Toward Delegated Democracy:
Vote by Yourself, or Trust Your Network
Hiroshi Yamakawa, Michiko Yoshida, Motohiro Tsuchiya

Abstract—. The recent development of Information andCommunication Technology (ICT) enables new ways of"democratic" decision-making such as a page-ranking system,
which estimates the importance of a web page based on indirecttrust on that page shared by diverse group of unorganizedindividuals. These kinds of "democracy" have not been acclaimed
yet in the world of real politics. On the other hand, a large amountof data about personal relations including trust, norms of reciprocity,and networks of civic engagement has been accumulated in acomputer-readable form by computer systems (e.g., social
networking systems). We can use these relations as a new type ofsocial capital to construct a new democratic decision-making
system based on a delegation network.
In this paper, we propose an effective decision-making support
system, which is based on empowering someone's vote whom you
trust. For this purpose, we propose two new techniques: the first isfor estimating entire vote distribution from a small number of votes,
and the second is for estimating active voter choice to promotevoting using a delegation network. We show that these techniques
could increase the voting ratio and credibility of the whole decisionby agent-based simulations.

Keywords— delegation, network centrality, social network,
voting ratio.

V

I. INTRODUCTION

OTING plays an important role in democratic systems. It

is an effective means to reflect the majority's intention
within a limited amount of time. However, it is also true thatvoting is not a perfect solution for making decisions.
The recent development of computer and communication
technologies and the digitalization of information are
producing new ways of "democratic" decision-making. For
example, page-ranking systems by search engines andrecommendation systems of online shopping sites use such"democratic" systems.
In the world of real politics, this kind of "democracy" hasnot been acclaimed yet. A voter still does not want to use acomputerized system to recommend a candidate whose
policy perfectly matches his/her preferences.
Decision-making by delegation networks in organizations
depends on rich social capital. Social capital includes trust,norms of reciprocity, and networks of civic engagement [1].
Hiroshi Yamakawa is with Solution Technology Lab., FUJITSULABORATORIES, 1-1, Kamikodanaka 4-chome, Nakahara-ku, Kawasaki,
Kanagawa,211-8588, Japan, (e-mail: ymkw@jp.fujitsu.com)
Michiko Yoshida is with Economic Research Centre, FUJITSU ResearchInstitute, 11th Fl. New Pier Takeshiba South Tower, 1-16-1 Kaigan,
Minato-ku,
Tokyo
105-0022,Japan(e-mail:michiko.yoshida@jp.fujitsu.com).
Motohiro Tsuchiya is with the Graduate School of Media and Governance,
Keio University, 5322 Endo, Fujisawa-shi, Kanagawa, 252-8520, Japan(e-mail: taiyo@sfc.keio.ac.jp).

As the phenomenon known as Web 2.0 gathers attention,
trends such as blogs (diaries) and social networking services(SNS), where individuals transmit information and share iton the internet, are becoming prominent. SNS can be thoughtof as one example of the utilization of delegation networks inorganizations. In SNS, one can search for a key person who
is knowledgeable in a certain field of study and entrust thatexpert with one’s vote.
Minetaki and Yoshida indicate in the analysis of intranet
social networking services that there exists rich social capital,
and those employees have mutual consideration throughconsequences of communication. Even within a closed
company environment, the visibility of communication
chains among employees from various departments
disseminating knowledge from different domains fosters asense of shared trust [2].
In SNS, users can visit key persons’ pages and find out
what they say in their diaries, as well as their comments madeon other diaries. We assume that key persons are those whohave many networks of contacts (the number of “friends” in
the SNS), comment on various employees’ diaries, and write
appropriate comments as occasion may demand. They arealso unique persons whom many employees pay attention to.
Other employees can visit these key persons’ pages directly
and it may enhance awareness for these employees. Social
capital in social networking services enhances
decision-making.
In this paper, we will propose a new way ofdecision-making with the help of a computerized system. It
is not a fully computer-dependent voting system. It is asystem to empower someone whom you trust, and to makethe whole decision-making process more effective. Somepeople don't take time to vote, because they are not interested
in current agendas or because they have different priorities.
Even so, it is not ideal to make a decision with fewer people's
votes. In our proposal, people give their votes to someone
whom they trust and a computer system monitors whattrusted voters do until the last minute of voting. This system
could raise the voting ratio and credibility of the wholedecision.
It is quite an unusual way in a democratic system to give avote to someone else. It is obvious that such a system isagainst the principle of equality in voting where everyone has
only one ballot. However, our system could minimize
wasted votes, which should not be overlooked in a
democratic system. In our system, people make the best useof their votes by trusting their networks, and they stop
wasting their ballots.

