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Manipulation in Conditional Decision Markets


Abstract and Figures

Conditional decision markets concurrently predict the future and decide on it. These markets price the impact of decisions, conditional on them being executed. After the markets close, a principal decides which decisions are executed based on the prices in the markets. As some decisions are not executed, the respective outcome cannot be observed, and the markets predicting the impact of non-executed decisions are void. This allows ex-post costless manipulation of such markets. We conduct two versions of an online experiment to explore scenarios in which a principal runs conditional decision markets to inform her choice among a set of a risky alternatives. We find that the level of manipulation depends on the simplicity of the market setting. When a trader is alone, has the power to move prices far enough, and the decision is deterministically tied to market prices or a very high correlation between prices and decision is implied, only then manipulation occurs. As soon as another trader is present to add risk to manipulation, manipulation is eliminated. Our results contrast theoretical work on conditional decision markets in two ways: First, our results suggest that manipulation may not be as meaningful an issue. Second, probabilistic decision rules are used to add risk to manipulation; when manipulation is not a meaningful issue, deterministic decisions provide the better decision with less noise. To the best of our knowledge, this is the first experimental analysis isolating the effects of the conditional nature of decision markets.
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Group Decis Negot
DOI 10.1007/s10726-017-9531-0
Manipulation in Conditional Decision Markets
Florian Teschner1·David Rothschild2·Henner Gimpel3
© Springer Science+Business Media Dordrecht 2017
Abstract Conditional decision markets concurrently predict the future and decide on
it. These markets price the impact of decisions, conditional on them being executed.
After the markets close, a principal decides which decisions are executed based on
the prices in the markets. As some decisions are not executed, the respective outcome
cannot be observed, and the markets predicting the impact of non-executed decisions
are void. This allows ex-post costless manipulation of such markets. We conduct
two versions of an online experiment to explore scenarios in which a principal runs
conditional decision markets to inform her choice among a set of a risky alternatives.
We find that the level of manipulation depends on the simplicity of the market setting.
When a trader is alone, has the power to move prices far enough, and the decision
is deterministically tied to market prices or a very high correlation between prices
and decision is implied, only then manipulation occurs. As soon as another trader is
present to add risk to manipulation, manipulation is eliminated. Our results contrast
theoretical work on conditional decision markets in two ways: First, our results suggest
Electronic supplementary material The online version of this article (doi:10.1007/s10726-017-9531-0)
contains supplementary material, which is available to authorized users.
BFlorian Teschner
David Rothschild
Henner Gimpel
1Karlsruhe Institute of Technology (KIT), Englerstr. 14, 76131 Karlsruhe, Germany
2Microsoft Research, 1290 Avenue of the Americas, New York, NY, USA
3University of Augsburg, Universitaetsstr. 12, 86135 Augsburg, Germany
F. Teschner et al.
that manipulation may not be as meaningful an issue. Second, probabilistic decision
rules are used to add risk to manipulation; when manipulation is not a meaningful
issue, deterministic decisions provide the better decision with less noise. To the best
of our knowledge, this is the first experimental analysis isolating the effects of the
conditional nature of decision markets.
Keywords Market design ·Market manipulation ·Conditional markets ·Prediction
markets ·Decision markets
JEL Classification C9 ·D8 ·G1
1 Introduction
Modern information systems increasingly facilitate organizations to engage in partic-
ipatory processes that harness collective intelligence by running prediction markets,
for example. Prediction markets incentivize experts to reveal information and prove
remarkably potent and robust as information aggregation mechanisms; frequently,
they outperform other information aggregation mechanisms (Berg et al. 2008;Led-
yard et al. 2009;Teschner et al. 2011;Bennouri et al. 2011). Canonically, markets have
contracts that are worth $1 if true and $0 if false; with enough investors maximizing
their return within the market, the market price is highly correlated with the probability
of the outcome occurring (Wolfers and Zitzewitz 2006). Hence, many organizations
endorse prediction markets—in a survey among 2609 entrepreneurs and employees,
9% reported to use prediction markets (Bughin et al. 2013). Corporate prediction mar-
kets are, for example, used to forecast product development performance, company
or industry news, demand, and sales. While the crowd is used to gather and aggregate
information and make predictions about the future; the final decision typically remains
with a principal, e.g., the management board.
Prediction markets used as decision making tool are termed conditional decision
markets or just decision markets (Hanson 1999;Berg and Rietz 2003). Such markets
have a key difference to prediction markets: they both predict and decide the future
(Chen et al. 2011). In decision markets, predictions need to be conditional on the
decision being executed. Some decisions are not executed and, hence, the respective
outcome cannot be observed. Markets for the non-executed decisions are void (Oth-
man and Sandholm 2010;Chen et al. 2011). Behavior in markets that are void has no
financial impact for the respective expert. Thus, decision markets allow for ex-post
costless manipulation. Othman and Sandholm (2010) prove that experts can bene-
fit from manipulating such conditional decision markets when the principal decides
deterministically based on the markets’ prediction.
We consider settings where the principal must make a choice over possible decisions
to execute, where the possible decisions will impact the probability of achieving a
desired outcome. The principal has access to experts who possess private information
on the probability of the outcome conditional on the possible decisions. An illustrative
example based on Chen et al. (2011); consider a project manager deciding whether to
hire developer A or B for her team. The objective is to finish the project on time, which
Manipulation in Conditional Decision Markets
might be unequally likely for the two candidates. Assume the manager has access to
knowledgeable experts, e.g., former colleagues of the two developers. To inform her
decision, she invites the experts to participate in two decision markets: one predicting
the likelihood to finish in time should developer A be hired, the other should B be hired.
