E-Journal of Advanced Maintenance Vol.2 (2010) 149-159
Japan Society of Maintenology

A Prediction Market Approach to Facilitating Consensus Building among
Supply Chain Partners
Hajime MIZUYAMA* and Toshiyuki KOMATSU
Kyoto University, Yoshidahonmachi, Sakyo-ku, Kyoto 606-8501, Japan
ABSTRACT
How to facilitate the process of consensus building among the partners in a supply chain is a crucial issue. As an
example of such a problem, this paper takes up perceptual mapping and develops a prediction market system forcollectively determining the location of an object on a two-dimensional perceptual map. It introduces a new typeof prediction security called SAPS (Square Area Prediction Security) and extends a widely used market making
algorithm LMSR (Logarithmic Market Scoring Rule) for handling SAPS in a batch updating environment. Thissystem feeds the location of the object back to the participants as the price distribution of SAPS, which isdetermined by the number of SAPS sold so far in each square area, and allows them to modify it throughtransactions of SAPS. The paper further conducts laboratory experiments to see whether the proposed system
can support a group of people to build consensus on a perceptual map. As a result, it is observed that thevariance of their subjective evaluations on the location of a specified object is reduced through operating thesystem but that the evolving consensus is not always captured properly by the price distribution. What causes
this problem and how to fix it are also discussed.
KEYWORDS

ARTICLE INFORMATION

collective intelligence, consensus building, Delphi method, perceptual map,
prediction markets

Article history:
Received 17 August 2010
Accepted 17 November 2010

1.

Introduction

In order for a supply chain to compete effectively in today’s changing market, the partnercompanies in the chain should share not only the relevant information on the changing environment
but also the policy/strategy on how they compete in the environment. Such a policy/strategy provides
a direction along which operational and investment decisions, including those on maintenance, of thecompanies can be aligned, and it enables the supply chain to function as a unified whole. Forming theshared policy/strategy is a consensus building problem among the partner companies in the chain. Itshould be deemed as a continual process especially in the changing environment. Further, since thepartner companies are geographically, sometimes globally, distributed and their working hours may bedifferent, the consensus building process is characterized by the difficulty and inefficiency of relying
wholly on face-to-face communication. Thus, how to facilitate the process is now a crucial issue.
Various consensus building processes have been effectively supported by Delphi method [1][2],which repeats the cycle of obtaining an opinion from each partner separately, aggregating the opinions
into a distribution, and feeding the distribution back to each partner. Recently, the prediction market
attracts attention as a mechanism that can realize the Delphi-like interaction efficiently andeconomically. The prediction market is a futures market where participants can buy and sell virtual
securities, called prediction securities, whose posterior worth is defined depending on the future
outcome of the issue of concern, and outputs a forecast on the issue reflecting the collective
knowledge of the participants as the price of the securities [3][4][5]. The prediction market is argued
to be helpful for information sharing in a supply chain [6], and it is actually used successfully inindustry for aggregating information, for example, on a demand forecast [7][8][9].
The aim of this paper is to investigate whether the prediction market can also support consensus
building among the partners in a supply chain. If the prediction market can replace at least some of the*Corresponding author, E-mail: mizu@me.kyoto-u.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

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H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

direct communication necessary for the consensus building process, the efficiency of the process will
be improved. The major difference between simple information sharing and consensus building is thatthe latter needs to ask a question without an objective right answer and thus needs to aggregate
subjective evaluations as well as objective information. As a concrete example of such a problem, thispaper takes up perceptual mapping. It locates the products or service offerings to be compared on amap so that their relative locations should represent how the market perceives the differences among
them. Thus, it can provide an important basis for a shared policy/strategy of a supply chain.
This paper first develops a prediction market system for determining the location of an object on
a two-dimensional perceptual map. In order to consider the location of the object, it introduces a new
type of prediction security called SAPS (Square Area Prediction Security) and extends a widely usedmarket making algorithm LMSR (Logarithmic Market Scoring Rule) for handling SAPS in a batch
updating environment. In the proposed system, the price distribution is determined by the number of
SAPS sold so far in each square area, and the distribution represents the agreed location of the object
at the time. This system can feed the location of the object back to the participants and allow them tomodify the location through securities transactions. It can take the difference and vagueness in theirsubjective evaluations into consideration, and can update the location of the object accordingly
whenever some additional information becomes available.
The paper then conducts laboratory experiments to see whether the proposed prediction market
system can support a group of people to build consensus on the location of an object on a perceptual
map. In the remainder, the proposed market system is presented first, then the laboratory experiments
and their results are described, and they are followed by discussion and conclusions.