II. OPINION COLLECTION AND CONSOLIDATIONTECHNIQUESIn an ordinary decision-making process, voters vote on
their opinions at the end of discussion. On the contrary, we
assume a different decision-making process. In this process,opinion proposals and voting for them are simultaneously
executed. Each voter can directly vote opinions and/or
delegate to other voters, and can change these attitudes
anytime during decision-making session.
A. Total vote estimator (TVE) using a delegation network
The delegation network is composed of each voter's
declaration of delegating to other voters. Each voter canfreely allocate the delegation rate to any other voters.
Transitivity is assumed on the delegation relations. In aword, "I partially trust someone who is trusted by any otherperson whom I trust." Recursive vote circulation is justified
under this assumption. Each voter can participate in adecision-making not only by estimating opinion, but also bydelegating to any other voters.
For calculating indirect vote to opinions, we propose thetotal vote estimator (TVE) technique by using a delegation
network. Here, the delegation network is composed of N
voters’ node and M opinions’ node. Edges between voters
are a subset of NxN delegation. Edges from voters toopinions are a subset of NxM direct vote.
We introduce LxL delegation matrix which values W (={wij). Each element wij represents delegation or vote fromvoter i to voter/opinion j. So sum of output from each voter
is one. ( ∑ wij = 1 ). Because we think delegation certaintyjdecreases through multiple delegation steps, we assume
vote propagation decay by propagation rate r (0 < r ≦ 1).
Firstly, all elements of L rows flow vector f(t) are
initialized to zero. ( f (0) = (1,...,1)T ). (t is iteration step). Votepropagating calculation process is repeated untilconvergenceconditionissatisfied.
(Condition:max( f i ) < 0.0001 or t>T, T is maximum iteration steps).

f (t + 1) = rWf (t )(1)

Indirect vote vector F is defined as an iteration sum of flow
vectors.
T

F = ∑ f (t )

(2)

t =0

The infinite iteration limit of this vector is proportional toeigenvector centrality (Bonacich's centrality). ( T → ∞ ).
Because one vote was arranged in the initial value on every
opinion, we obtain indirect vote value for opinions bysubtracting one from vector F.
Under this mechanism, voters can freely delegate to any
other voters; it means that any voter can receive delegation
without direct vote to any opinions.
By setting the iteration limit T=1, we can easily obtain

direct vote vector without delegation.
Network sampling is research field related to TVE
technique [3, 4, 5]. For example, the number of drug
addiction patients is estimated by using the friend network.
B. Active voter choice (AVC) using a delegation network
When members of an introvert group delegate to eachother and none of them vote to opinions, the TVE can notestimate an appropriate indirect vote.
We therefore propose the active voter choice (AVC)
technique which picks up powerful voters in a delegation
network. The chairman can effectively grasp various voters'
preferences by concentrating vote promotion on powerfulvoters. Here we propose the greedy voter sampling method
as AVC. This sampling selects powerful voter sequentially,so as to maximize the total indirect vote.
Formally, the vote action of voter i to opinion isrepresented by the change of delegation matrix W. Firstly,
voter i cancels delegation to other voters. Secondly, voter ivotes to opinions according to preference vector yi. Here,
preference vector yi represents the opinions preference ofvoter i.
Here, we call opinion voting voters subset s, and theindirect vote vector corresponding to s is F(s). Then the total
indirect vote is Φ ( s ) = ∑ Fc ( s ) . The variation of Φ byc∈C

adding one voter, who does not vote to opinions yet, isdescribed by the following expressions.