Assume developer B is hired. Then the manager can observe the development of the
project and reward experts based on their accuracy in predicting the likelihood given
B. She will never know what would have happened with developer A. Hence, market A
is void. Now assume, sometime before the markets are closed, the markets’ prices are
$0.60 for finishing in time given the recruitment of A and $0.80 given B (correlating to
60% for A and 80% for B) and an expert has the belief that the efficient prices would be
$0.70 and $0.80 (correlating to 70% for A and 80% for B). In either case—following
the current market prediction or the single expert—B should be hired. This decision
does, however, not yield a financial benefit for the expert in question, as he cannot
improve the prediction given the recruitment of B. On the other hand, he can correct
market A to $0.70 and manipulate market B to below $0.70. With this, the manager
will hire A, the expert expects a positive profit from trading in A, and manipulation
in market B is costless, as it becomes void. Such behavior is termed “manipulation”,
because it leads to a decision that does not confirm the expert’s beliefs.
Two features are required for this manipulation incentive to occur with decision-
agnostic experts. First, markets need to be conditional (i.e., not all markets are
executed) so that there is the possibility that manipulation can be costless. Second, the
price of the markets needs to have an effect on which market is executed and which
is void. Othman and Sandholm (2010) and Chen et al. (2011), among others, study
such conditional decision market settings theoretically for fully rational, risk-neutral,
self-interested, expected-utility-maximizing experts.
To complement this theoretical perspective, we study conditional decision markets
empirically in two online experiments. We create a decision task, recruit and instruct
participants, train them on our market, and weed out potential participants who do
not understand the market. We then turn participants who proved having understood
the experimental setup into experts by providing them information and allowing them
to trade in decision markets for eight rounds. In Experiment 1, participants solely
interact with a market maker and in Experiment 2 they interact with a market maker
and one fellow trader. Each participant is randomly assigned to one of four treatments
where treatments differ by the decision rule applied. With this, we study how and when
participants manipulate the markets depending on to experimentally controlled factors,
the changing quantity of traders and the decision rules. Our experiment sheds light
on the extent and influence of manipulation on information aggregation and decision
quality. The contribution of our work is that we study informed manipulators in very
stylized conditional decision market settings and provide the first empirical evidence
that the issue is not substantial.
Our experimental results show that manipulation impairs information aggregation,
however, only to a very limited extent. The extent of manipulation depends on the deci-
sion rule—manipulation disappears as the correlation between the market prices and
the decision disappears. While manipulation in conditional decision markets occurs in
highly stylized settings, our data suggest that it does not in the commonly used prac-
tice of running decision markets. As soon as another trader is present to eliminate the
F. Teschner et al.
guarantee of last move, manipulation is eliminated. While theoretically a probabilistic
decision rule should preclude manipulation, we find no evidence for this in our data.
Rather on the contrary, a probabilistic decision rule leads to more incorrect decisions
than a deterministic one. We note the difficulties in generalizing experimental work to
the real world, but understanding those considerations these results add to the knowl-
edge base of market design research; designers can draw on these insights and apply
them to future corporate decision markets.
2 Related Work
Scoring rules are well known as incentive compatible mechanism to elicit a single
expert’s belief in the probability of an outcome (McCarthy 1956;Savage 1971;Gneit-
ing and Raftery 2007). In recent years the application of this traditional mechanism
has been extended by adding two levels of strategic complexity.
1. Multiple experts Hanson (2003,2007) and Pennock and Sami (2007)extended the
notion of single-expert scoring rules to scoring rules sequentially shared among
multiple experts.
2. Decisions Othman and Sandholm (2010)formalized the strategic interaction of
experts with the principal when the event upon which predictions are conditioned
is not random but its realization is decided by the principal.
These two levels of strategic complexity lead to overall four settings—each of which
has been studied theoretically.
Single expert, random event (Scoring rule) Facing a proper scoring rule, a sin-
gle fully rational self-interested risk neutral expert maximizes expected utility by
truthfully revealing his belief (Chen et al. 2011;seeHanson 2003, p. 109 for a brief
review on scoring rules). The same holds true for a set of parallel, unconditional
elicitations. In a more complex setting, the principal might be interested in elicit-
ing the probability of an outcome conditional on an event. With a random event
(not to be influenced by either the principal or the expert), this can be reduced
to eliciting the beliefs regarding the joint probability distribution of events and
outcomes—again, scoring rules are incentive compatible.
Multiple experts, random event (Market scoring rule) A scoring rule sequentially
shared by multiple experts is myopic incentive compatible (Hanson 2003). An
expert interacting with the scoring rule only once or for the last time maximizes
expected utility by truthfully revealing his belief. An expert with foresight and
multiple interactions with the sequentially shared scoring rule can, however, benefit
from delaying his revelation or bluffing his fellow experts (Dimitrov and Sami
2008;Chen et al. 2010). An alternative interpretation of a sequentially shared
scoring rule is seeing it as prediction market with an automated market maker
(Hanson 2003). With this, market scoring rules tie into the large body of literature
on prediction markets, e.g. based on continuous double auctions or pari-mutuel
Single expert, decision (Conditional scoring rules) Othman and Sandholm (2010)
were the first to formalize the incentive problem when a single expert knows that
Manipulation in Conditional Decision Markets
the principal will decide based on the expert’s prediction which in turn affects
which of the scoring rules is payoff relevant for the expert. The principal’s most
natural decision rule is deciding in favor of the alternative where the expert predicts
the highest likelihood of achieving the outcome desired by the principal. Othman
and Sandholm (2010) call this decision rule the ‘max decision rule’ and prove
that no symmetric scoring rule nor any asymmetric scoring rule from literature is
incentive compatible.
Randomness can result in incentive-compatibility, as e.g. seen in voting mecha-
nisms (Gibbard 1977;Wagman and Conitzer 2008). Chen and Kash (2011) apply
this idea to single expert with conditional scoring rules and prove that with a prob-
abilistic decision rule incentive compatibility is restored. This comes, however,
at the cost of the principal knowingly taking a sub-optimal decision with positive
Multiple experts, decision (Conditional decision markets) Incentive compatibility
of single expert, random event scoring rules is challenged by both the existence of
multiple experts and the payoff being conditional on the principal’s decision. Not
surprisingly, with a deterministic decision rule, no (known) market scoring rule is
incentive compatible, not even myopic incentive compatible; an expert rather ben-
efits from exaggerating the success probability of a suboptimal decision (Othman
and Sandholm 2010;Chen and Kash 2011). The intuition: as markets predicting
based on counterfactuals are void, experts deterministically know that manipu-
lation in markets which are void is costless. They use this costless manipulation
to steer the decision in a direction that increases their expected gains from trade.