2.

Prediction Market System for Perceptual Mapping

2.1.

Perceptual mapping problem

Most methods of drawing a perceptual map, such as factor analysis, principal component analysis,
multidimensional scaling, are static in a sense that they determine the locations of the objects ofinterests on the map based on the data gathered at a time. As a result, the obtained map often fails tosatisfy even those who provided the data. Alternatively, this paper deems perceptual mapping as aconsensus building problem among the multiple partners in a supply chain.
A perceptual map contains multiple objects, and it is their relative locations that need to beagreed upon among the supply chain partners. In this paper, however, only the location of a single
object in a two-dimensional perceptual map is considered as the first step, assuming that those of theother objects are given. Thus, the variable of concern in the proposed prediction market system is theabsolute location (x, y) of the specified object in a two-dimensional space where the other objects are
already located. It is assumed that the feasible region of the location is bounded within a square(−1 ≤ x ≤ 1,−1 ≤ y ≤ 1) .
2.2.

Square area prediction security

As the prediction security for the two-dimensional variable of concern (x, y), we generalize FIPS
(Fixed Interval Prediction Security), which is introduced by Chen and Plott [7] for a scalar variable
such as a sales volume, to a two-dimensional vector and call it SAPS (Square Area Prediction
Security). In SAPS, the feasible region of x is cut into M equal width slices and each of them is cut
again into M equal height pieces along y-axis, as shown in Fig. 1. This divides the whole region of the
map into M × M smaller square areas, and we denote the center of mth square as (xm, ym), where m( ∈ {1,2, K , M × M } ) is the index of a square area. Each piece of SAPS is assigned to one of the squareareas, and if and only if the resultant location is included in the area, it will be given a prefixedamount of payoff after the market is closed.
The number of slices M should be carefully determined in practice. The higher the number ofslices, the more precisely the plausible region of the location can be specified but the moresophisticated user interface and background calculation will be required. In the following laboratory
experiments, it is set as M = 20. Thus, the whole perceptual map is covered by 400 square areas, and150

H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

each participant can choose any combination of them. However, the number of SAPS held isrestricted to be equal for all the chosen square areas, so as to reduce the mental workload of theparticipant.
y(1, 1)

M slices(-1, 1)x
mth square(xm, ym)(-1, -1)(1, -1)
M slices

Fig. 1. Definition of square areas for SAPS

2.3.

Batch updating market making algorithm

In order to ensure enough liquidity in the market of SAPS even when operated with a small
number of participants, a batch updating central market maker is introduced. The market maker offersa price to any bid or ask offer of SAPS. Hence, in extreme cases, even only two participants caninteract through the prediction market system. It is for providing the participants a certain length oftime between transactions of SAPS exclusively for consideration on the location why batch updating
is preferred.
The most popular and widely-used market making algorithm for the prediction market would be
LMSR (Logarithmic Market Scoring Rule) proposed by Hanson [10][11]. Suppose that there are N
participants and participant n has qnm unites of SAPS assigned to the mth square area, where n( ∈ {1,2, K , N } ) is the index of a participant. Then, the whole number of the mth SAPS sold so far to all
the participants is given by:

Qm =

N

∑q

nm

(1)

n =1

LMSR defines a cost function based on Q = (Q1, Q2, …) as:⎤⎡ M ×M
C (Q) = b ⋅ log ⎢ exp(Qm / b )⎥
⎦
⎣ m=1

∑

(2)

where b is the sensitivity parameter. When participant n changes her/his asset position from qn = (qn1,
qn2, …) to q n + Δq n , the cost function determines how much to charge as:

Cost = C (Q + Δq n ) − C (Q)Thus, the unitary price of SAPS corresponding to the mth square area is given by:

151

(3)

H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

Pm =exp(Qm / b )dC (Q)= M ×M
dQm
exp(Qi / b )

(4)

∑
i =1

Since LMSR is a continuous updating market maker, we translate it into a batch updating one to
make it more suitable for perceptual mapping. A straightforward way of this translation would be to
update the value of Q in equation (3) only at the beginning of each round and to fix it during theround no matter what transactions are conducted. Hereafter, we denote the fixed value of Q in round k
as Qk. However, a market maker simply taking this approach can be ripped off easily by a team ofparticipants. That is, obvious arbitrage opportunities against the market maker arise. If theseopportunities are taken, the price distribution will not properly reflect the participants' subjective
evaluations. Thus, we further introduce two additional functions into the market maker to diminish the
problematic arbitrage opportunities.
The first function is cancellation. When participant n sells some pieces of SAPS, their current
price and purchase price are compared and, if the current price is higher, the transaction will betreated as a cancellation and only as much as the purchase price will be refunded. If the purchase priceis higher, on the other hand, it will be treated as a normal selling at the current price. When the piecesof SAPS to be sold are composed of several parts which have been purchased separately, theirpurchase price is evaluated on a last in first out basis. Once this function is introduced, the participants
can increase their wealth only through the posterior payoff to their SAPS. Although this function has aside effect of slightly decreasing the sensitivity of the price distribution, this makes it difficult for theparticipants to rip off the market maker by selling it SAPS at an intentionally raised price.
The second function is stepwise transaction. When participant n wants to change her/his asset
position by Δq n and it contains a part to be sold, then the sold part Δq nS is first processed
separately as described above. Then, this function distinguishes increasing amount and expandingarea and divides the remaining purchased part Δq n − Δq nS into two parts Δq nI and Δq nE
corresponding to these two actions as:

Δq n = Δq nS + Δq nI + Δq nE(5)

Increasing amount means the action of buying some additional pieces of SAPS for the square areas
for which she/he already owns SAPS. Whereas, expanding area indicates the action of buying SAPS
for some other square areas for which she/he has no SAPS at the beginning of the round. The stepwise
transaction function determines the price c (Δq nI + Δq nE ) of these parts in round k by the following
equations:{}+ max{[C (Q + Δq ) − C (Q + Δq )], [C (Q + Δq ) − C (Q )]}

(6)

{
}
+ max{[C (Q + Δq ) − C (Q + Δq )], [C (Q + Δq ) − C (Q )]}(7)

c IE (Δq nI + Δq nE ) = max [C (Q k + Δq nI ) − C (Q k )], [C (Q1 + Δq nI ) − C (Q1 )]
k

n

k

I
n

1

E
n

1

c EI (Δq nI + Δq nE ) = max [C (Q k + Δq nE ) − C (Q k )], [C (Q1 + Δq nE ) − C (Q1 )]
k

n

k

E
n

1

c (Δq nI + Δq nE ) = max[c IE (Δq nI + Δq nE ), c EI (Δq nI + Δq nE )]

I
n

1

(8)

The first term on the right hand side of equation (6) calculates the price for the part of increasing
amount, which is defined as the higher one between the costs calculated under the value of Q in thecurrent round and the initial round. The second term calculates the price for the part of expandingarea similarly, assuming that increasing amount has already been processed. Thus, equation (6)152H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

evaluates the price of Δq nI + Δq nE in two-steps, where the first step determines the price of Δq nI andthe second step calculates that of Δq nE . As is obvious, equation (7) conducts the same evaluation by
reversing the order of the two parts. Finally, equation (8) determines the price c (Δq nI + Δq nE ) as thehigher one between those calculated by the equations (6) and (7). This stepwise transaction function
also makes the price distribution slightly insensitive, but it makes it difficult for the participants tointentionally compress the price of SAPS in some square areas, for example, by buying it in otherareas beforehand.
2.4.

