remunerationequal to 2ß_^^^. The ideal motivation vector goes (this index is closely related to the degree ofthrough the centre of the N-dimension circle satisfaction of non-material consumptive needs of thissubtended by this solid angle of the surface of a N- employee in this company);dimension sphere with radius equal to the value of P - probability of the fact that thethe ideal motivation vector. A possible indication for remuneration will satisfies this employees needs 71
- 7. PANORAMA SOCIOECONÓMICO AÑO 24, N" 33, p. 66-74 (Julio - Diciembre 2006)(depends on how the remuneration offered and fringe benefits. In order to spare place in thecorresponds to importances and intensities of this journal I will study below the problems of managementemployees motivation factors). of intensities of motivation factors. However, as I stated above the same reasoning is true for importances.It is obvious that the formula 12 is absolutely equivalentto Vrooms formula indicated in the beginning of the There are three such problems:article - the only difference is that the index R inVrooms formula (expectations that the efforts will lead 1. There is an amount of the resource R, that shouldto the necessary results) is decomposed into L and S. be used to modify motivation factors so that the motivation increase be maximal. The inverse MOTIVATION MANAGEMENT task: we have to reduce the amount of the resource R used for motivation so that theTraditional approach to motivation management motivation decrease be minimal. -consists in modification of intensities of motivationfactors offered by the employer (the employer ôR=consl,SM=,decreases or increases the sets of goods transmittedto employees in exchange for their work and satisfying 2. It is necessary to increase the motivation M bytheir needs). This approach can me defined as ÔM so that the expenses of the resource R beextensive. The approach concentrating on motivation minimal (the inverse task - to reduce themanagement through modification of importances of motivation by a defined value so that themotivation factors of individual employees can be economy of the resource R be maximal):considered intensive. R„ +ÔR) - ± afm min (16)Decreasing or increasing the set of goods means fora company expenses or economy of a resource R.Intensities of motivation factors can therefore be 3. Replace one motivation factor by another ensuringpresented as functions of this resource (it is very that the motivation remains unchanged and soimportant to remember that the precise description of that the economical effect of this replacementthese functions is to be found; it seems to be logical, be maximal (economy of a resource R):however, to suppose that due to the specificity of"different types of goods and services satisfyingdifferent categories of human needs the functionslinking resource expenses and intensities of motivationfactors offered by the company will be different for (17)different groups of needs). In order to simplify theanalysis (but without any reduction of general A good sample of such replacement could becharacter of our approach) lets suppose that numerous construction and industrial projects carriedintensities of all motivation factors depend on the same out by Soviet workers before the WWII: their salaryresources - most probably, on finance. The value of was very low, but their enthusiasm was high and theythe intensity of a given motivation factor does not were proud to participate in the building of adepend on the total expenses of this resources - it communist society (in other words, non-materialdepends only on the part of the expenses of this consumptive needs replaces material consumptiveresources channeled to the modification of the ones).intensity of this precise factor. The third problem is worth being studied separately.It is obvious that the same stipulation applies to First of all, it should be mentioned that it could beimportances of motivation factors as work with generalized: it might be necessary not to maximizepersonnel requires resource expenses. the economic effect but simply to calculate it in case the company has to change dramatically its motivationIt means that from the point of view of financial and scheme. But it is not the most important thing: theproduction management all tasks of motivation problem is that the task 3 contradicts the axiom 7 aboutmanagement could be described as optimization the independence of groups of motivation factors.problems dealing with maximization of effectivenessof resources assigned to modify employees salary This paradox can be easily solved if we realize that72
- 8. Mathematical Modelling of Human Motivation: A Vector hypothesis Ivan Kotliarovthe third task is not completely correct. Indeed, the R. - quantity of resources (in most cases -replacement of motivation factors is possible in 2 ca- money) spent to modify the intensity of the i-thses only: if the modification of their respective motivation factor coefficient used to transform theimportances is relatively small or if their importances logarithm of motivation into motivation feeling.change simultaneously with the change of intensities.In the sample above - the momentary material Most probably Z depends on the time - the employeeprosperity was considered by Soviet workers as less simply gets used to his/her salary and its psychologicalimportant compared to the participation in the buil- value decreases. So in full analogy with extinctionding of the Communist future. If we take out a set of processes, the function Z (t) will be exponentialgoods from the compensation package of an asymptotic (due to the fact that the employee getsemployee and replace it with a different set of goods accustomed o the constant values of intensities of(for completely different groups of needs), the value motivation factors offered by the company and theof motivation offered by the company will remain natural change of his/her priorities over the time, thatunchanged, but the orientation of the motivation vector is, dur to the growth of divergence of his/her andwill change dramatically compared to the orientation companys interests):of the motivation vector of this employee. Theemployee will accept it if this difference in orientation (19)is small (that is, if the changes of intensities of thesemotivation factors is small) or provided that the z - value of the multiplicator Z in