Effect of Communication Error on

“Iterated Proposal–Voting Process”

Hiroshi Kawakami, Toshiaki Tanizawa, Osamu Katai and Takayuki Shiose

Graduate School of Informatics, Kyoto University,

Yoshida-Honmachi, Kyoto 606-8501, Japan

Abstract. This paper proposes the framework of a multi-agent simulation called

“iterated proposal–voting process” and reports the effect of communication error

on the decision-making of a relatively small community. The community try to

decide on a shared rule via iteration of “propose and vote.” In this framework,

each agent decides its action based on two criteria: satisfying “physiologically

ﬁxed needs” and satisfying “social contextual needs (SNs),” which sometimes

conﬂict with each other. These criteria are derived from a Nursing Theory that

puts special emphasis on the relation between subjects and others. SNs are sat-

isﬁed when such relations are balanced. Employing “Hyder’s theory of cognitive

balance,” SNs are evaluated for whether they are balanced. The simulation yields

some interesting phenomena that are not observed by conventional static analy-

ses, e.g. power indices.

1 Introduction

Through the process of decision-making by a community, the ﬁnal decision should re-

ﬂect all members’ preferences and beliefs, but it is difﬁcult to arrive at such an ideal

decision because personal preferences vary with personalities, and the relations among

members are not simple [1]. Especially in relatively small communities, it is well known

that a personal decision can strongly inﬂuence the ﬁnal decision, leading the so-called

“groupthink,” “risky shift [2],” and so on. Recently, multi-agent simulations have been

applied to analyze such phenomena that emerge in decision-making processes in a bot-

tom up manner, e.g. [3].

The target of our agent-based simulation is a relatively small community that tries to

decide a shared rule of community through a process that can be modeled as “iterated

proposal and voting.” One of the characteristics of our model is the mental model of

each agent based on Nursing Theory, especially the Behavioral Systems Model [4],

which focuses not only on personal preferences but also on social relationships. The

social relationships are assessed by employing Heider’s theory of cognitive balance [5].

The preference of voting of each agent is revised through the “iterated proposal and

voting” by using Q-learning [6]. Our model is applied to examine the effect of errors

on decision-making. The results of simulation are compared with those of conventional

methods of analyzing voting systems [7].

Kawakami H., Tanizawa T., Katai O. and Shiose T. (2006).

Effect of Communication Error on “Iterated Proposal–Voting Process”.

In Proceedings of the 2nd International Workshop on Multi-Agent Robotic Systems, pages 83-92

DOI: 10.5220/0001224200830092

Copyright

c

SciTePress

2 Decision Making via “Iterated Proposal–Voting Process”

Decision-making is an interesting topic for Game Theory, Social Psychology, Politics,

Sociology, etc., and many research efforts have been carried out. This paper aims to

contribute to this research ﬁeld by considering the notions of “personal needs vs. social

relationship” and “iterated proposal-vote process.”

2.1 Model of Each Agent and Shared Rule

The iterated process of decision-making by a community is affected by the actions,

preferences, and beliefs of each constituent and by the relationships among them. In

order to simulate this process, the method of modeling each agent emerges as the main

issue. Recent researches has attempted to model agents based not on a simple strategy

such as “chasing optimality” but on complex and human-like strategies. For example,

some agents are deﬁned by introducing the notion of physiology based on Transactional

Analysis, while others are deﬁned by introducing the notion on ethics [8]. This paper

deﬁnes agents by introducing the notion of Nursing Theory, especially the Behavioral

Systems Model [9], which is derived from a tremendous number of observations of

“patterns of human behavior.” The main feature of this model is its treatment of instincts

by considering the motivation of maintaining relationships.