Market session flow

Accordingly, the flow of a market session can be summarized as follows:
Step 0. Set k = 0 and Δq n = (0, 0,K) ( n = 1, 2,K , N ) . Initialize Qk so that it should represent anappropriate prior distribution.
Step 1. Add one to k and update Qk with the following equation:
Q k = Q k −1 +

N

∑ Δq

n

(9)

n =1

Step 2. Apply the stepwise transaction function to any request of SIPS transaction submitted fromthe participants. When round k finishes, go to Step 3.
Step 3. If the value of k has reached the predetermined round limit, end the procedure. Otherwise, goback to Step 1.

3.

Laboratory Experiments

3.1. Experimental objectives

The primary objective of the laboratory experiments is to see whether the proposed system cansupport participants to build consensus on the location of an object on a perceptual map. If this supporting
function is confirmed, it is also studied whether the function is affected by the number of rounds and theavailability of chatting function. Since the proposed system is a batch updating system, each experimental
term consists of several rounds and the price distribution is renewed after every round. The number ofrounds specifies how many times the price updating cycle is repeated until the supporting function isevaluated. The effect of the number of rounds on the supporting function is related to the efficiency of
the function. Whereas, when chatting function is available, the participants can exchange comments
through it. Thus, the effect of its availability on the supporting function investigates whether the
proposed system encourages constructive or disruptive discussion among the participants.
3.2. Experimental outline

The perceptual map dealt with in each experimental term is concerned with a certain productcategory and includes ten currently available products in the category. Since the proposed system at
the moment can deal with the location of only one of the products, those of the other nine products
should have been set in advance. Thus, we rely on principal component analysis for locating the nine
products as a last resort. The participants are given a same table which shows some technicalspecifications of the ten products as related information1, and they are requested to evaluate theproducts in several aspects using a five level likert scale before starting the market session on the
products. The obtained evaluation scores are averaged over the participants and principal component
analysis is applied to the averaged scores. Then, the scores of the first and second principal
1

The technical specifications on the table can be deemed as an example of the objective information. All theparticipants have been provided the same objective information in the experiment.

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H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

components are used to determine the locations of the nine products on the map.
In the corresponding market session, the location of the remaining one product is speculated onby the participants. Here, what we are interested in is whether the participants can agree on thelocation rather than whether they can find the predefined answer of it. Hence, the resultant location of
the remaining product is determined independently of its principal component scores as follows: Ineach experimental term, two parallel markets, Market 1 and Market 2, are run on the same theme. The
participants are randomly assigned to one of the markets and they cannot see any information on theother market during the market session. After a final round of the term, the resultant location of theobject in a market is defined by the expected value taken with respect to the price distribution of theother market.
This parallel market approach can mitigate the problem of Keynesian beauty contest, whichappears whenever applying the prediction market to an issue without an objective right answer.
3.3. Experimental design

The laboratory experiments are composed of eight terms. The profiles of the terms are shown
below in Table 1. The experiments include two control factors, Round and Chatting. Round specifies
the number of rounds and its levels are two and five. Chatting distinguishes whether the participants
can exchange comments through chatting function during the corresponding market session. When its
level is on, chatting function is activated, and otherwise, it is not. The experimental terms are
conducted in the order of the term number shown in the table. Since it was not clear before starting
the experiments whether all of the eight terms and a couple of testing terms can be finished within thelimited time, we determined to conduct the five round terms first so that at least the data on theseterms can be obtained. This means that Round is confounded with the potential learning effect. So thefour terms of five rounds, and those of two rounds as well, are divided into halves, and whether theterm is included in the first half or the second one is treated as a block factor in order to handle thepossible learning effect.
Table 1 Profiles of experimental terms
Term
1
2
3
4
6
5
8
7

Product
Range
Note PC
Clothes washer
Air conditioner
Cell-phone
Blu-ray recorder
Desktop PC
Video camera

