=Paper=
{{Paper
|id=Vol-2212/paper57
|storemode=property
|title=Analysis of the influence of citizens’ altruism on the effectiveness of the socially-optimal actions stimulation system
|pdfUrl=https://ceur-ws.org/Vol-2212/paper57.pdf
|volume=Vol-2212
|authors=Mikhail Geras’kin
}}
==Analysis of the influence of citizens’ altruism on the effectiveness of the socially-optimal actions stimulation system ==
https://ceur-ws.org/Vol-2212/paper57.pdf
Analysis of the influence of citizens’ altruism on the
effectiveness of the socially-optimal actions stimulation system
M I Geraskin1
1
Samara National Research University, Moscowskoe shosse 34, Samara, Russia, 443086
Abstract. The problem of the development of the state information stimulation system of
Russian citizens’ socio-optimal actions is considered according to the optimum of collective
utility function as criterion. The algorithm of the information system is formed taking into
account the conditions of individual rationality, Pareto efficiency and non-manipulability. The
algorithm for analyzing the effect of various functions of the probability distribution density of
the altruism degree of Russian citizens on the effectiveness of the system for stimulating
socially-optimal actions is developed. The simulation of social groups behavior, covering more
than ten percent of Russia's economically active population, is confirmed the stability of the
stimulation system for citizens’ opportunistic behavior.
1. Introduction
In a transitional economy [1,2] trends of individual rationality are growing in the society. The state
develops the moral improving programs [3,4] to overcome this trends. In this case, the purpose of the
state is the social effect of citizens’ acts, performing on the basis of maximization of collective but not
individual utility function, hereinafter referred to as socio-optimal actions. Achieving this purpose
requires the involvement in socially useful activity of large group of the population and personified
registration of socio-optimal actions. It needs to organize the state information system, based on the
information resources of currently working in Russia programs [5-7].
The concept of socio-optimal actions’ stimulation provides for the establishment of information
system of personified registration of the actions of citizens (hereinafter, agents). The system also
includes the distribution of state stimulation fund in the form of incentives between agents according
to certain mechanisms. The dynamics of the system is a two-period. In the first period (registration
period) performed socio-optimal actions are recorded, and in the end of this period the stimulation
fund is distributed. In the next period (period of stimulation) the earlier distributed incentives are used.
In addition to the utilitarian stimulating function information system also solves the problem of the
formation of the agent’s status in the hierarchy of the citizens, used for non-material motivation. On a
longer time horizon, the state’s social priorities could changed by varying the attributes of socio-
optimal actions and their monetary valuation can be varied as a result of inflation. Therefore, to
comparability of agents’ statuses the system accumulates not only incentives as the current cash
equivalent of social activity, but also agents’ rating in comparable dimension.
The object of stimulation is socio-optimal actions of citizens, that is, actions that correspond to
certain attributes. The actions should maximize collective utility function without increasing the
individual utility function. Therefore, the attributes correspond to the terms of gratuitousness, public
utility and unconnectedness with professional activities of citizens. Consequently, socio-optimal
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M I Geraskin
actions do not require special qualification, whereby the stimulation object’s dimension is duration of
action excluding the content of the action. The subject of stimulation is citizen, performing a socio-
optimal action in certain period. The apparatus of stimulation is the state represented by certain
ministries (departments).
2. Methods
The investigations of stimulation systems and distribution mechanisms produce the following
mechanisms corresponding the individual rationality. Competitive mechanism is developed with
noncooperative [8] and cooperative [9] behavior of agents, its Pareto efficiency and optimality
according to additive utility function criterion are proved. The step-by-step resource distribution
mechanism (SRDM) is obtained [10], for which proved [11] that nonmanipulability and Pareto
efficiency simultaneously only for SRDM; also SRDM, as shown in [12], is equivalent to mechanisms
of direct and reverse priorities. It was shown [13] that unique SRDM exists, in which the incentive is
distributed [14] as minimum of agent’s information and the average undistributed rest of incentives.
The approach to the distribution based on the penalty and incentive functions [15] showed the Pareto
efficiency and optimality according to additive utility function criterion for compensatory
mechanisms; according to a compensatory mechanism incentives are equal to agents’ costs. Thus, only
SRDM satisfies [16] all above conditions. Since SRDM implies consistent registration of agents’
actions and further distribution of the incentives, it is impossible to use in the system, where actions
perform independently and record simultaneously with asymmetrical agents’ behavior [17,18]. The
interaction distribution algorithm in a strongly coupled system with a transferable utility is developed
[19,20].