Although the monumental book “Notes on Nursing [10]” by F. Nightingale has not

been cited for a long time, various theories motivated by the Notes have been devel-

oped since 1950 [4]. These theories vary depending on the basic philosophy. Among

them, we employ “system theories [4]” as the basis of modeling agents. The common

standpoint of system theories is that a human being consists of several systems, which

are categorized into two groups: physiologically personal ones and social ones. For

example, the Behavioral Systems Model [9] deﬁnes the “behavior system of humans”

as an integration of seven subsystems, called “afﬁliative,” “dependency,” “ingestive,”

“eliminative,” “sexual,” “aggressive,” and “achievement” subsystems. Afﬁliative and

dependency subsystems are social while the others are personal. Hereafter, we call the

requirement derived from the former “social contextual needs (SN)” and that from the

later “physiologically ﬁxed needs (PN).”

Each subsystem tends to satisfy its requirements and be in a balanced state. If some

subsystem of a person is imbalanced, he/she feels nonconformity and is thus motivated

to take certain actions, which lead to subsystems becoming balanced. Furthermore, sub-

systems sometimes conﬂict with each other. An action made to balance a subsystem

may lead to another subsystem becoming imbalanced.

Physiologically ﬁxed Needs (PN) and Shared Rule. Physiologically ﬁxed Needs (PN)

reﬂect personal and physiologically requirements, e.g., preferable temperature, bright-

ness, and calmness of a room, which are independent of relationships with other people

but sometimes conﬂict with the preferences of other people. Therefore, a community

needs a shared rule for governing such requirements.

84

Initial shared rule P = {4, 4, 1}

P N

0

= {4, 3, 5}

P N

1

= {1, 5, 2}

P N

2

= {5, 3, 2}

zw

Shared Rule

n0 n1 n2

Φ(a0) Φ(a1) Φ(a2)

adopt

p0 p1 p2

a0

1

proposer

1

a1

1

a2

2 1 3

Fig.1. Example of initial P , P N

i

, and “a step of proposal-vote and alteration of Φ(a

i

)”.

Shared Rule: Deciding the value of a shared rule is the objective of our simulation.

A shared rule is represented by a set of values that governs all of the members of the

community. Such a rule must be decided through discussion among all members. Our

“proposal–voting system” implements a shared rule as a list of integers:

P = {p

0

, p

1

, p

2

, · · · , p

R

l

−1

},

where R

l

denotes the number of factors that commonly affect all members, and each

factor p

j

is assigned an integer (0 ≤ p

j

< R

s

).

Coding PN: PN of each agent reﬂect factors of the shared rule. Therefore, each need

(n

i

j

) of an agent a

i

is represented by an integer (0 ≤ n

i

j

< R

s

), and each “PN of an

agent a

i

” is encoded into a list of needs:

P N

i

= {n

i

0

, n

i

1

, n

i

2

, ..., n

i

R

l

−1

}.

An example of a set of a shared rule (P ) and PNs is shown in the left part of ﬁg. 1,

where R

l

= 3, R

s

= 7 and the number of agents L = 3. The right upper part of ﬁg. 1

illustrates this situation.

Satisfaction of PN: If the difference between the value of each element of PN (n

i

j

) and

that of the shared rule (p

j

) is within the tolerance range (σ), each element is satisﬁed.

Φ(a

i

) shows the number of satisﬁed needs under a certain state of shared rule P . We

deﬁne that P N

i

is satisﬁed as a whole if and only if Φ(a

i

) ≥ R

l

/2, i.e., “more than half

of its elements are satisﬁed.”

The Proposal: The objective of each agent is to revise the shared rule to satisfy its own

needs. In this revision, one of the agents becomes the proposer and the others are voters.

The proposal is uniquely determined by the PN of the proposer. The proposer tries to

shift the shared rule toward his PN. The proposal is represented by a set of strings that

consists of “stay,” “down,” and “up” for each p

j

. The revision of a shared rule through

discussion of members should not be drastic, so the incremental/decremental value is

ﬁxed to 1. Figure 1 shows an example. If σ = 1 and a

0

is the proposer, n

0

1

, n

0

2

are

85

p o

x

rely on

agree

disagree

antipathy

agree

disagree

(+) (-)

(+)

(+) (-)

(-)

(+) (+)

(+)

(-) (-)

(+)OR OR

imbalance balance

Fig.2. Heider’s cognitive balance and imbalance.

not satisﬁed by the initial P = {4, 4, 1}, so a

0

proposes {stay, down, up}. After a

1

disagrees and a

2

agrees, the number of supporters (a

0

, a

2

) exceeds that of opponents

(a

1

), so the proposal is adopted and P becomes {4, 3, 2}. Finally, Φ(a

i

) is revised to

Φ(a

0

) = 2, Φ(a

1

) = 1, and Φ(a

2

) = 3.