Δi Φ( s) = Φ( s + i) − Φ( s)= ∑ ( Fc ( s + i ) − Fc ( s ))

(3)

c∈C

Here a new subset of votes including newly added voter i
is described as s+i.
This sampling method greedily accumulates total indirect
votes, so that a powerful voter i(s) suitable for votepromotion is selected by this expression.

i ( s ) = arg max Δ i Φ ( s )
i∉s

(4)

If a voter who is promoted by this sampling method could
really vote to opinions, total indirect votes will increase
quickly and the chairman will grasp various voters’
preferences effectively.
To evaluate the basic performance of the AVC technique,we assume that promoted voters always vote to opinions, andvoters do not vote to opinions without promotions.
III. MODELING VOTERS AND DELEGATE NETWORK
A. Model of voters
We assume that opinions are allocated on the one
dimension value spaces v (= [0, 1]).
The preference center of voter i is represented by vi. Thesevi are allocated in value space with a mixture of two beta

As
distribution manners. ( 2 B (1.2, 5.0) + B (5.0,1.2)) / 3 .
shown in figure 1, the largest faction stands at v=0.05 and thesecond faction stands at v=0.95. This distribution ispreserved in all of the experiments in this paper.
There are ten opinions on values space (M=10), and these
opinions are allocated in even intervals (vc = [0.05, 0.15,…,0.95]). Opinion preference vector yi of each voter is
specified by normal distribution around center value vi.

exp( β (vc − vi )2 )yic =∑ c exp(β (vc − vi )2 )(5)

Parameter β is set to 15.7, in experiments, and then the halfband width in the value space is about 0.4.

15

3.rd

centrality: Fagent frequency/

voting counts for all agents

10

6
5

1
1

10
11
3
3

16 4
3
18
17 5
1

7
3

4.th
31
4

37
5
36
2

29302
3

14
3
15 20412
12 192 22
3
9
5 8 2
23
1
1
23
1
41
10

0

2

wi

2

(6)

j∈Ki

Finally, wij is normalized ∑ wij = 1 . Thus, the delegationj

network is constructed from the acquaintance network.
The upper figure of Figure 2 shows one example of thecomposed delegation network. The vertical axis is a numberof indirect votes, and the delegation relations between voters
are described by links without distinguishing direction.

We simulated 50 voters by using the voter model and thedelegation network model. The number of direct votes andindirect votes are calculated for two kinds of voter choices.
Here, propagation rate r=0.8.

35
4

32
4

25
26 27
24 32 28
2
2
1

33
2

34
1

42

38
3

45 5
2 47 49
41 2 2
3
50
1
39 44
2 2
40
2
43 4624812

50

minimize [[y i − ∑ wij y j ] + ε | w i | ]IV. SIMULATION RESULTS

2.nd

5.th
21

0
9

minimize the error between self vote vector yi and a weighted
linear total the vote vector of the acquaintance using
quadratic programming. Here Ki is acquaintance set of voteri, and ε is small positive.

1.st
13
6

5

each voter i selects delegation weights w i (= {wij | j ∈ K i }) to

0.2

0.4

0.6

0.8

1

value axis: v

Figure 1. Example of delegation network in value space.
The 50 voters are arranged on the horizontal value axis. In
the lower figure below, the blue histogram describes the
distribution of voter's value center, and the red line describes
all voters' voting sum. In the upper figure, the vertical axis isindirect votes, nodes are voters, and delegation relation is
described by the link. For each node, ID is described by ablack number and the degree of receiving delegation is
described by a pink number. The first five selected voters areindicated by the red circle.