Myopic incentive-compatibility can, however, theoretically be achieved with a
probabilistic decision rule that makes experts indifferent between their gains from
manipulation and the expected costs of manipulation (Chen et al. 2011).
In summary theory suggests that conditional decision markets are strategically
complex. First, experts can benefit within a single market by delaying trade or bluff-
ing fellow traders. There is no full characterization of equilibrium behavior by fully
rational risk neutral decision-agnostic experts (not to mention a relaxation of these
assumptions). Second, with a deterministic decision rule they can benefit from strate-
gically manipulating the principal’s decision. A probabilistic decision rule annuls this
incentive and should, consequently, result in the same accuracy of prediction as market
scoring rules either predicting conditional on random events or unconditional market
scoring rules. Thus, we study four settings that cover all of these key alternative sce-
narios, we denoted them as: DETERMINISTIC, PROBABILISTIC, RANDOM, and
All of the above holds for decision-agnostic experts. Recently, several papers ana-
lyzed experts having a vested outside interest in the principal’s decision (Dimitrov
and Sami 2010;Gimpel and Teschner 2013a,b). Empirical evidence on the issue of
users maximizing their outside vested interest relative to the market’s price is mixed.
Hanson et al. (2006) find that manipulators are unable to distort price accuracy. Rhode
and Strumpf (2006) show that markets with many users confined to limited amounts
of wealth are very hard to manipulate. In addition, Rothschild and Sethi (2013), argue
that principals do not rely just on the final price, but the trading as well. Hence, it is
F. Teschner et al.
relatively easy to identify manipulation strategies. On the contrary, Deck et al. (2013)
present experimental data on manipulation being successful and market observers
being tricked by manipulation. Similarly, Gimpel and Teschner (2013b) present data
on manipulation in experimental conditional decision markets where experts have an
outside incentive to manipulate the decision. The present paper is, however, restricted
to decision-agnostic experts to isolate the effect of conditional markets.
More generally, on the empirical side, research on prediction markets suggests that
prediction markets generally aggregate dispersed information well; typically better
than other information aggregation and prediction mechanisms (Berg et al. 2008;
Ledyard et al. 2009;Teschner et al. 2011;Bennouri et al. 2011). Market scoring rules
tend to be easy to use and produce reliable predictions (Healy et al. 2010;Jian and
Sami 2012). Overall, empirical evidence suggests that prediction markets are by and
large robust to manipulation (Rhode and Strumpf 2006;Deck et al. 2013). To the best
of our knowledge, however, behavior in conditional decision markets has not yet been
studied empirically.
3 General Design and Procedures
The experiments compare information aggregation and market outcomes in stylized
conditional decision market settings. There are two binary lotteries represented by two
urns, A and B, holding 100 balls each. Per urn, 32 or 68 of these are black, the others
white. A principal—who will draw one ball from one of the urns—is interested in
drawing a black ball. She decides which urn to draw from, the draw itself is random.
The principal does not know the number of black balls in either of the urns. To gain
information prior to deciding, she runs two parallel prediction markets for experts to
share their private information: One market for urn A and one for B. The market price
is assumed to reflect the aggregate prediction of the probability to draw a black ball
from the respective urn. Experts are financially compensated based on their trading
performance. Recall the hiring decision from Sect. 1: the two urns represent the two
potential employees. Drawing a black ball stands for the desired outcome to get the
project completed on time. The executive is the principal and employees participating
in the market are the “experts”.
Each experiment is a series of 8 payoff-relevant periods. Each period follows 3
1. Private information: The number of black balls per urn is determined and par-
ticipants receive fully revealing private information. Thus, participants become
experts via private information (like in the experiments by Oprea et al. (2007),
Healy et al. (2010), Jian and Sami (2012), Deck et al. (2013) and many others
before that). Further, the true state of each urn remains visible to the participants
during the trading period.
2. Prediction market: Participants can buy and sell virtual stocks in two parallel
markets. The market uses a logarithmic market scoring rule (Hanson 2003). The
value of the stocks is linked to the color of the ball that will be drawn. The final
market price is used by the decision maker as the best predictor for the number
Manipulation in Conditional Decision Markets
of balls in the respective urn. Bennouri et al. (2011), Jian and Sami (2012), and
others use similar approaches.
3. Decision: After the markets close the decision maker picks an urn and a ball is
drawn (in treatment UNCONDITIONAL, two balls are drawn, one from either
urn). Across the two experiments, we consider four different treatments that cor-
respond to decision strategies. In UNCONDITIONAL, there is no decision but the
principal draws from both urns. In the other three treatments, the principal decides
which urn to draw from. In RANDOM, she relies on hidden or unobserved informa-
tion; thus, we set this a-priori probability to 50% for either urn, because that is what
it is to the experts, who are not influencing the decision. In DETERMINISTIC, she
chooses the urn where the markets predict the higher likelihood of drawing a black
ball, (i.e. the urn with the higher final market price). In the case of tied prices, the
choice is random. In PROBABILISTIC, the principal uses a logit decision func-
tion: each choice has positive probability but she is more likely to choose the urn
with the higher market price; the likelihood increases with the price difference.
The exact form is defined in the Appendix in Electronic supplementary material.
Markets are conditional on the principal’s choice (Berg and Rietz 2003); for the
urn chosen by the principal, a ball is drawn and its color determines the experts’
compensation for trading. The other market is voided. Experiment 1 includes all
four treatments, while Experiment 2 uses just RANDOM and DETERMINISTIC;
we explain this difference in more detail below.