Social contextual Needs (SN) and Theory of Cognitive Balance. In contrast to PN,

Social contextual Needs (SN) reﬂect relationships with others, e.g., being close, famil-

iar, dependent. In decision-making by a small community, SN can be interpreted as that

which reﬂects approval/disapproval, sympathy/antipathy, and so on.

In order to analyze whether SN is balanced, we refer to the Naive Psychology pro-

posed by F. Heider [5], especially to his “Theory of Cognitive Balance.” He focused his

attention on the consistency of these relations in local setting of situations, that is, the

cognitive balance of a person (p) with another person (o) concerning an entity (x), as

shown in the left part of ﬁg. 2.

For example, let us consider three relations:

– p agrees to a proposal x (positive (+)), and

– p relies on a person o (positive (+)), but

– o disagrees with x (negative (−)).

Accordingly, these relations are imbalanced. The balance of this triangular relation is

deﬁned as the sign of the product of the signs of these three relations. In this case, we

have (+) × (+) × (−) = (−), so the triangular relation is imbalanced.

The balanced situation is accepted by p without stress, but the imbalanced situation

makes p stressful and uncomfortable, and is forced to be altered by emotion of p toward

restoring its balance. Concerning the above example, if p feels antipathy to o, we have

(+) × (−) × (−) = (+); if o changes his/her mind and agrees to x, we have (+) ×

(+) × (+) = (+), then p feels comfort.

Coding SN: The proposed framework interprets p, o, and x as “a voter (a

i

),” “another

voter (a

j

),” and “a proposal,” respectively. Therefore, the triangular relation consists of

three relations:

– a

i

agrees/disagrees with the proposal,

– a

i

feels a positive/negative relationship with a

j

, and

– a

j

agrees/disagrees with the proposal.

86

Each a

i

is required to make each triangle balanced by his/her emotion.

The relations between two agents (a

i

, a

j

) are assessed by the ratio of agreement by

a

i

for proposals by a

j

. Even though a

j

is now a voter, a

i

imagines the situation where

a

j

will be a proposer someday, and all possible situations are evaluated for whether a

i

wants to agree to a

j

. For this evaluation, Q-table, explained in section 2.3, is employed.

Assume the table shows that a

i

wants to agree to x cases, we deﬁne that the relation

between a

i

and a

j

is positive if and only if x ≥ 3

R

l

/2, i.e., “more than half of situations

make a

i

agree to a

j

.”

Balance of SN: We deﬁne the balance of SN of a

i

in terms of Heider’s Cognitive

Balance. SN of a

i

for each voter is represented by the above triangle, and L−2 triangles

are supposed because the number of agents is L and one of them is the proposer and

one of them is a

i

itself. We deﬁne “the satisfaction of SN of an agent a

i

as a whole” as

“more than half of triangles of a

i

are balanced.”

2.2 Framework of the Simulation

The “iterated proposal–voting simulation” is a kind of Multi-agent Simulation. In con-

trast to methods of static analysis such as power indices [7], this simulation shows

sequential shifts of states of agents, relationships among agents, and the effect of the

shared rule on agents. This simulationis partially inspired by “a game of self-amendment:

NOMIC” [11], which imitates the legislative process. All members of a community pro-

pose in turn either “establishing a new rule,” “revising a rule,” or “abolishing a rule,”

and for each proposal, members take a vote. If a proposal is approved, it becomes im-

mediately effective and shared by all members.

NOMIC is a game for humans, so rules are described in natural language. On the

other hand, our proposed simulator describes a shared rule by a set of integers and

conﬁnes the proposal to a “revision.”