On the base of this ideas an algorithm of the information system (Fig. 1) was developed [21]. The
algorithm satisfied the conditions of individual rationality, Pareto efficiency, non-manipulability and
optimality by the collective utility criterion.
In [19] and later in this paper the following notation is used:
Z = {z i , i = 1,..., I } is a set of attributes of socially-optimal actions;
K (t ) = {1,..., n(t )} is a set of agents, including citizens who perform actions that correspond to the
attributes of Z; index n(t) denotes the number of agents in a certain period t;
A(Z , t ) = {a k (Z , t ), k ∈ K } is a vector of socially-optimal actions; the vector includes quantitative
estimations of the actions of the k-th agent corresponding to the attributes Z in the t-th period;
estimation a is expressed in the time spent by the agent for performing these actions; the vector
{ }
belongs to the allowable set A = a k ∈ [0, a max ] , a max > 0, k ∈ K , where the symbol a max denotes the
upper limit of the agents’ available time;
F (t ) ∈ (0, F max ] , F max > 0 is a stimulation fund in the t-th period t ∈ (0, T ] ; further, the index t is
omitted, all parameters of the model correspond to a certain period of time;
u k = ψ (a k ), k ∈ K , ψ (a k ) = αa kβ , α ∈ (0, α max ] , β ∈ (0, β max ], β max ∈ (0,1], k ∈ K is dimensionless
function of registration of socially-optimal actions; where u is a score, α , β are constant coefficients;
E = ∑ a k is a system effectiveness indicator;
k∈K
x k = ϕ (u k ) = ϕ min + b1 − b2 ∑ u k a k , k ∈ K is monetary incentive function; where ϕ min is
k∈K
guaranteed incentive of non-zero agent’s action, b1 , b2 > 0 are coefficients of the incentive function,
calculated from formulas
2u + ∑ u k
F − nϕ min F − nϕ min , 1
b1 = k ∈K
, b2 = u= ∑ uk .
∑u
k ∈K
k 2u 2u ∑ u k
k ∈K
n k ∈K
The algorithm of a one-period cycle of the information system is shown in Fig. 1.
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M I Geraskin
Figure 1. Algorithm of information system cycle.
The action registration block identifies agents’ actions in the scoring. The stimulation block is
intended for distribution of the stimulation fund depending on the vector of scoring actions. The
effectiveness analysis block controls the dynamics of the change in the social efficiency criterion of
the system in the selected time interval until the maximum number of work periods is reached.
Let us consider the problem of the information system algorithm modeling for various probability
density functions of the existence of social groups with a greater or lesser inclination for altruism.
3. Results and discussion
Let the following continuous functions are defined for the k-th agent
a k (D k ) = D kδ ak , d k (D k ) = D kδ dk , δ ak , δ dk ∈ [0,1], δ ak + δ dk = 1, D k >> 1, k ∈ K , (1)
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where d k is the working time interval; Dk is an available time fund equal to the physical time fund
except for the rest time; δ ak , δ dk are elasticity coefficients of «charitable» time and working time on
Dk .
The functions (1) express the connection between the time interval of charitable actions, the time
interval of working time and the available time fund. The derivatives of the functions (1) decrease
with increase of Dk , expressing the propensity of individuals [22] to increase the rest time with
growth Dk .
Definition: altruism (propensity to charity) of the k-th agent is a type of function (1), under which
δ ak > δ dk .
Figure 2. Graphical interpretation of the problem (2), (3).
The introducing of the socially-optimal actions stimulation system by the algorithm (Fig. 1) leads
to the fact that altruistic actions bring a non-zero income.
Therefore, to select the value of the action, the k-th agent, taking into account the individual
rationality, solves the following problem: to maximize the total income from the working and
«charitable» time with a restriction 1 on the available time fund:
max I k = max( pak ak + pdk d k ), pak , pdk > 0, pak = k ,
x
(2)
ak ∈ A ak ∈ A ak
1 1
δ ak δ dk
a + d = Dk , k ∈ K ,
k k
(3)
where pak is the price of the «charitable» time; p dk is the price (tariff rate) of working time.
Note that the restriction (3) does not coincide with the identity ak + d k = Dk , because of the
«charitable» time is not an absolute substitute in relation to working time, as shown in Fig. 2.
The solution of the problem (2), (3) has the form 2:
δ dk −1
δ dk
1 1
* * −1 pak
ak
Dk − ak δ ak δ ak
= , (4)
δ ak
pdk
δ dk
*
1
d = Dk − ak δ ak , k ∈ K ,
*
(5)
k
1 1
1 δ ak δ dk
The restriction (3) follows from (1): Dak = a k , Ddk = d k
, Dak + Ddk = Dk
.
