Prediction of Political Elections from Social Media Postings
Mathematical Model of Hit Phenomena

Akira Ishii1, Yosuke Hayashi1, Hidehiko Koguchi2,3, Shitaro Takahashi4 and Koki Uchiyama5
1 Department of Applied Mathematics and PhysicsTottori University, Koyama, Tottori 680-8554, Japan
2 Perspective Media, 3-6-9 Kakinokizaka, Meguro-ku, Tokyo 152-0022 Japan
3 M Data Co.Ltd., Toranomon, Minato-ku, Tokyo 105-0001 Japan
4 Digital Hollywood University, Sotokanda, Chiyoda-ku, Tokyo 101-0021, Japan
5 Hottolink, Kanda-nishikicho, Chiyoda-ku, Tokyo 101-0054, Japan

it as time-dependent non-equilibrium phenomena. In themathematical model of hit phenomena, we calculate thepurchase intention of each consumers as the result of theeffect of advertisements, direct communication among
consumers and indirect communication or rumor as an
solution of differential equation for time. For the purpose of
the present paper, we apply the similar equation for voteintention.
In this study, we consider the hit phenomena of political
votes with both experimental and theoretical ways. For
experimental viewpoint, we observe daily weblog-postingdata and twitter-posting data for several candidates in each
Japanese political election using the Hottolink Co.Ltd, asocial media monitoring platform vendor in Japan. We also
obtain the daily exposure for each candidate on televisionusing the database presented by M Data Co. Ltd. in Japan.
For theoretical viewpoint, we present here a mathematicalmodel for hit phenomena as microscopic voter model where
we treat the TV exposure as an external force from thecandidate side and the voter to voter interaction as many
body interaction just like many-body theory in solid statephysics. In the present model, equation of voter action ispresented for each voter persons.

Abstract—Using the mathematical model for hit phenomena,
we analyze the political elections in Japan. The mathematicalmodel of hit phenomena is a theory of time-dependent humanhuman interaction based on the many-body theory in physics.
In contrast to the simple measurement of the total number of
posting to weblogs and twitter for each candidate of elections,
we found that the direct communication strength and theindirect communication strength defined in the mathematicalmodel for hit phenomena play significant role in the analysis of
the daily number of posting to weblogs and twitter. The orderof voting for each political elections in Japan can be
reproduced exactly using our model for the Oaka mayor
election in 2011 and the election of the Osaka area of theHouse of Councillors of Japan in 2010.

Introduction
Today, social media becomes very popular so that everysocial activities are affected at least partially from social
media like weblogs, Twitter, Facebook and Google+. For
economic activities, social media should be considered inmarketing. For political activities, the effect of social media
is also considered to be very strong not only the Arab Springin 2010-2011 but many other countries in the world[1,2].
Especially for political elections, the effect of social media isvery significant to predict the result of the elections before
the pol. For the Japanese election we concern, there are somestudies for the correlation between political election andsocial meda[3].
In this paper, we apply the mathematical model for hit
phenomena to analyze the effect of social media to thepolitical elections in Japan. Our approach can be used for theprediction of results of political elections.
The mathematical model of hit phenomena we used here ispresented by one of the author for the prediction of hit
phenomena in entertainment businesses[4-9]. Hit phenomena
in entertainments are very popular dynamical phenomena inreal economics. For analysis of hit phenomena, we consider

Observation of election
We observe three Japanese political elections; Osaka
Mayor election in November 2011 and the election of Osakaand Tokyo prefectural constituencies of the House ofCouncillors of Japan in July 2010. The daily weblog postingdata is monitored by using the social media monitoring
platform "Kuchikomi Kakaricho" of Hottolink for thesethree elections. For the recent Osaka Mayor elections, theTwitter posting is also monitored. For the three elections, theexposure of election candidates on television is monitored byusing the data set presented by M Data.
The data of the weblog posting and the exposure data on
television are collected about one month duration before the