Flow of “Iterated Proposal–Voting Simulation”. Our proposed “proposal-voting

simulation” shares the basic concept of NOMIC, i.e., it consists of three processes:

– an agent proposes a revision of a shared rule,

– other agents express agreement/disagreement with the proposal, and

– the revised rule affects all agents.

Furthermore, each agent learns preferences of voting by past experiences of voting and

its effect on the agent.

First, the values of ﬁxed parameters are determined:

L: the number of agents, R

l

: the length of shared rule P ,

M: the number of iteration, R

s

: the range of the value of “each element of P .”

Then, the simulator

1. Initializes a set of agents: A = {a

0

, a

1

, a

2

, · · · , a

L−1

}.

2. Initializes a shared rule: P = {p

0

, p

1

, p

2

, · · · , p

R

l

−1

}, where each p

i

(i = 0, 1, · · · R

l

−

1) is assigned a random integer (0 ≤ p

i

< R

s

).

87

3. Repeats M times,

– for i = 0 · · · L − 1

(a) a

i

proposes a revision of P

(b) for j = 0 · · · L − 1; j 6= i

• a

j

expresses agreement/disagreement with the proposal

(c) if (agreement exceeds disagreement)

• the proposal is adopted

• P is revised

(d) for j = 0 · · · L − 1; j 6= i

• a

j

learns to revise its preference of voting

4. The ﬁnal P is the result of the above decision-making.

According to the Behavioral Systems Model, each effect of the shared rule has to

affect the learning process of each a

i

.

2.3 Learning Preference of Voting

The objective of each agent is to satisfy its needs by revising the shared rule, but the

situation for each agent is not simple. It must be concerned about not only its personal

needs but also its relationships with others. We employ Q-learning [6] based on the

“ε−greedy strategy” as a learning method of agents, using the following parameters.

Range of value Q: 0.0 ∼ 1.0 zwRate of random behavior ε: 0.05

Initial value of Q: 0.5 zw Learning ratio α: 0.8

Alternatives of action: agree/disagree zw Reduction rate γ: 0.9

Each agent ﬁrst perceives the current state q(a

i

, currentP ) and then selects an action

v

∗

. The selection is based on the value of Q(q, v), where v is either agree or disagree.

After voting, the state is revised to q

′

(a

i+1

, newP ), and then the value of Q(q, v

∗

)

is revised as follows:

Q(q, v

∗

) = (1 − α)Q(q, v

∗

) + α

r + γmax

Q(q

′

, v)

.

The reward r is determined by how P makes agents comfortable. Namely, it is deter-

mined by how PN and SN are satisﬁed. Humans tend to act to satisfy their own needs.

Our system simulates this tendency through learning voting preferences by using re-

wards that reﬂect satisfactions of SN and PN.

Size of Q-table The variation of the proposer is L − 1, since the number of agents is

L and one of them is a

i

itself. The value of P is estimated by a

i

according to whether

each p

j

is within a tolerance range σ. The number of p

j

is R

l

, and each p

j

is estimated

as “within σ,” “too much,” or “too small,” so the number of all possible estimations is

3

R

l

. Therefore, each Q-table has (L−1)×3

R

l

cases of states. The alternatives of action

are “agree” or “disagree.” After all, each Q-table is a matrix of {(L − 1) × 3

R

l

} × 2.

Revision of Q-value The Q-value is revised by estimation of P. After a

i

takes an action,

if P satisﬁes a

i

’s needs, a

i

gets positive rewards, else if P shifts far from a

i

’s needs,

a

i

gets negative rewards. Either positive or negative, a

i

gets rewards if and only if its

vote affects approval/disapproval of a proposal. In this paper, a positive reward is ﬁxed

to 0.10, and a negative reward is ﬁxed to −0.02.

88

3 Result of Simulation with Communication Error

Our simulation focuses on successive changes in the relationships that are important

for decision-making by a small community. These relationships are represented by SN.

This section shows the possibility of making a decision shift only by altering the rela-

tionships, without any enforcements.