The main substantial difference between the two experiments, noted in more detail
below, is that in Experiment 1 we do not note the existence or non-existence of another
trader (there is none), but in Experiment 2 we explicitly note the existence of one other
trader. The default state among Mechanical Turk users is that they perform their work
alone, without interaction with other Mechanical Turk workers. In Experiment 1, we
do not address the non-existence of another trader as we do not want the participants
to overthink the implications of something that is default assumption. In Experiment
2 we explicitly inform participants on the deviation from default.
When participants arrive at the market there is an initial price the market maker is
willing to trade. The participants are never told if the starting position was determined
through earlier trading or the market maker has determined it or if it is random.
The initial pricing was randomized over a pre-determined set of prices to ensure
that the participants encountered a meaningful selection of initial scenarios which
would induce varying theoretically maximizing trading strategies. The values were
randomized between rounds and right and left in the trading platform. The eight starting
price scenarios are noted in the Appendix in Electronic supplementary material.
We recruited participants via the online labor market Mechanical Turk. Recruit-
ment was restricted to workers registered as residing in the US. Each participant took
part once in exactly one treatment in one experiment (between-subject design). As
participants dropped out or failed our pre-experiment survey the numbers are not
fully balanced over the treatments. The experiment was run with a custom-made web
application on Mechanical Turk. From an organizational and technical perspective we
followed the guideline of Mason and Suri 2012. We add more detail on Mechanical
Turk users in the Appendix in Electronic supplementary material. Also, we prop-
F. Teschner et al.
Fig. 1 Screenshot from the trading interface in Experiments 1 and 2
erly incentivized participation and performance. Each participant could take part at
their own pace without a time limit. Sessions lasted around 15 minutes. Payments
were linked to individual performance in the experiment; the average payment was
$2.49, with a variance of $0.26 in Experiment 1 and $2.42, with a variance $0.28, in
Experiment 2. (Instructions for participants are attached in the Appendix in Electronic
supplementary material). See Fig. 1for a screenshot of the trading interface for phase
2, the prediction market.
Participants have full knowledge of the rules of the game including the decision
rules. We wrote the instructions to ensure that we had all of the correct technical termi-
nology, but also included more vernacular wording for the participants to understand.
Prior to trading, we test all potential participants with key questions about the markets
and rules, and drop anyone who cannot get perfect scores; we drop nearly half of all
potential participants, consistent with both experiments, through this test.
Contrary to the forecasters in the experiments by Oprea et al. (2007) and Deck
et al. (2013), in our experiments the principal is automated and her decision rule
depends on the experimental treatment. In Experiment 1 we compare an UNCON-
DITIONAL situation with three treatments—termed RANDOM, PROBABILISTIC,
and DETERMINISTIC—in a between subject design. RANDOM corresponds to the
single expert, random event (scoring rule) scenario (cf. Sect. 2), PROBABILISTIC
and DETERMINISTIC are variants of the single expert, decision (conditional scoring
rules) scenario. In Experiment 2 we pare this down to just RANDOM and DETER-
The RANDOM and UNCONDITIONAL determination serve as benchmarks.
UNCONDITIONAL does not provide incentives for manipulation, as there is no deci-
Manipulation in Conditional Decision Markets
sion to be manipulated. The same holds for RANDOM, which has a decision but the
decision is not to be manipulated by strategic trading.
The PROBABILISTIC determination mimics the current common use of condi-
tional decision markets in practice. The markets’ information is taken into account but
the principal has discretion to decide otherwise. DETERMINISTIC is an alternative
where the principal pre-commits to following the markets’ suggestion. In DETER-
MINISTIC, experts can sometimes gain more by trading in the market with lower
likelihood of approval. Thus, depending on an expert’s risk aversion and the potential
gain in each market, she will prefer either a choice of urn A or B. The same hold
for PROBABILISITC but, following theory, to a lesser extend as expected costs of
manipulating become strictly positive.
In the PROBABILISTIC and DETERMINISTIC treatments, experts have an incen-
tive to manipulate the market price to willingly mislead the principal to increase gains
from trade. In the DETERMINISTIC treatment, there is no risk of the inefficient
market being chosen, if the final price is less than the other market, but in the PROB-
ABILISTIC treatment, this potentially costly risk is unknown to the participants.
Participants’ behaviors in the UNCONDITIONAL and RANDOM treatments
should be about equal and serve as empirical benchmark for manipulation-free
behavior. In DETERMINISTIC one should observe manipulation and, thus, some
level of incorrect decisions. PROBABILISTIC should theoretically feature less
manipulation—whether this holds true and whether any manipulation remains are
questions to be explored empirically. These decision rules are the same irrespective
of whether the principal is assumed to be risk neutral or risk averse.
There are several factors that should influence the amount of manipulation. First, we
weed out nearly half of the potential participants, with our pre-experiment survey, to
ensure that the participants really understood the decision rule, the payout structure,
and the potential to benefit from manipulation in treatments PROBABLISITC and
DETERMINISTIC. Second, we are very explicit in the introduction what the expected
payout is by market and how a participant maximizes that in any given market. Third,
to ensure the participants can see which market would payout more, we do the math for
them and show the expected payout in each market explicitly on the trading wizard.
Fourth, we provide an exact underlying probability (i.e., composition of each urn),
where any uncertainty of the probability would decrease the incentive for manipulation,
because the participant could not be sure they getting a higher return for their risk.
Fifth, in the results below we drop any participants who did not trade, as a minimum
test to ensure the results are not overwhelmed by noise from lazy participants. Sixth,
the return from manipulation exceeded the return from honest revelation on average by
a factor of 5. As we paid relative to performance per treatment there was a significant
incentive to manipulate.
4 Experiment 1: One Trader Results
As noted above, there are two distinctions between this experiment and Experiment 2:
traders and treatments. First, to clearly control for the incentives and beliefs of a par-
F. Teschner et al.
Tab le 1 Participant characteristics for Experiment 1
n 67 85 134 112
Age (years) 34.9 33.1 34.2 31.8
Share female 43% 40% 34% 42%
Duration (min) 15.0 13.3 15.8 14.5
# Trades (per round,
11.5/9 9.3/6 10.3/7 10.5/8
# Trades (per round:
1/118/162.8 1/182/158.2 1/199/154.5 1/98/100.6
ticipant, there is no interaction with other traders (unlike, e.g., Healy et al. 2010 or Jian
and Sami 2012). Second, we use all four decision rules as treatments in Experiment 1.