1/7election day. The formal election season for Osaka Mayor
election is 14 days and that for the House of Councillors is
17 days.
We show our observed data for the Osaka Mayor election.
The data for the election of Osaka and Tokyo prefectural
constituencies of the House of Councillors will be used in
the calculated result as comparison. For Osaka Mayor
election in November 2011, the two major candidates are
Toru Hashimoto and Kunio Hiramatsu. Toru Hashimoto was
the Governor of Osaka prefecture. He is lawyer and is very
popular as an entertainer on Japanse television. Kunio
Hiramatsu was the Mayor of Osaka City. Toru Hashimoto
get the election.
Figure 3 Daily Twitter data and TV exposure data for Toru
Hashimoto of Osaka Mayor election. The blue is TV
exposure and the red is the Twitter. The horizontal axis is thedate. The last of the date corresponds to the one day before
the election.

Figure 1 Daily Twitter data and TV exposure data for Kunio
Hiramatsu of Osaka Mayor election. The blue is TV
exposure and the red is the Twitter. The horizontal axis is thedate. The last of the date corresponds to the one day before
the election.
.

Figure 4 Daily weblog data and TV exposure data for Toru
Hashimoto of Osaka Mayor election. The blue is TV
exposure and the red is the weblog. The horizontal axis is thedate. The last of the date corresponds to the one day before
the election.
Figs.1-4, we show the observed daily weblog posting data,
daily Twitter data and the daily exposure data on televisionin Osaka area . The horizontal axis mean the date and the last
day of the horizontal axis is the last day of election season(one day before the vote).
From the data, we found that there is a lot of tweet for
Toru Hashimoto. For weblog, the difference between Kunio
Hiramatsu and Toru Hashimoto is very small. Especially for
the weblog for Kunio Hiramatsu in fig.1, we found thestrong correlation between the daily number of weblog andthe daily TV exposure. Kunio Hiramatsu is not popular in
Twitter as we can find in fig.2. For the weblog, we found thevery stable weblog posting for Toru Hashimoto.

Figure 2 Daily weblog data and TV exposure data for Kunio
Hiramatsu of Osaka Mayor election. The blue is TV
exposure and the red is the weblog. The horizontal axis is thedate. The last of the date corresponds to the one day before
the election.

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Mathematical Modeltime to effect the information to the vote intention to theperson “i” can be described as Dij I j (t ) where I j (t ) is the

Vote Intention
In the mathematical model for hit phenomena [4-9], we use
the equation for the purchase intention. Similarly, we
consider here the vote intention I i ( t ) for each voter i as avote intention of the person “j” and Dij is the coefficient of
the direct communication.
Rumor effect is named as indirect communication where
the person hears the rumor from chats on a street, chats fromthe next table in restaurant, chats in the trains or finds the
rumor in an Internet blogs and Twitter. Let consider that theperson “i” hear the chat between the person “j” and theperson “k”, the strength of the effect of the chat can be
described as D jk I j (t ) I k (t ) . The probability per unit time tofunction for time. We assume here that the vote intention
for the voter i corresponds to the intention of the voter who
want to vote to the candidate in the election.
The equation we use here is the equation for the voteintention as the effect of television exposure, directcommunication and indirect communication. Each effect is
explained below.

affect the chat to the purchase intention of the person “i” isdefined as Qijk D jk I j (t ) I k (t ) where Qijk is the coefficient.
Thus, the indirect communication coefficient can be definedas Pijk = Qijk D jk .