δ dk δ dk −1
2 1
δ
1
1
−1
The equation d k = Dk − akδ ak follows from (2) ; therefore d /
= − dk Dk − akδ ak δ ak
ak ; as at the
kak
δ ak
tangency point B the angular coefficients of the functions (2) and (3) are equal, the optimum condition has the
form (4).
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where the symbol «*» denotes the optimal values.
The elasticity coefficients δ ak , δ dk are known, and price vectors are given
Pa = {pak , k ∈ K }, Pd = {pdk , k ∈ K } , (6)
the first vector is calculated on the basis of the results of algorithm (Fig. 1) by formula (2), and the
second vector is given based on the statistics of the national labor market. Thus, the solution of the
equation (4) gives an individually rational vector of socially-optimal actions А.
Let the coefficient δ ak in the general population of agents (population) is a random variable [23]
with a normal distribution law [21]:
−
(
w δ a −δ l )
2
f (δ a ) =
1 2σ 2 . (7)
e
σ 2π
where δ , σ are the mathematical expectation and the standard deviation of the initial distribution of
the random variable; l is a coefficient taking into account the asymmetry (l > 1 - left asymmetry, l <1 -
right asymmetry at 0 < δ < 1 ) in comparison with the normal law (l = 1); w is a coefficient that takes
into account kurtosis (w <1 is a more uniform distribution, w > 1 is a less uniform distribution)
compared with the normal law (w = 1).
In this case, the expected values of the agents’ number having these values of the elasticity
coefficients δ ak , δ dk = 1 − δ ak , are calculated by the formulas
nˆ (δ a ) = f (δ a )n, nˆ (δ d ) = n − nˆ (δ a ) ,
where nˆ (δ a ), nˆ (δ d ) are the expected values of the agents’ number at given values of the elasticity
coefficients.
The algorithm of the effectiveness analyzing block of the information system for various parameters
of the probability density function of the social groups presence with a greater or lesser inclination for
altruism is shown in Fig. 3.
The simulation of the stimulation effect on the population’s behavior is carried out by changing the
asymmetry and kurtosis of the probability density function (7) of a normal distribution. The
characteristics of the population’s distribution variants by social groups with greater or lesser
inclination for altruism are given in Table. 1. The variant θ = 1 corresponds to the normal distribution
law; variant θ = 2 simulates the case of exceeding the mathematical expectation of the population's
inclination to altruism over the median value due to right asymmetry; variant θ = 3 simulates the case
of a more uniform distribution of the population's propensity for altruism in comparison with the
normal distribution law due to the decrease in kurtosis.
Table 1. Variants of population’s distribution.
Model Variant
parameter θ=1 θ=2 θ=3
Characteristics normal normal distribution with right normal distribution with reduced
distribution asymmetry excess
l 1 0,8 1
w 1 1 0,5
The following initial data are considered: the value of the stimulation fund is set F = 1000000
thousand rubles, the values of the registration function coefficients (α = 67, β = 0,8) are selected from
the condition u = 100 at the initial value of the time price and θ = 1, the minimum stimulus is assumed
equal to zero, the number of the population n = 9727 thousand corresponds to the group of Russian
Federation population with income below the subsistence minimum, the price of working time is Pd =
0.21 thousand rubles per hour based on the average wage of 35.369 thousand rubles per month, the
range of the elasticity coefficient of the «charitable» time is chosen taking into account the possibility
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M I Geraskin
of equation (4) solution equal to δ a ∈ [0,1;0,7] . Since ϕ min = 0 , the price of «charitable» time is the
xk
same for all agents and it is equal to Pa = = b1 − b2 ∑ u k .
ak k∈K
Figure 3. Algorithm of the effectiveness analyzing block of the information system.
In Fig. 4 the distribution functions of the population depict depending on the elasticity coefficient
of the «charitable» time for various simulation variants.
In Fig. 5 the functions of average per capita effectiveness indicator E av. = E / n for different
simulation variants are given. The sharp increase in the effectiveness indicator at t = 1 is due to the
increase in the price of the «charitable» time (Fig. 8) in the first period in comparison with the initial
date adopted by Pа=Pd to adjust the stimulation system in the zero period. From Fig. 6 it follows that
the reason for this growth is a significant increase in socially-optimal actions in groups with relatively
low of «charitable» time elasticity coefficient in the range (0.2, 0.5).