B. Model of delegates networks
In our acquaintance network model, when voter i knows
the sense of values of voter j, there is an acquaintance relation.
To generate a network, k voters are randomly selected among
the N-1 voters as each voter’s acquaintance. These relations
are asymmetric, so voter i does not always knows voter jwhile voter j knows voter i.
Each voter delegates to his acquaintance, so as toreproduce his sense of values as much as possible. Formally,

Table 1. Four types of experimental setup.
Total vote estimation Indirect vote Direct(TVE))
vectorvote vector
Voter
AVC
Avc-I
Avc-D
choiceRandom
Rnd-I
Rnd-D
For Avc-D, Avc-I, and Rnd-I setups, 100 kinds ofdelegation networks are generated and the result is averaged.
For all setups, 100 kinds of delegation networks are
generated and the result is averaged. For the Rnd-I setup,
three different random voter choice sequences s are simulated
and averaged in each delegate network anymore. For Rnd-D
setup without delegate network, 1000 of different random
voter choice sequences s are simulated and averaged.

A. Evaluation of fairness and costs
We simply assume that decision-making costs are thenumber of voting voters. For evaluating fairness, we
introduce two measures. Firstly, we introduce total vote as ameasure. Φ( s) = ∑ Fc ( s) Secondly, we introduce essentialc∈C

distribution estimation ability (EDEA).
To evaluate the EDEA, we use the logarithm absolute error
between the vote distribution with partial voters Fc ( s ) andthe vote distribution with all voters yic .

e( s) = log ∑ |cFc ( s) ∑ i yic
−
|
Φ( s)
N

(7)

Maximum iteration step T must be large enough for an
indirect vote vector F calculation on equation 2. On the other
hand, T is set to 1 (T=1) for a direct vote vector calculation.

As a standard, logarithm absolute error e(s) using Rnd-D
setup is averaged with 1000 voter sequences. EDEAs arelogarithm absolute error e(s) normalized by former standard.
B. Result 1: Number of acquaintances k is ten (k=10)
An acquaintance network in which each voter has ten
acquaintances is generated.
Basically voters are selected one by one from the voter
who has a larger indirect vote by using the AVC. In thisexample, voter selecting sequence [13, 35, 21, 45, and 32]
does not completely match the order of indirect vote value.
The phenomenon of order changing is derived from thefollowing two mechanisms. For instance, a strong delegation
relation exists from a voter i to a voter j. In the first case, if
voter i voted choices directly, the indirect vote of voter j isdecreasing. In the opposite case, when a voter i alreadyvotes to choice, voter j's vote action to choice is notcontributed to enhance the total indirect vote.
So when there is a strong delegation relation between two
voters, these two voters are not probably selected
simultaneously. We assume that voters who have a similar
sense of values have a delegate relation with each other.
Therefore, voters who have mutually different values tend to
be chosen.
Figure 2 shows an averaged total vote to the number ofvoting voters. By the Rnd-I (random voter choice & indirectvote) setup even 15 voting voters can collect 35 total votes.
By the Avc-I (active voter choice & indirect vote) setup, 10
voting voters can collect 37 total votes, and even four voting
voters can win a majority.
Next, effective EDEA (essential distribution estimation
ability) for assessing the fairness against the number ofvoting voters are shown in Figure 3. Values of EDEA are
also the average of hundreds of simulation trials. By the
Rnd-I setup, 30 voting voters achieve EDEA by over 40
voters in Rnd-D setup. By the Acv-D setup, 10 voting votersachieve EDEA by over 25 voters in Rnd-D setup. In thissetup, EDEA performance is unstable but it does not standout because the graph curve is the average of 100 trials. By
the Avc-I setup, 15 voting voters achieved EDEA by about
45 voters in Rnd-D setup, and even six voting voters can win
a majority. In this setup, a total vote estimator techniquestabilizes the EDEA performance.

voters who do not have similar senses of value, EDEA
performance unexpectedly degrades when each voter has lessthan three acquaintances.