TV exposure
TV exposure of the election candidate in the news program,the new shows and the advertisement on television is thevery important factor to increase the vote intention of thevoter in the society. We consider the exposure effect as anexternal force in the equation of the vote intention as follows,
dI i ( t ) / dt = Cadv A ( t ) + communications (1)Therefore, the direct communication is the two-bodyinteraction and the indirect communication is the three-bodyinteraction. Thus, including the effect of the directcommunication and the indirect communication into theequation (11), we obtain the following equation for themathematical model for hit phenomena,N
N N
dI i (t)= Cadv A(t) + ∑ Dij I j (t) + ∑ ∑ Pijk I j (t)I k (t)
(2)
dt
j≠i
j
k

where A(t) is the length of the exposure of the candidate on
television and Cadv is the strength of the exposure of thecandidate to affect the vote intention. Though the effect of
exposure can be different for each person, we assume here,
for simplicity, that the exposure affects to every persons
equivalently. The effect of political news can be included inthis exposure term additionally.

Because of the term of the indirect communication, thisequation is a nonlinear equation.

Mean field approximation
To solve the equation (2), we introduce here the mean fieldapproximation for simplicity. Namely, we assume that the
every person moves equally so that we can introduce theaveraged value of the individual vote intention.

Communication effect
Usually, the campaign success in the political election isrelated to the spread by word of mouth (WOM). Such WOM
is sometimes very significant effect to the election. Thus,
such WOM effect should be included in the mathematicalmodel of hit phenomena.
The WOM effect can be distinguished into the two types;
WOM direct from friends and indirect as rumor. We namethat the WOM effect from friends is direct communication,
because voters obtain information directly from their friends.
€
The voters should be distinguished into two; the voters who
decide the vote and the voters who have not yet decided. The
decided voter corresponds to the adaptor in marketing theory.
Usually in previous WOM theories [10-13], thecommunications from the adaptor to non-adaptor have been
considered. Here, in this paper, we include also thecommunication between non-decided voters. It is verysignificant for political elections, because many voters fix
their decision to vote in the last of the election campaign
duration. Let consider that the person “i” hear the
information form the person “j”. The probability per unitI=1
∑ I j (t )N j

(3)Thus, the equation (12) is
N
⎤
d ⎡1
1
I i (t )⎥ = +A(t) + ∑ ∑ Dij I j (t)∑⎢dt ⎣ N i
N i j≠i⎦1+ ∑ ∑ ∑ Pijk I j (t)I k (t)
N i
j
k

(4)

Introducing the number of potential voter Np, we obtain the
direct communication term from the person who do not
dicide the vote as follows,

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dI (t )= Cadv A (t )
dt

1
1
1
∑ ∑ Dij I j (t ) = N ∑ N N ∑ Dij I j (t )
N i j
i
j
=

N p − N (t )1
( N p − N (t )) N − N t ∑ D nn I j (t ) (5)
Np
() j
p

+

( N − N ( t )) D I + N ( t ) ( N − N ( t )) D I=

N p − N (t )( N p − N (t )) D nn I (t )Np+

( N − N ( t )) P I + ( N ( t )) ( N − N ( t )) P I

2

+

Np

(9)

yy 2

Np

(

N (t ) N p − N (t )
Np

)P I
2

ny 2

(10)

Thus, the equation (37) with (38) is the nonlinear integrodifferential equation. However, since the handling data isdaily, the time difference is one day, we can solve theequation numerically as a difference equation.

(6)

Calculated Results
Reliable factor
Using the equation (9) and (10), we calculate the voteintention for Japanese political elections where the TV
exposure data presented from M Data is inputted into A(t)with the unit of seconds. The calculated result is comparedwith the daily blog entry counts observed by using the social
media monitoring platform “Kuchikomi Kakaricho” of
Hottolink in Japan. In order to adjust the parameters to fit thecalculation with the observed blog data, the reliability of theadjustment is required.
For the purpose of the reliability, we introduce here the socalled “R-factor” (reliable factor) well-known in the field of
the low energy electron diffraction (LEED) experiment [14].
In the LEED experiment, the experimentally observed curveof current vs. voltage is compared with the corresponding
theoretical curve using the R-factor.
For our purpose, we define the R-factor for our purpose as
follows,(7)
where Dny is the factor of the direct communication
between decided and non-decided voter. For the indirectcommunication, we obtain more two terms corresponding to
the indirect communication due to the communication
between decided voters and that between decided and nondecided voters as follows,( N ( t )) ( N − N ( t )) P I
2

yy 2

Np

Np

p

t

N (t )( N p − N (t )) D ny I
Np

N ( t ) ( N p − N ( t ))