3.1 Introducing Communication Error

Misunderstanding the relation with other people affects the state of SN, which reﬂects

the triangular relationship among an agent, a proposal, and another agent. The state

of SN affects rewards, which further affects the actions of the agent. This local per-

sonal misunderstanding yields, through iterations, global changes such as alteration of

a shared rule or the ﬁnal decision.

Misperceptions of the environment, trouble in the communication route, and other

problems sometimes cause misunderstandings. We implement “misunderstandings” by

reversing the perception. Namely, if an agent a

i

misunderstands the environment, it

reversely perceives the votes of all other agents. Hereafter, the character “*” denotes

such a misunderstanding. For example, in a community A = {a

0

, a

∗

1

, a

∗

2

}, a

1

and a

2

are misperceiving the environment.

3.2 Results of Simulation

We implemented “Proposal–Voting Simulation” in C language and examined all pos-

sible combinations of normal and reversed agents. For each combination, simulations

were carried out 1,000 times, in which the order of proposals were randomly shufﬂed.

This section reports the mean value of 1,000 trials.

All simulations employ the following settings:

number of agents: L = 3 zwrange of the value of rules: R

s

= 7

iterations: M = 500 zwinitial value of shared rule: P = {3, 3, 3}

length of rules: R

l

= 3 zw tolerance range: σ = 1

We conﬁrmed that shared rules are converged before 500 iterations in all simulations.

We also conﬁrmed that the result is independent of the initial value of the common rule,

so this section only reports the case where initial P is ﬁxed to {3, 3, 3}.

This section reports three cases, where P N

i

varies to a certain degree, P N

i

varies

drastically, and a dictatorial party exists.

Case 1: P N

i

varies to a certain degree: In the case where P N

i

varies to a certain

degree, we ﬁx the values to N

0

= {2, 2, 1}, N

1

= {1, 1, 6}, N

2

= {4, 6, 3}.

In the normal case, i.e., there is no misperception ({a

0

, a

1

, a

2

}), P = {p

0

, p

1

, p

2

}

converges at {2.35, 2.53, 2.88}. For the other seven cases ({a

0

, a

1

, a

∗

2

} · · · {a

∗

0

, a

∗

1

, a

∗

2

}),

ﬁg. 3 roughly illustrates the differences in ﬁnal p

i

with the normal case and the ﬁnal

number of satisﬁed PN (Φ(a

0

), Φ(a

1

), and Φ(a

2

)).

The results of shared rules are categorized clearly into two types, i.e., whether a

1

is reversed or not. When a

1

is normal, shared rules converge at almost the same value,

89

{a0, a1, a2 }

{a

0, a1, a2 }

{a

0, a1, a2 }

{a

0, a1, a2 }

* *

{a

0, a1, a2 }

*

*

{a

0, a1, a2 }

*

{a

0, a1, a2 }

**

**

{a

0, a1, a2 }

***

0.00

p1

0.00

p0

0.00

p2 Φ(a0) Φ(a1) Φ(a2)

-0.03

0.02

-0.07

0.17

0.16

0.19

0.18

-0.03

0.06

-0.06

0.04

0.05

-0.07

0.08

2.21

2.28

2.16

2.08

2.30

2.25

2.16

2.10

1.00

1.43

1.35

1.48

1.71

1.01

1.03

1.03

1.41

1.32

1.05

1.16

1.28

1.47

1.48

1.43

0.15

0.50

0.77

0.14

0.18

0.60

0.60

Fig.3. Results of case 1: (P N

i

varies).

but in any case where the perception of a

1

is reversed (denoted by a

∗

1

), the shared rule

shifts substantially. Reversing a

1

particularly affects the increase in p

2

, as shown the

meshed graphs of p

2

in ﬁg. 3. We interpret this phenomenon based on the facts that

1. n

1

0

≃ n

2

0

∧ n

1

1

≃ n

2

1

, and

2. n

0

2

< n

2

2

< n

1

2

.

The ﬁrst fact implies that p

0

and p

1

are stabilized around “2,” with which a

0

and a

1

agree, but reversing the perception of a

1

leads to a

1

agreeing with a

2

instead of a

0

.