Round
5
5
5
5
2
2
2
2

Chatting
On
Off
On
Off
On
Off
On
Off

Block
1st
1st
2nd
2nd
1st
1st
2nd
2nd

The number of participants was twelve until term 6 and it was reduced to eleven in terms 7 and 8,
but all the terms have been conducted. The participants are endowed with P$2000 (Prediction Dollars)at the beginning of each experimental term and they are supposed to trade SAPS with this virtualmoney. They are prohibited from short selling SAPS as well as the virtual money. Each round lasts
two minutes. After the final round, the proposed system determined the square area including theresultant location as described earlier. If a participant has SAPS corresponding to this square area,
she/he will be given P$1000 per share as the payoff, otherwise, the payoff will be nothing. The actual
fee paid to each participant for each term is set proportional to her/his posterior wealth of the termwith preset upper and lower bounds.
The value of the sensitivity parameter of LMSR is set as b = 100 according to some preliminary
experiments.
3.4. Evaluation measures

Before and after the market session of every experimental term, each of the participants isrequested to identify a square area which, she/he thinks, will include the resultant location. The

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H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

answers are hidden to the other participants. If the proposed market system actually supported theparticipants to built consensus on the location, the variance of the answered locations will be reduced
through the market session. Thus, we define a measure F1 for evaluating the supporting function as:∑ [ (x − x ) + (y − y ) ]
N

2

1, n

n =1
N

F1 =

∑ [ (x
n =1

2

1, n

1

1

− x 0 ) + ( y 0, n − y 0 )
2

0,n

2

(9)

]

where N is the number of participants in the corresponding market, (x0,n, y0,n) and (x1,n, y1,n) are thecenter of the square area that participant n choose before and after the market session, and ( x0 , y 0 )and ( x1 , y1 ) are the averages of them taken over the participants, respectively. When F1 is smaller
than 1.0, we can see that the variance of the answered locations is reduced through the market session.
We also define another evaluation measure F2 based on the price distribution, because thevariance of the price distribution will be decreased through rounds if the supporting function of the
proposed system gradually leads the participants to a consensus. We define this measure as:∑ P [ (x − x ) + ( y − y ) ]

M ×M

2

F ,m

m

2

F

F2 = Mm =×1M

m

F

(10)

∑ P [ (x − x ) + ( y − y ) ]
2

I ,m

m

2

I

m

I

m =1

where PI,m and PF,m are the price distributions after the initial round and the final round, and ( x I , y I )and ( x F , y F ) are the expectations of (x, y) with respect to the distributions, respectively. When F2 issmaller than 1.0, we can see that the variance of the price distribution is reduced through rounds.
3.5. Results and discussion
3.5.1. Results overview

Variance
Prior

1st

2nd

Posterior

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Variance

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Figure 2 a) and b) show how the variance of the participants’ evaluations changes over market
rounds. The prior and posterior evaluations are directly asked to each participant as described earlier,but her/his evaluation in each round itself is not clear. Hence, the center point of her/his whole chosensquare areas is treated as a surrogate. There are four two-round terms as well as five-round terms, andeach term has two markets. Thus, eight values are obtained for each variance, and they are represented
by a box plot. We can visually confirm that each figure shows a decreasing trend. Further, it is alsointeresting that the variance seems to reach its minimum value in the second or third round and theminimum value seems to be smaller than the variance of the posterior evaluations, and that theprocess seems to exhibit not only the decreasing trend but also a slight fluctuation. However, sincefurther data will be required to properly study these points, this paper does not go into them in theremainder.

Priora) 2-round terms

1st

2nd

3rd

4th

b) 5-round terms

Fig. 2. How variance of evaluations changes over rounds

155

5th Posterior

0.4
0.0

0.0

0.1

0.1

0.2

0.3

Variance

0.3
0.2

Variance

0.4

0.5

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0.6

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H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

Prior

1st

2nd

Posterior

Prior

1st

a) 2-round terms

2nd

3rd

4th

5th Posteriorb) 5-round terms

Fig. 3. How variance of price distribution changes over rounds

0.0

0.1

0.2

0.3

0.4

0.5

-0.1

0.0

0.1

0.2

0.0
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5 rounds–chatting off-2nd

-0.4

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Prior evaluation

-0.2

-0.1

0.0

0.1

-0.4

-0.3

-0.2

-0.1

0.0

0.1

2 rounds–chatting off-2nd

Market rounds

Fig. 4. How mean of evaluations moves over rounds

156

-0.3

2 rounds–chatting off-1st

0.2

0.0
-0.2

0.1

2 rounds–chatting on-1st-0.5 -0.4 -0.3 -0.2 -0.1

0.4
0.3
0.2
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5 rounds–chatting on-2nd-0.4 -0.3 -0.2 -0.1
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-0.2 -0.1-0.2 -0.1