2

nn 2

0

where Pnn is the factor of the indirect communication
between the persons who do not decide the vote at the time t.
For the direct communication between decided and nondecided voters can be written as follows,111∑ ∑ Dij I j (t ) = N ∑ N N ∑ Dij I j (t )
N i j
i
j

+

p

N (t ) = N p ∫ I (τ ) dτ

3

p

ny

p

Np

where

1
1
1
1
∑ ∑∑ Pijk I j (t ) I k (t ) = N ∑ N N ∑ N N ∑ Pijk I j (t ) I k (t )N i j k
i
j
k

⇒

nn

Np

3

where the summation is performed only for the persons who
do not dicede the vote. Dnn is the factor of the directcommunication between non-decided voters at the time t.
Similarly, we obtain the indirect communication term dueto the communication between the person who do not decide
the vote at the time t,3$ N − N (t ) '( N − N (t )) P nn I 2)) N p2 P nn I 2 = p⇒ && p
Np
Np
%
(

p

2

P ny I 2(8)where Pyy is the factor of the indirect communication
between decided voters and Pny is the factor of the indirectcommunication due to the communication between decided
and non-decided voters at the time t.
Finally, we obtain the equation of the mathematical modelfor hit phenomena within the mean field approximation as
follows,(11)
where the function f(i) and g(i) is defined in figure 5. The
smaller R, the function f and g show that better matches.

4/7

Calculation for Osaka Mayor election. The calculation of the vote intention is shown in fig.6 and
7 for Kunio Hiramatsu and Toru Hashimoto. The parameters
we adjust to the daily weblog data is the strength of TV
exposure Cadv , the strength of the direct communication D
and the strength of the indirect communication P. Here weassume that D nn = D ny and P nn = P ny = P yy for simplicity.
For Kunio Hiramatsu, we adjust our calculation to the daily
weblog of the last 10 days of election season. For Toru
Hashimoto, we adjust our calculation to the first high peak ofthe daily weblog. The parameters we obtain are shown in
Table 1.

Figure 5 Example to explain the R-factor

Cadv
D
P

Hiramatsu
2.3
0.003
0.00009

Hashimoto
6.0
0.02
0.0002

Hashimoto Twitter
115
0.00090.00002

Table 1 Parameters of our calculation.
From table 1, we found that every parameters of Toru
Hashimoto are larger than that of Kunio Hiramatsu. Largeparameter means large popularity. Since the Toru Hashimoto
get the election, our obtained value of the strength of TV
exposure, direct and indirect communication are consistent.
House of Councillors election in Osaka
For the election of Osaka and Tokyo prefectural
constituencies of the House of Councillors of Japan in July
2010, there were four major candidates, Ishikawa, Kitagawa,Odate and Okabe. M Okabe is very popular female
entertainer having some regular TV programs. In Table 2,
we show the number of weblog posting for the fourcandidates during the election duration.

Figure 6 Calculation for Kunio Hiramatsu. The horizontal
axis is the date. The last day of the axis is one day before thevote. The blue, the red and the green curve correspond to TV
exposure, the weblog and our calculation.

Candidate
Okabe
Odate
Kitagawa
Ishikawa

number of posting
4424
1254
858
701

Table 2 Total number of posting in House of Councillors
election in Osaka, 2010.
From the table 2, we found that the entertainer Ms Okabecollect a lot of posting. However, the results of election isshown in table 3 that the order of candidate in the real vote iscompletely upside down. Thus, we cannot use the total
number of weblog posting as the key parameters of theelection.