Then the above second fact leads to p

2

shifting toward n

1

2

, and p

2

comes to the middle

value between n

1

2

and n

2

2

.

Focusing on the number of satisﬁed PN, neither Φ(a

0

) nor Φ(a

2

) varies, and only

Φ(a

1

) tends to be small when a

0

is reversed, as shown the meshed graphs of Φ(a

1

) in

ﬁg. 3.

Case 2: P N

i

varies drastically: In the case where P N

i

drastically varies, i.e., for

each agent a

i

, and for each need, n

i

x

6= n

i

y

where x, y ∈ {0..R

s−1

}, x 6= y, and

n

k

j

6= n

l

j

where k , l ∈ {0..L − 1}, k 6= l. We ﬁx these values to N

0

= {1, 3, 5}, N

1

=

{5, 1, 3}, N

2

= {3, 5, 1}. Since σ = 1, no p

i

is allowed to satisfy all of agents at the

same time.

In this case, all p

i

converge at the mean value of the allowed range. The satisﬁed

PN also converge at the same value, but Φ(a

i

) of the reversed agents are slightly higher

than those of other agents. These results are just what we expected. Since PN

i

varies

drastically, agents are symmetrical for any reversion.

Case 3: a dictatorial party exists: In the case where a

0

and a

1

establish a dictatorial

party, we ﬁx values of P N

i

to N

0

= {1, 1, 1}, N

1

= {1, 1, 1}, N

2

= {4, 4, 4}.

Figure 4 roughly illustrates the differences in ﬁnal p

i

for the normal case and that in

the ﬁnal number of satisﬁed PN. In this case, both a

0

and a

1

tend to agree/disagree with

the same proposal. Therefore, the needs of a

2

are always ignored. In the normal case,

i.e., no agent is reversed, the result is just what we expected. The dictatorial party (a

0

,

a

1

) wins a great victory and it’s members needs are satisﬁed. The numbers of satisﬁed

needs, Φ(a

0

) and Φ(a

1

), mark almost the maximal value (3.00). On the other hand,

Φ(a

2

) marks almost the lowest value.

90

p1p0 Φ(a0) Φ(a1) Φ(a2)p2

2.90{a0, a1, a2 } 0.000.00 2.90 0.100.00

2.88{a0, a1, a2 }

*

0.01 2.88 0.120.01 0.01

2.67

{a0, a1, a2 }

*

0.08 2.67 0.33

0.08 0.08

2.70

{a0, a1, a2 }

**

0.07 2.70 0.300.07 0.07

2.52

{a0, a1, a2 }

*

0.13 2.52 0.480.13 0.13

2.61

{a0, a1, a2 }

**

0.10 2.61 0.390.10 0.10

2.12

{a0, a1, a2 }

* *

0.26 2.12 0.880.26 0.26

2.28

{a0, a1, a2 }

***

0.21 2.28 0.720.21 0.21

Fig.4. Results of the case 3: (dictatorial party exists).

In the case where the perceptions of more than one agent are reversed, the difference

between the number of satisﬁed needs of the dictatorial party and that of a

2

is slightly

narrower than in the normal case. In particular, when a

0

and/or a

1

have reversed per-

ceptions, the results shift far from the normal case. Even though the absolute values

are small, in the case of {a

∗

0

, a

∗

1

, a

2

}, Φ(a

2

) marks almost nine times the value of the

normal case.

4 Discussion and Conclusions

Game Theory has analyzed the effects of the scale of a community on decision-making,

the effects of personal preferences on the form of community, and so on [7][12]. Among

various approaches, power indices represent the effect (power) of party on a voting

system [7]. The Sharpley-Shubik index, Banzhaf index, and Deegan-Packle index are

known as representative ones. To compare our simulations in cases 2 and 3, power

indices are applied to a community where each of three agents forms its own party,

which consists of the agent alone. Therefore, the “voting weight” of each party is “one,”

and the approval criterion is “more than half.”