theimportances of these motivation factors are changed moment t=0;accordingly. Y - a constant of weakening of perception (its mathematical meaning - it is the inverse value to RESOURCES, INTENSITIES OF MOTIVATION the period of time during which the multiplicator Z* FACTORS AND PRODUCTIVITY decreases by e times).However, the formulas presented in the part 4 of this Finally, we have to propose a connection betweenarticle have a very limited value: they do not tell motivation level M and the productivity level P. Indeed,anything about the correlation between resources the motivation itself is not very important for a mana-expenses and the intensity of motivation factors, they ger - (s)he is interested in maximal productivity, andsimply suppose that such a correlation exists. the motivation is just a tool to reach this goal. I believeObviously, this is not enough for practical purposes - that it would be difficult to establish a direct correlationa manager has to know how to spend money in order between the motivation and the productivity, however,to get the maximal effect. there should be a clear connection between the motivation and the intensity of work. It would be logicalWe may cautiously suppose that the money paid to to suppose that the more the person is motivated thean employee (as salary and fringe benefits) can be more intensively (s)he works, so we may cautiouslyconsidered as a stimulus. Thus, the quantity of money make the following assumption:is the physical magnitude of this stimulus, and theintensity the motivation factor this money is spent for I = qM, (20)is therefore the perceived intensity of this stimulus.This analogy has to be empirically and statistically I - intensity of work;proved but is seems to be logical. M - total motivation; q - a coefficient depending on theSo we can use Weber-Fechner law [Javorskij, Detlaf psychological and physiological aspects of the1979; Weber-Fechner law] to establish a connection employee.between the resources spent and the intensity of amotivation factor: This assumption has also to be proved empirically. m.= ZlnR,, (18) SCALES FOR IMPORTANCES AND INTENSITIES m. - intensity of a motivation factor; Z - a coefficient depending on the way the In order to give a quantitative evaluation of differentmoney is used (and finally - on the managers groups of motivation factors and to ensure therequalification) and individual psychological properties comparison it would be logical to use special scalesand features of the employee; in which motivation factors are measured by experts 73
- 9. PANORAMA SOCIOECONÓMICO AÑO 24, N° 33, p. 66-74 (Juiio - Diciembre 2006)evaluation and weighing. These scales are not uni- This model can also be easily developed further if weversal. replace some axioms. Indeed, the axiom 7 seems to be over-simplistic, so we may replace it by theImportances of motivation factors can be measured following statements:through psychological tests and interviews in order to • Different motivation factors may influencedefine employees priorities. The recommended scale each other (change in intensity and/or importance offor importance is from 0 to 1. a given group of motivation factors may lead to a change in intensity and/or importance of other groupsIntensities of motivation factors can be measured on of motivation factors) or - the same goods can satisfya scale from 0 to 100. In case of material consumptive different groups of needs.factors (that are directly measured as the employees These restatements of axiom are especiallywages) 0 is equal to zero wage, 100 - maximal wage important in order to generalize this model and toexisting within this company. build up a theory of consumers motivation. This development will be described in the next article.Calculation of intensities of non-material consumptiveand creative groups requires clear definition of the REFERENCESstructure of these groups. As soon as the precise listof needs composing each of these 2 groups is defined, Herzberg F., Mausner B. and Snyderman B.B. Theeach need gets a weight and then the degree of Motivation to Work. New-York: John Wiley, 1959.satisfaction of every need is measured from 0 to 100(via interviews). After that the average weighed lljin Je.P. Motivacija i motivy. "Piter", Sankt-Peterburg,satisfaction of the corresponding group is calculated, 2000.and this average satisfaction represents the intensityof the corresponding motivation factor offered by the Javorskij B.M., Detlaf A.A. Spravonik po fizike dlacompany. The respective formula is as follows: inenerov i studentov vuzov. "Nauka", Moskva, 1979. Maslow A. Motivation and Personality. 2"" edition. 5 New-York: Harper and Row, 1970. where m - intensity of the motivation factor; McClelland D. C. The achieving society. Princeton: n - number of sub-needs; Van Nostrand, 1961. ij)- weight of the corresponding sub-need; |j.-intensity ofthe corresponding sub-need. Mescon M.H., Albert M., Khedouri F. Osnovy menedmenta. "Djelo", Moskva, 1992 (Translated from English: Mescon M.H., Albert M., Khedouri CONCLUSiON F. Management. 3"* edition. Harper and Row, New-York, 1988)This mathematical model of motivation is consistentand may provide HR professionals with a reliable tool Motivation. Wikipedia. English edition, http://for calculation and forecasts of motivation level (both en.wikipedia.org/wiki/Motivation (Retrieved onindividual and group). Of course, additional empirical 05.08.2006)researches are necessary in order to check all aspectsof this model, but we may hope that eventually it will Motivation. Wikipedia. French edition, http://be possible to transform this model into an HR soft- fr.wikipedia.org/wiki/Motivation (Retrieved onware. 05.08.2006)The key advantage ofthe present model of motivation Solomanidina T.O., Solomanidin V.G. Motivacijais that it builds up a bridge between content and trudovoj dejatelnosti personala. 0 0 0 "urnalprocess theories as it provides a link between needs upravlenija personalom", Moskva, 2005.as main reasons of human behaviour (as stated incontent models) and the internal psychological Vroom V. Work and motivation. Jossey-Bass, 1995.process of motivation (vector model). In addition, itgives tools for quantitative estimation of human Weber-Fechner law. English edition, http://motivation. en.wikipedia.org/wiki/Motivation (Retrieved on 16.01.2007)74

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