Figure 2. Relation between numbers of voting voters andtotal votes (Number of acquaintances: k=10)
Number of voters N=50. Propagation rates r= 0.80.

Figure 3. Relation between numbers of voting voters andeffective EDEA (Number of acquaintances: k=10)
Number of voters N=50. Propagation rates r= 0.80.

C. Result 2: Changes of Number of acquaintances k(Avc-I)For checking the EDEA performance against the change of
network character, we compare the result of different
numbers of acquaintance k. In Figure 4, we show the EDEA
curve of the Avc-I (active voter choice & indirect vote) setup.
In simulation, the numbers of acquaintance equal {1, 2, 3, 4,
5, 6, 7, 8, 10, 12, 15, 20, 30, and 40}.
By fewer voting voters, the higher the number ofacquaintances are, and the higher the EDEA performancesare. EDEA performances are apparently enhanced wheneach voter has more than five acquaintances. EDEA
performances almost saturate when each voter has more thanfifteen acquaintances. Because each voter delegates otherFigure 4. Relation between numbers of voting voters andeffective EDEA for the different number of acquaintances.
(Avc-I)
Number of voters N=50. Propagation rates r= 0.80.

V. CONCLUSION
We proposed two vote supporting techniques using adelegation network which is based on trust, norms ofreciprocity, and networks of civic engagement. First, total
vote estimator (TVE) technique estimates total votedistribution from a small number of votes by assuming
transitivity relation on delegation network. Second, theactive voter choice (AVC) technique picks up powerfulvoters who are suitable for to target for vote promotion in adelegation network.
To estimate the ability of these techniques, we simulated
the decision-making process using an artificial multi-agent
system. In this simulation, we assumed that 50 voters werearranged in a different position on a one-dimensional value
space. Each voter had ten friends, knew their values andgave the commission of authority to some of them. The voter
was selected one-by-one using the active voter choicemethod, and indirect vote number counting was used forevaluating voting distribution. Six voters using the proposed
method could outperform the half voters, concerning
capability for estimating entire poll results.
These simulations showed that the proposed methods one
to grasp the entire vote distribution from a small number of
powerful voters.
Although voters' attitudes in realdecision-making processes have some differences from thissimulation, we believe this system could potentially increase
the voting ratio and credibility since people delegate tosomeone they trust and monitoring each other by using thissystem.

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[2]

[3]
[4]
[5]

R. D. Putnam, Making Democracy Work: Civic Traditions in Modern
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K. Minetaki, and M. Yoshida, “Service Innovation Generated by
Innovation in ICT --- Blogs/SNSs and Innovation ---The Effect ofBlogs/SNSs as seen from a Survey of Employees,” Fujitsu ResearchInstitute Research Paper, No. 282, 2006.
K. Krippendorff, Content Analysis: An Introduction to Its Methodology,
Sage Pubns, 1980.
M. G. Sirken, “A Short History of Network Sampling,” in Proc. SRMS,
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S. K. Thompson, "Adaptive Web Sampling," Biometrics, vol.62, no.4,
pp.1224--1234, 2006.

Hiroshi Yamakawa (Dr. Engineering)
Physical master's course of Department of Science at The University ofTokyo is completed in 1989. An electronic doctor's course of Department ofEngineering at The University of Tokyo is completed in 1992. I joined
Fujitsu Laboratories in 1992, and then I participate in the national projects
sensor fusion.
After 1994 I joined the Real World Computing project till 2000. I am
engaged in the researches on a neural net, reinforced study, the concept
learning, and bioinformatics, etc.
Now I work for IT core laboratory, Fujitsu Laboratories ltd. I am memberof the Institute of Electronics, Information and Communication Engineers,
Japanese Cognitive Science Society, Japanese Neural Network Society,Japanese taste, smell academic society, Japan tennis society, and Artificial
Intelligence Society.