In case 2, P N

i

varies drastically, so the interests of agents are symmetrical. The

target of analysis by power indices is each voting, which correspond to a set of “a pro-

posal, voting, and the alteration of P .” Interpreting case 2 as a voting game, the major

power indices have the values shown in Table 1. On the other hand, the experimental

results show that the rate of each Φ(a

i

) against

P

j=0···L−1

Φ(a

j

) has nearly the same

value as power indices shown in Table 1. This comparison implies that, for a commu-

nity in which P N

i

varies as case 2, the satisfaction of each agents can be predicted by

using the power indices.

In case 3, the three indices have the values shown in Table 1. In each index, the dicta-

torial party {a

0

, a

1

} wins perfectly. As shown in Table 1, the rate of each Φ(a

i

) against

P

j=0···L−1

Φ(a

j

) is almost the same as the indices when no communication error is

allowed, i.e., the case of {a

0

, a

1

, a

2

}. On the other hand, these rates drift, especially

in the case of {a

∗

0

, a

∗

1

, a

2

} where both members of the dictatorial party contains mis-

perception. This comparison implies that when a dictatorial party exists static analysis,

91

Table 1. Power Indices and Φ (a

i

) in case 2 and 3.

case 2 case 3

index

a

0

a

1

a

2

{a

0

, a

1

} {a

2

}

Sharpley-Shubik 1/3 1/3 1/3 2/2 0/2

Banzhaf 4/12 4/12 4/12 4/4 0/4

Deegan-Packle 1/3 1/3 1/3 1/1 0/1

Rate of Φ(a

i

) at {a

0

, a

1

, a

2

} 178/532 175/532 179/532 290/300 10/300

Rate of Φ(a

i

) at {a

∗

0

, a

∗

1

, a

2

} 212/300 88/300

such as the use of power indices, is not always applicable. In some cases, the behavior

following the iterated voting process shows some special phenomena.

Remarkable progress has been made in communication technology to overcome the

diverse cases where trivial communication error causes unexpected serious results. This

paper reported that some kind of misperception inﬂuence the ﬁnal result of a “proposal–

voting system” and that the type of misperception makes a difference in the results. In

particular, we investigated three cases: where personal needs vary to a certain degree,

where they vary drastically, and where there exists a dictatorial party.

By following the process of iterated proposals and voting, the proposed framework

of decision-making can show phenomena that cannot be detected by static analysis

methods. We are now planning to extend our simulation to a method for analyzing

phenomena related to decision-making by humans, such as risky shifts, cautious shifts,

and so on.

References

1. Yamaguchi, H.: Social Psychology of Majority Formation Behaviors. Nakanishiya Shuppan

(in Japanese). (1998)

2. Stoner, J.A.F.: A comparison of individual and group decisions involving risk. Master’s the-

sis. Massachusetts Institute of Technology, School of Industrial Management. (1961)

3. http://www.dis.titech.ac.jp/coe/

4. George, J.B.: Nursing Theories, The Base for Professional Nursing Practice. Appleton &

Lange, A Simon & Schuster Company. (1995)

5. Heider, F.: The Psychology of Interpersonal Relations. John Wiley (1961)

6. Sutton, R.S., Barto, A.G.: Reinforcement Learning. The MIT Press (1998)

7. Muto, S., Ono, R.: Game Theoretical Analysis of Voting Systems. Nikkagiren (in Japanese).

(1998)

8. Ueda, H., Tanizawa, T., Takahashi K., Miyahara T.: Acquisition of Reciprocal Altruism in a

Multi-agent System. Proc. of IEEE TENCON2004, (2004). B334.pdf

9. Wesley, R.L.: Director of Nursing. Rehabilitation Institute of Michigan (1998)

10. Nightingale, F.: Notes on Nursing - What it is and what it is not -. Bookseller to the Queen,

London (1860)

11. Nomic A Game of Self-Amendment.

http://www.earlham.edu/ peters/nomic.htm

12. Axelrod, R.: The Complexity of Cooperation: Agent-Based Models of Competition and Col-

laboration. Princeton University Press (1997)

92