We start by describing the basic statistics on participants and then turn to analyzing
manipulation and its effects. Manipulation is assessed via absolute differences from
market prices to the true underlying state of nature. Recall that participants know the
true underlying value, so are intentionally providing false information to the princi-
pal. Effects of manipulation are assessed by analyzing how a principle would decide
based on market information and in how far this decision coincides with her pre-
ferred decision she would make would she have perfect information on the state of
nature. We call deviations from the preferred decision given private information, to the
decision given market information, as “binary incorrectness”. In this, we disentangle
binary incorrectness resulting from misleading market prices on the one hand and
from probabilistic elements in the decision rule on the other hand.
Descriptive: Due to random assignment, participant characteristics are balanced
across treatments. Age and gender are very similar. There is no significant difference
between the treatments in duration (which was not limited for the participant) and
number of trades per round. Table 1has the details. Each participant participated
in eight sets of two markets, all with the same treatment. Again, we have dropped
participants who did not trade. While introduction into the treatments is random, we
We analyze the information aggregation in our stylized market setting by examining
the pricing error per treatment. As we know the underlying probability of the outcomes,
we can ex-post calculate the absolute error, (i.e., the absolute difference between
the last market price and correct price given the true probability). We break up the
results into two different groups, first situations where it would be optimal for the
participant to manipulate if there was a deterministic decision rule (i.e., there is a
higher expected value from the market with the lower underlying probability) and
second situations where it would not be optimal for the participant to manipulate. This
breakdown assumes purely financially motivated experts without innate preference
for truth telling or manipulation. By design, the breakdown between groups is almost
perfect with 1,548 market pairs in situations where manipulation is efficient and 1,544
market pairs where it is not. In a pair of markets, manipulation might affect either of
the markets or both markets. In order to detail the treatment differences we use linear
Manipulation in Conditional Decision Markets
Tab le 2 OLS regression on absolute errors by treatment for Experiment 1
Manipulative situations Non-manipulative situations
Estimate Std. Error Estimate Std. Error
(Intercept) 33.38∗∗∗ 2.29 29.72∗∗∗ 2.18
RANDOM 2.02 2.98 1.61 2.66
DETERMINISTIC 5.74∗∗ 2.61 1.25 2.50
PROBABILISTIC 5.83∗∗ 2.58 0.63 2.33
Round 0.26 0.25 0.04 0.22
** Significance at 1%, and *** significance at 0.1%. The manipulative situation has 1548 observations and
2of 0.021. The non-manipulative situation has 1544 observations and a R2of 0.002. Standard errors
are clustered on the respondent
regressions on the sum of absolute pricing errors in both markets in a pair. As baseline
we use the UNCONDITIONAL treatment which has no decision rule. Table 2gives
the regression results.
As expected we find no significant difference between our two benchmark
treatments RANDOM and UNCONDITIONAL for either manipulative or non-
manipulative situations. Similarly, we find no significant difference between DETER-
MINISTIC and PROBABILISTIC for either manipulative or non-manipulative
situations (the p-value is 0.95). Errors in both DETERMINISTIC and PROBABILIS-
TIC are significantly higher than in UNCONDITIONAL for manipulative situations
whereas no such difference exists for non-manipulative situations. This clearly indi-
cates that participants in DETERMINISTIC and PROBABILISTIC acted differently
and provide the principal prices that are not as close to the true probability when
they have an incentive for manipulation. The effect size is, however, only small to
small/medium—Cohen’s d ranges from 0.24 to 0.33 for different pairs of UNDCON-
commonly considered a small effect and 0.5 a medium effect.
As a robustness check the magnitude and significance are very similar as regres-
sions with interactions of the manipulation setting, if the errors are squared, and various
attempts at controlling for individual-level errors. As a second robustness check we
run an anova. We see that there is a significant effect of the treatment and on the trading
error [F(3,1544)=10.94, p<0.1%] for the states with manipulation incentives
(The post-hoc results are displayed in the Appendix in Electronic supplementary mate-
rial). Using the same analysis for the non-manipulative states we find no differences
[F(3,1540)=1.02, p=0.38].
Market prices are the outcome of trading behavior. As an additional metric for
manipulation, we consider trading behavior. Specifically, for each individual trade we
classify whether it drives the price towards the correct value for that market or not.
We then calculate the ratio of trades that participants do to drive the price towards
the correct value and compare it across treatments. The lower the ratio, the more
manipulation. Table A2 in the Appendix in Electronic supplementary material has
the results. In the DETERMINISTIC/PROBABILISTIC treatments traders are more
likely to go in the opposite direction of the true underlying value than the baseline. And,
F. Teschner et al.
Tab le 3 Logit regression on binary incorrectness by treatment and situation for Experiment 1
Manipulative situations Non-manipulative situations
Estimate Std. Error Estimate Std. Error
(Intercept) 1.75∗∗∗ 0.19 1.67∗∗∗ 0.20
RANDOM 0.11 0.22 0.07 0.32
DETERMINISTIC 0.430.21 0.09 0.22
PROBABILISTIC 0.390.21 0.10 0.21
Round 0.07** 0.03 0.01 0.03
* Significance at 5%, ** significance at 1%, and *** significance at 0.1%. The manipulative situation has
1548 observations and a Pseudo-R2of 0.010. The non-manipulative situation has 1544 observations and
a Pseudo-R2of 0.000. Standard errors are clustered on the respondent
this manipulation pays off; participants in the DETERMINISTIC/PROBABILISTIC
treatments make more money, on average, than the participants in UNDCONDI-
TIONAL/RANDOM (see the Appendix in Electronic supplementary material for
There are treatment differences in the markets’ information revelation. The next
question is, whether these significant yet small/medium differences have a meaning-
ful and significant impact on the principal’s decision. Each time the principal faces
a decision, she has a preferred decision (i.e., drawing from the urn with more black
balls). Thus, we can measure the rate of incorrect decisions by treatment and situation.