Figure 7 Calculation for Toru Hashimoto. The horizontal
axis is the date. The last day of the axis is one day before thevote. The blue, the red and the green curve correspond to TV
exposure, the weblog and our calculation.

5/7

predict the result of election. The communication strength E
for β = 1 explain the results of the Osaka Mayer election,
Candidate
Ishikawa
Kitagawa
Odate
Okabe

number of votes obtained
864278706986698933617932also.
To confirm it, we perform one more example of theelection, the House of Counsillors election for Tokyo
prefectural constituency. The result of our calculation isshown in table 6. Table 6 show us that the communication
strength E for β = 1 explain the results of the House of

Table 3 Results of the votes of House of Councillors
election in Osaka, 2010.

Counsillors election for Tokyo prefectural constituency.

Renho

Cadv
D
P

Ishikawa
50
0.093
0.00217

Kitagawa
50
0.001
0.00628

Odate
50
0.001
0.0061

Cadv
D
P
E
votes

Okabe
190
0.001
0.001437
0.09
0.0000037
0.0900037
1710734

Taketani
6.8
0.06
0.005
0.065
806862

Nakagawa
5.3
0.008
0.009
0.017
711171

Ogawa
5.9
0.003
0.003
0.006
696672

Table 4 Parameters of model for the vote of House ofCouncillors election in Osaka, 2010.

Table 6 TV exposure strength Cadv, D, P andcommunication strength E for the four candidates of Houseof Counsillors election in Tokyo, 2010.

We perform the same calculation of the vote intention for theHouse of Counsillors election in Osaka. The parameters we
obtain from the adjusting of our calculation to the daily
weblog posting is shown in table 4. From table 4, we foundthat the entertainer Mari Okabe obtain large value for thestrength of TV exposure. However, for the directcommunication strength D, Ishikawa obtain the largest value.
For Kitagawa, Odate and Okabe, the indirect communication
strength values are different though the direct is same.
Therefore, as an assumption, we test the following
communication strength,.

E = D + βP

(12)

the sum of the direct and the indirect communication
strength. If we set β = 1 for simplicity, we obtain table 5.
Candidate
Ishikawa
Kitagawa
Odate
Okabe

Figure 8 Calculation of the vote intention of Ishikawa using
the parameter D and P of Okabe. The blue is the original andthe red is the calculation using Okabe parameters of D and P.

E
0.00950.00720.00710.0024

Discussion
From our results, we found that the communication strength
E defined by eq.(12) is very consistent with the real election
result. For the House of Counsillors election in Osaka. ourresult explain why the famous entertainer Mari Okabe lostthe election. Though she has very large TV exposure
strength, the communication strength is very weak. It meansthat the posting on Mari Okabe did not continued after the
TV exposure. In fig.8, we show the calculation of the vote

Table 5 Communication strength E for the four candidates ofHouse of Counsillors election in Osaka, 2010.

Table 5 agrees very well with table 3, the final results of theelection of the House of Counsillors in Osaka 2010. It meansthat the communication strength E defined by eq.(12) can

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intention of Ishikawa using the parameter D and P of Okabe.
As we can see, the vote intention is clearly different.
For the House of Counsillors election in Osaka, we foundthat the total number of posting has no meaning for the
analysis of elections. Instead, the communication parameter
E we introduced here using the mathematical model for hit
phenomena is significant to predict the political election.
Important point for the actual applicaton of our study forpolitical elections is that the communication parameter E canbe obtained everytime, even before the formal duration ofelection. Thus, our result can be applied to decide thecandidate of each constituency far before the election.

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CONCLUSION[physics.soc-ph]

We present the mathematical model of hit phenomena as an
equation for the vote intention for each voter. We found thatthe communication strength measured from social mediausing our model can be applicable for the analysis ofpolitical and can predict the result of political elections. ourtheory.

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A.Ishii, T.Matsumoto and S Miki, Prog.Theor.Phys. in press;
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