0.0

0.0

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0.2

0.2

-0.5 -0.4 -0.3 -0.2 -0.1

0.3

0.0

Figure 3 a) and b) are intended to represent the same process in terms of the price distribution. It
is understandable that the variance of the price distribution tends to take a higher value than that of theprior or posterior evaluations, because the former contains not only the variation among theparticipants but also that within each participant. However, it cannot be overlooked that no clear
decreasing trend can be observed for the variance of the price distribution over rounds in the figures.
This point is revisited in 3.5.2 quantitatively through examining evaluation measure F2.
Figure 4 shows the trajectory of the equally-weighted mean of the participants’ evaluations,which are defined above, for each market of every term. It seems from the figure that the interaction
among the participants through the proposed prediction market system not only reduces the varianceof their subjective evaluations but also moves the mean of them, that is, what the interaction does is
not just averaging the evaluations.
Figure 5 represents the trajectory of the mean of the price distribution for each market of every
term. Although each trajectory in figure 5 is similar to the corresponding one in figure 4, the former is,in general, more winding than the latter. Further, the intermediate points of each trajectory in figure 5
seem to be dragged toward the center of the map (0, 0). This is found to be due to the exponentialfunction appears in equation (4). It assigns a non-zero price to even a square area for which no SAPS
has been sold so far, and its effect drags the mean to the center. Further, when used in a batch
updating environment, the exponential function sometimes drastically changes the price distribution
between rounds, and it also makes the trajectory sensitive.

Posterior evaluation

0.0

0.1

0.2

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0.5

-0.1

0.0

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H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

-0.4

-0.3

-0.2

-0.1

0.0

2 rounds–chatting on-2nd
Prior evaluation

-0.4

-0.3

-0.2

-0.1

0.0

0.1

2 rounds–chatting off-2nd

Market rounds

Posterior evaluation

Fig. 5. How mean of price distribution moves over rounds

3.5.2. Resultant values of evaluation measures

The obtained values of F1 are shown in Table 2. The values in the table are smaller than 1.0
excepting that of Market 1 of term 3 treating cloth washers. Further, the null hypothesis that the
population value of F1 is equal to or greater than 1.0 is rejected with a p value of 0.26 × 10 −4 . Thus,
we can judge that the proposed system has a significant supporting function in terms of F1, that is, thesystem supports the participants to built consensus on the location at least inside of their minds. As an
outlier, the value of F1 of Market 1 of term 3 was abnormally higher than those of the other cases.
Studying the comments exchanged through chatting function in the market reveals that this wascaused by a participant's proposal to the other members to intentionally sell all SAPS at hand in the
fourth round. This might be intended to find some arbitrage opportunities, but it seems to have failed
in vain and the same proposal was not seen after this term.
Table 2 Resultant values of F1
Round
5
5
5
5
2
2
2
2

Chatting
On
Off
On
Off
On
Off
On
Off

Block
1st
1st
2nd
2nd
1st
1st
2nd
2nd

Market 1
0.64
0.54
1.51
0.37
0.82
0.63
0.40
0.06

Market 2
0.58
0.27
0.62
0.08
0.73
0.36
0.06
0.32

Table 3 shows the obtained values of F2. Some values in the table are greater than 1.0 and theothers are smaller than 1.0. This time, the same null hypothesis on F2 cannot be rejected, since its pvalue is 0.79. This means that the consensus evolved in the participants' minds is not properly
represented by the price distribution. As the outlying case described above implies, the supporting
function in terms of F1 is not independent of the price distribution. Hence, this problem should be
resolved in order to further refine the function. In addition to the effect of the exponential function inequation (4) described earlier, we suspects that this problem is also caused by the restriction imposed