To analyze this, we first apply a deterministic decision rule to any pair of markets, irre-
spective of the treatment. Subsequently, we analyze the treatment decision rule itself
applied to market prices. This two-step process disentangles two sources of incorrect
decision: imprecise information and randomness induced by the decision rule itself.
First, we apply a deterministic decision rule to market prices from each treatment:
Given the differences in information revelation by treatment and situation (cf. Table 2),
one should expect differences in incorrect decisions. Logit regressions show that
indeed statistically significant differences in binary incorrectness exists. The results in
Table 3show a statistically significant increase in the likelihood of incorrectness for the
DETERMINISTIC and PROBABILISTIC treatments only. In the non-manipulative
setting this increase does not exist. As for the absolute errors, again, there is not a sta-
tistically significant difference between the DETERMINISTIC and PROBABILISTIC
treatments for either manipulative or non-manipulative situations (the p-value is 0.77).
In the manipulative situations, both the error and the binary outcome are meaning-
fully positively correlated with the round within the experiment. It is not significant
in the error outcome, but it is in the binary outcome. Also, it is important to note here
that we have eight rounds, so the effect has a non-negligible impact. Yet, we do not
find a significant positive interaction with DETERMINISTIC and/or PROBABILIS-
TIC treatments (data not shown). Thus, we cannot rule out that this is tied to some
underlying round effect that is exogenous to learning about manipulation.
Table 4demonstrates the percent of the time that the lower probability market
has the higher final price per treatment (i.e., how often would the principal pick the
Manipulation in Conditional Decision Markets
Tab le 4 Binary incorrectness by treatment for Experiment 1 with different decision rules
decision rule
17.4% 18.9 21.5 21.8
decision rule
50.0 40.2 21.8
wrong market if she applied a deterministic decision rule). Unsurprisingly,this happens
more often in PROBABILISTIC and DETERMINISITIC (Table 4,firstrow).Forthe
comparison of UNDCONDITIONAL/RANDOM on the one side and DETERMINIS-
TIC/PROBABILISTIC on the other side, we estimate Cohen’s d based on odds ratios
(Chinn 2000): it ranges from 0.09 to 0.15. By convention, this is a small effect. For
manipulative settings only, the effect size ranges from 0.15 to 0.24, i.e. small. We thus
conclude that in manipulative settings in the DETERMINISTIC and PROBABILIS-
TIC treatments our experiment reliably creates and measures manipulation which
does, however, only marginally worsen the information provided to the principal.
However, a decision maker running prediction markets is interested in the choices
she has to make based on the design of the markets. Hence she is interested in the
correctness after applying the ex-ante communicated decision rule. We applied the
treatment’s decision rule on our data we get 50% incorrect by design for RANDOM
and 40.2% for PROBABILISTIC. It is easy to see that in this case, if she cannot run
UNCONDITIONAL her best choice is a DETERMINISTIC rule. The reduction of
manipulation suggested by theory under the PROBABILISTIC rule is—if it exists at
all—out weighted by the incorrectness of applying the decision rule.
Of course, the PROBABILISTIC decision rule can vary from close to the RAN-
DOM to close the DETERMINISTIC and one could argue whether our experiment
featured the optimal probabilistic decision rule for the principal. Let us assume that the
rule was closer to random than optimal; in that case, an excessively random decision
rule did not substantially lower manipulation, as binary incorrectness is virtually indis-
tinguishable between PROBABILISTIC and DETERMINISTIC. We would conclude
that probabilistic elements do not solve the issue of manipulation. On the contrary,
assume the rule was closer to deterministic than optimal; following theory, more ran-
domness should result in less manipulation, i.e., moving the binary incorrectness with a
deterministic rule from the observed 21.5% closer to 18.9%. Given that the probabilis-
tic decision rule used in the experiment already distorts 21.5–40.2% incorrectness, it
appears unlikely that more truthful behavior paired with more random decisions could
bring incorrectness down to the 21.8% for DETERMINISTIC. In summary, our data
suggest that a probabilistic decision rule does not outperform a deterministic rule.
There are two main findings of the first experiment. First, respondents do manipulate
the prices in the DETERMINISTIC and PROBABILISTIC treatments. A select group
of participants move the price of the higher probability outcome downward in order to
ensure or raise the probability of the lower probability outcome market being chosen
by the principal with the expectation of a higher return. Second, any benefits of having
F. Teschner et al.
a probabilistic scoring rule, which could deter manipulation, are dominated by the cost
of not choosing the outcome picked by the market, which is generally accurate.
5 Experiment 2: Two Trader Results
We play the same setting but now match people into pairs. So, rather than being the
last play in the markets, the participants are now matched against a live partner. It is
still possible to guarantee a higher expected profit with manipulation, but it is much
harder for participants to both see and realize that strategy. Theoretically, we move
from single expert scenarios tested in Experiment 1 to multiple expert scenarios in
Experiment 2. Again, we compare both the random event and decision variants to test
the different theoretical predictions outlined in Sect. 2.
The specific steps of the game are as identical as possible to Experiment 1 while
accommodating the change to a two player setting. First, the instructions are just
slightly updated to state that there is another player and a set amount of time (3 min
for the first round to get used to the experiment and the interface, 2min per round
thereafter). Second, knowledge of this is inserted into the pre-test. Third, potential
participants are placed in a waiting room until a pair arrives. Most players waited
just a few seconds, as the game filled up quickly (half of matched pairs waited
no time, as their match was in the waiting room). A few players towards the end
waited the full possible time of 5 min without a match and were just paid for their
With the complexity and loss of power (we would have needed twice as many partic-
ipants for the same number of completed markets) we decided to limit the experiment
to two treatments. Since we saw no significant differences between the DETER-
MINISTIC and PROBABILISTIC treatments, we only keep the DETERMINISTIC.