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n(δа) 6000
5000
4000
3000
2000
1000 Figure 4. Distribution functions of the
0 population (thousand) depending on the
0,1 0,2 0,3 0,4 0,5 0,6
δа
0,7 value of the elasticity coefficient of the
«charitable» time for various simulation
θ=1 θ=2 θ=3
variants.
Eav. 3,3
3,1
2,9
2,7
2,5
2,3
2,1
1,9
1,7
1,5
t
0 1 2 3 4 5 Figure 5. Dynamics of the average per
θ=1 θ=2 θ=3 capita effectiveness indicator for various
simulation variants.
Population groups with very low values (0,1 ... 0,2) and very high (0,5, 0,7) values of the
«charitable» time elasticity coefficient are less susceptible to the stimulating effect of the high price
Pа: the first because of the prevalence of work in their disposable time fund, the latter due to high
altruism. Since at t = 2, as the price Pа decreases (Fig. 8), the effectiveness indicator also decreases
taking into account (Fig. 6) sharp reduction of such actions in the range (0.2, 0.5). Consequently it can
be concluded that population groups with relatively low «charitable» time elasticity coefficient are
prone to opportunistic behavior, that is, the motivation for socially-optimal actions for them is
individual rationality. As a result, in all variants θ = 1,2,3 the value of the average effectiveness
indicator stabilizes even at t = 3.
а* 8
7
6
5
4
3
2
1
0 Figure 6. Dependence of socially-
0,1 0,2 0,3 0,4 optimal actions on the elasticity
0,5 0,6 0,7
δа
t=1 t=2 t=3
coefficient of the «charitable» time for
θ=1.
Stimulation is most effective at θ = 2, the least effective at θ = 3. Consequently, the results of the
simulation are consistent with the following provisions: 1) an increase in the prevalence in a society of
citizens with a higher propensity for altruism leads to an increase in the social effect from charity
stimulating; 2) in case of stimulation a more equal prevalence in a society of individuals with high and
low inclination to altruism leads to a reduction in the number of socially optimal actions in comparison
with the normal distribution.
In Fig. 7 the average registration score per capita u av. = u dependences on the period for different
simulation variants are given. In all variants, the value u av. stabilizes at t = 3. The highest values of
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average score are recorded at θ = 2, the lowest values are recorded at θ = 3, which is due to the
dependence of the average score through the registration function on the social effect E av. .
In Fig. 8 the «charitable» time price dependences on the period for different simulation variants are
given, which also stabilize at t = 3. The lowest price Ра corresponds to θ = 2, the highest price is
reached in the case θ = 2. Since the price Ра is a state incentive for a single socially-optimal action, the
stimulation system is most economically effective at θ = 2, the least effective at θ = 3.
uav. 180 Pa 1,2
170
160 1,0
150 0,8
140
130 0,6
120
110 0,4
100
0,2
90
80 0,0
t
0 1 2 3 4 5 t 0 1 2 3 4 5
θ=1 θ=2 θ=3 θ=1 θ=2 θ=3
Figure 7. Dynamics of the average score per Figure 8. Dynamics of the «charitable» time
capita of the registration function for various price (thousand rubles / hour) for various
simulation variants. simulation variants.
The stabilization of the effectiveness indicator of the simulation system (Fig. 5) and the price of time
(Fig. 8) at t> 2 leads to the conclusion about the stability of the simulation system for opportunistic
behavior of citizens: persons with relatively low values of «charitable» time elasticity, performing
socially-optimal actions based on individual rationality, demonstrate the greatest negative sensitivity
to the change in the price of time as a stimulus. Due to this, the positive deviation of the stimulus in
one period from a certain equilibrium value is damped by the opportunistic behavior of citizens,
leading in the next period to a decrease in the number of socially-optimal actions.
4. Conclusion
The problem of informational support of the state strengthening morality strategy by stimulating
citizens’ actions performed on the basis of maximizing the collective utility function is considered.
The following main results are obtained in the article.
The algorithm for analyzing the effectiveness of the information simulation system for various
parameters of the probability distribution function of social groups with greater or lesser inclination to
altruism in society is developed.
The influence of stimulation on the population’s behavior is studied by changing the asymmetry
and kurtosis of the probability density function of the normal distribution. The case of exceeding the
mathematical expectation of the population's inclination to altruism over the median value is simulated
by introducing asymmetry. The case of a more uniform distribution of the population's inclination to
altruism in comparison with the normal distribution law is simulated by the introduction of kurtosis.
The analysis shows that the stimulation system is resistant to opportunistic citizens’ behavior due
to the fact that persons performing socially-optimal actions based on the individual rationality
demonstrate the greatest negative sensitivity to the change in the stimulus.
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