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H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

on the numbers of SAPS. In the experiments, the participants are not allowed to hold different
numbers of SAPS for different square areas. This restriction is aimed at enhancing the operability ofthe simple prototype GUI for the participants. Thus, sophisticating the GUI as well as the market
maker will be necessary. If more degree of freedom can be provided for them to form their assets
through the GUI without requiring much mental workload, the price distribution will also become
more flexible.
Table 3 Resultant values of F2
Round
5
5
5
5
2
2
2
2

Chatting
On
Off
On
Off
On
Off
On
Off

Block
1st
1st
2nd
2nd
1st
1st
2nd
2nd

Market 1
1.62
0.80
1.56
0.95
1.14
0.98
0.99
0.85

Market 2
1.16
1.32
0.84
0.86
1.41
0.69
0.70
1.11

3.5.3. Factorial effects on evaluation measures

Next, analysis of variance is applied to F1 and F2. Tables 4 and 5 show the results. The main
effects of Round on both F1 and F2 do not seem so significant. This means that the level of consensus
achieved in the experiments can be reached with only two rounds. However, if the problem of GUI
described above has been resolved and the price distribution has become more flexible, a higher levelof consensus may become achievable and more rounds may be required for it.
Table 4 ANOVA table for F1
Round
Chatting
Block
R:C
Residuals

Df
1
1
1
1
11

Sum Sq
0.094
0.474
0.082
0.131
1.145

Mean Sq
0.094
0.474
0.082
0.131
0.104

F value
0.904
4.557
0.790
1.257

P(>F)
0.362
0.056
0.393
0.286

F value
1.313
2.930
1.330
0.337

P(>F)
0.276
0.115
0.273
0.574

Table 5 ANOVA table for F2
Round
Chatting
Block
R:C
Residuals

Df
1
1
1
1
11

Sum Sq
0.098
0.219
0.099
0.025
0.820

Mean Sq
0.098
0.219
0.099
0.025
0.075

The main effect of Chatting on F1 is significant at 90% confidence level, and that on F2 has arelatively small p value. Thus, we can judge that the availability of chatting function has some effects
on the level of consensus achieved, and the effects may be intermediated by the price distribution. A
significant part of the exchanged comments was found to be related to the SAPS to hold and/or the
price distribution. Hence, it seems that the proposed market system provides a shared context for
discussion. Studying the main effect of Chatting on F1 in detail shows that the chatting function wasused disruptively in the experiments. A typical example is the outlying case of Market 1 of term 3
described earlier. The participants in a market looked for any arbitrage opportunities against themarket maker as a team using the chatting function. This means that, even though it is in an

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H. MIZUYAMA, et al./ A Prediction Market Approachto Facilitating Consensus Building among Supply Chain Partners

unfavorable form, cooperation among the participants appeared. When they have fully understood that
there are no arbitrage opportunities against the market maker, the form of the cooperation may bechanged into a productive one.
The main effects of Block on F1 and F2 were also not significant, but again we should not simply
conclude that there is no learning effect of the proposed system. Rather, we suspect that theparticipants are still in the early phase of learning. This is why they are looking for arbitrage
opportunities which do not actually exist. However, it is not clear only from the experimental results
how many preparatory sessions will be required for first-time uses to become able to properly interact
through the system. Further, it will depend on, among others, the GUI design. Thus, ongoing researchshould deal with these issues.

4. Conclusion
This paper proposed a prediction market system for supporting geographically distributed supply
chain partners to collectively determine the location of an object on a perceptual map. It utilizes a
newly introduced prediction security called SAPS and an original market making algorithm suitable
for the security type. The paper also conducted laboratory experiments to show how the proposedsystem works. As a result, it is observed that this system can support consensus building on thelocation, but the price distribution does not always represent the evolving consensus properly. Thus, itis necessary to refine the GUI as well as the market making algorithm in order to resolve the problem.
Further, it is also found that the performance of the system was affected by the availability of chatting
function, but the function was used disruptively rather than constructively. Hence, how to motivate
the participants to use the function constructively should also be studied. It is also important togeneralize the system so that it can handle the locations of multiple objects at the same time.

Acknowledgement
This research is supported by a Grant-in-Aid for Creative Scientific Research 2007-2011(19GS0208) funded by the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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