The DETERMINISTIC has a higher likelihood of manipulation, in theory, so again
we want to allow for that. Similarly, we saw no significant differences between the
UNCONDITIONAL and the RANDOM treatment, so we use the RANDOM treatment
The ability to manipulate is slightly different in this setting. While Experiment 1
had no clock, we provide a clock in this version to allow participants to manipulate
right at the end with diminished concern of the other player countering their move.
But, in some scenarios the other player could sabotage a manipulation strategy for
Tab le 5 Participant characteristics for Experiment 2
Age (years) 30.7 30.8
Share female 43.1% 48.9%
# Trades (per round, mean/median) 14.2/10 14.8/11
# Trades (per round: min/max/var) 1/71/158.5 1/154/175.1
Duration is pre-set at 17 min for all participants in Experiment 2, as the experiment was timed, such that
participants stayed synchronized throughout the session
Manipulation in Conditional Decision Markets
Tab le 6 OLS Regression on absolute error for Experiment 2
Manipulative situations Non-manipulative situations
Estimate Std. Error Estimate Std. Error
(Intercept) 39.84∗∗ 4.71 29.60∗∗ 3.68
DETERMINISTIC 0.60 5.01 2.07 4.43
Round 0.05 0.67 0.80 0.74
** Significance at 1%. The manipulative situation has 283 observations and a R2of 0.000. The non-
manipulative situation has 274 observations and a R2of 0.007. Standard errors are clustered on the trader
pair (cohort)
their advantage. Imagine a situation where player 1 has driven the price of the lower
probability market to its true value and driven the price of the higher probability market
downward to ensure that the lower probability market would be chosen. This is risky,
as the second player could drive the price in the higher probability market back up,
reaping a high expected return and leaving player 1 with a lower expected return in
the market that is ultimately chosen. Of course, player 1 can make the move on the
higher probability market right at the end as the clock closes out trading, locking in
the expected profit.
We use the same set of characteristics as in Table 1in Table 5to show that the users
are similarly representative. Each participant was randomly paired in a cohort with
one other participant and then participated in eight sets of two markets, all with the
same treatment.
For the following analysis we selected only rounds in which both participants
were active; results are robust when using a less strict selection criterion. We ran the
regression with the RANDOM treatment as the baseline and the dummy for DETER-
MINISTIC was slightly negative and insignificant, for both the manipulative and
non-manipulative situations (Table 6). Since there is no benefit for manipulation with a
random decision method, we believe this is a strong demonstration of no manipulation
in the DETERMINISTIC treatment.1
With no meaningful difference in the error it is not surprising we find no significant
difference in the binary answer. As robustness check, we again run an anova finding
no significant treatment effects in both settings. Table 7shows the results for the logit
regression on whether the decision would be correct if it utilized a deterministic rule.
There is no meaningful or significant coefficient in either the manipulative or non-
manipulative situations on the DETERMINISTIC versus the RANDOM treatment.
There are two main findings of the second experiment. First, respondents no longer
manipulate when you add a second player. Second, while Experiment 1 has some
indication of the possibility of learning, in the more realistic Experiment 2 there is no
learning effect in the manipulative situation that would indicate participants learning
1Comparing Tables 2and 6, the absolute pricing error in the RANDOM treatment appears to be higher in
Experiment 2 as compared to Experiment 1. We suspect that this might reflect the higher complexity and
anxiety of having an opponent and a clock in Experiment 2.
F. Teschner et al.
Tab le 7 Logit regression on binary incorrectness by treatment for Experiment 2
Manipulative situations Non-manipulative situations
Estimate Std. Error Estimate Std. Error
(Intercept) 1.16∗∗ 0.30 2.11∗∗ 0.39
DETERMINISTIC 0.18 0.29 0.48 0.41
Round 0.00 0.06 0.17+0.09
+Significance at 10% and ** significance at 1%. The manipulative situation has 283 observations and
a Pseudo-R2of 0.002. The non-manipulative situation has 274 observations and a Pseudo-R2of 0.040.
Standard errors are clustered on the trader pair (cohort)
how to manipulate. This finding is robust to testing a range of further interactions not
shown in the tables.
6 Conclusion
In this paper, we review the current literature on conditional decision markets and their
antecedents. To understand the extent and influence of manipulation on information
aggregation and decision quality, we study such markets experimentally. The contri-
bution of our work is that we study informed manipulators in very stylized conditional
decision market settings. Decision markets have been extensively analyzed in theory;
we provide the first empirical evidence that the issue is not substantial.
In line with select previous work (e.g., Deck et al. 2013), our experimental results
show that manipulation impairs information aggregation. The extent of manipulation
depends on the decision rule—manipulation disappears as the correlation between the
market prices and the decision disappears. While manipulation in decision markets
occurs in highly stylized settings, it vanishes once the setting becomes more natural.
Specifically, we experimentally test the theoretical prediction that a probabilistic
decision rule reduces manipulation and hence improves the decision maker’s decision
quality. We find the contrary, manipulation is not reduced and the probabilistic decision
rule adds randomness to the decision taken. As for any experimental work, one has
to be careful in generalizing the results as the details of the environment matter. The
reward mechanism, different incentives in the field, the time for the experiments,
the instructions, risk attitudes, the type of decision to be made—all of these play
a role. Nevertheless, theoretical predictions on decision markets should apply in our
experimental settings but our data only partially supports these theoretical predictions.
Thus, despite the general limits to external validity, we believe that our experimental
results shed some light on which theoretical predictions to follow when implementing
decision markets.
We used different metrics on participants’ behavior and market outcomes to test
for manipulation. Strictly speaking, the metrics show that depending on the treatment
and situation, participants deviate from truth-telling. Besides intentional manipula-
tion, there might be other reasons for these deviations. Nevertheless, we refer to such
deviations from truth-telling as “manipulation” throughout the paper as they are in line
Manipulation in Conditional Decision Markets
with theoretical predictions on where to expect manipulation and in which direction
(buy/sell, price up/down) participants might want to manipulate.
In both experiments we design the platform to encourage manipulation; in the real
world it will be more difficult for participants to manipulate prices. Markets are not
explicit on expected returns, they do not weed out users who do not understand the
decision rules or expected returns. Further, the participants have subjective probabili-
ties with error. And, even though we saw no evidence of it in our study, markets can
randomize end time to avoid the possibility of sniping at the last moment.2
Participants learning, over time and with higher incentives, how to maximize
expected returns with manipulation is a potential issue in both laboratory and field. We
are confident that we provide adequate stakes for a laboratory experiment. Prior work
tested the validity of running experiments on Mechanical Turk and consistently found
that even with stakes substantially lower than in traditional laboratory experiments,
Mechanical Turk workers put reasonable effort in participating in economic experi-
ments and produce results comparable to laboratory settings (e.g., Horton et al. 2011;
Amir et al. 2012). For a further discussion on this topic, please see the Appendix in
Electronic supplementary material. Our experiments paid an average hourly wage of
around $10 which is competitive in the Mechanical Turk labor market. In addition, we
observed manipulation in some settings and none in others suggesting that behavior
was guided by the experimental setting presented to participants, not by randomness.
There was no increase in manipulation over eight rounds in the two-player version
of the experiment; eight rounds with direct explicit feedback over 17min is a serious
amount of investments and feedback for the participants to not learn. Although, that
does not exclude the possibility of learning and the value of future extensions of fol-
lowing participants over longer periods of time. Nor does it exclude the possibility of
manipulation under great incentives, both within and outside of the markets, which
can occur in a real-world setting.
There is no reason to assume that participants in real markets will be more expert at
gaming the markets than the participants in this study. Most participants in company
prediction markets are domain experts, not market experts. And, it takes a dedicated
expert in markets to know how to manipulate. The authors of this paper, experts in
how to manipulate a conditional decision market, were even tempted to not manipulate
in one player deterministic treatments during the training runs for this experiment; it
is just extremely engrained in most market investors to push the price towards their
subjective probability. But, the more users and the more open the market, the more
likely it would be subjected to some users with both market and domain expertise to
induce manipulation. And, ultimately, the manipulation happens at the margin, not on
the average.
2A good example of this is the American Civics Exchange which trades on political outcomes for real
cash prizes. They are not conditional decision markets, but since they freeze their market once per month
and provide prizes based on the performance of the participants with the current prices, they are subject
to a very similar form of manipulation. In their first month they found out that traders were manipulating
prices just under the deadline, which would only work if no other trader had time to counter and take the
free money (in expectation). Thus, they switched to a random, unannounced, closing time on the announced
final day:
F. Teschner et al.
In summary, contrary to theoretical work on conditional decision markets, our
results suggest that manipulation may not occur, even when conditions favor it. These
results add to the knowledge base of market design research; designers can draw on
these insights and apply them to future corporate prediction markets for reshaping
social decision making.
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... Jian and Sami conducted laboratory experiments and found the two mechanisms are comparable [17]; but they stated that further validation was required in 'field settings', which familiarity with how to report forecasts may be an important factor. While similar experimental comparisons in decision markets do not exist yet, it is worth noting that securities trading is frequently used in the experimental literature about decision markets [23]. ...
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We review theoretical results and conduct laboratory experiments to explore scenarios in which a principal runs conditional decision markets to inform his choice among a set of a risky alternatives. To the best of our knowledge, this is the first experimental analysis of conditional decision markets. We find that both the nature of conditional markets and the vested interest that experts have in the decision lead to manipulation of market prices in order to influence the principal's decision. The level of manipulation and severity of the detrimental effect on decision quality both depend on the principal's decision making rule and alignment of the experts' preferences. We present evidence that in the worst case, market prices become fully uninformative and the principal could rather toss a coin than run prediction markets. However, when the decision is deterministically tied to market prices, the principal can at least partially restore decision quality. Contrary to most theoretical and empirical work on market manipulation, our results suggest that manipulation can be effective and is an issue in decision markets. Standard prediction market results do not carry forward when using such markets as decision support systems in corporate settings with few experts who have a vested interest in the decision.
Proper scoring rules, i.e., devices of a certain class for eliciting a person's probabilities and other expectations, are studied, mainly theoretically but with some speculations about application. The relation of proper scoring rules to other economic devices and to the foundations of the personalistic theory of probability is brought out. The implications of various restrictions, especially symmetry restrictions, on scoring rules is explored, usually with a minimum of regularity hypothesis.
Documented results indicate prediction markets effectively aggregate information and form accurate predictions. This has led to a proliferation of markets predicting everything from the results of elections to a company’s sales to movie box office receipts. Recent research suggests prediction markets are robust to manipulation attacks and resulting market outcomes improve forecast accuracy. However, we present evidence from the lab indicating that well funded, single minded manipulators can in fact destroy a prediction market’s ability to aggregate information. Our results clearly indicate that the usefulness of prediction markets as inputs to decision making may be limited.
Prediction markets (also known as information markets) are markets established to aggregate knowl- edge and opinions about the likelihood of future events. This chapter is intended to give an overview of the current research on computational aspects of these markets. We begin with a brief survey of prediction market research, and then give a more detailed description of models and results in three areas: the computational complexity of operating markets for combinatorial events; the design of automated market makers; and the analysis of the computational power and speed of a market as an aggregation tool. We conclude with a discussion of open problems and directions for future research.
Macroeconomic forecasts are used extensively in industry and government even though the historical accuracy and reliability is questionable. We design a market for economic derivatives that aggregates macro-economic information. The market generated forecasts compare well to the Bloomberg- survey forecasts, the industry standard.It is an ongoing debate in finance whether short selling has positive or negative effects on market efficiency. We discuss how short selling can be implemented in such markets. Using an event-study approach we find that introducing short selling further improves forecast accuracy. By allowing traders to short sell, mispricing is reduced and hence market forecasts are closer to actual macro economic outcome. Furthermore, we find short selling lowers quoted spreads, a measure for market uncertainty.