The introduction of the ESP Game and other Games With A Purpose (GWAP) has
demonstrated the potential of human computation in solving AI-hard problems.
In such systems, users are normally required to input answers for questions
proposed by the system, e.g., descriptions about a picture or a song. Since
users may bring up irrelevant inputs intentionally or carelessly, and often the
system does not have "correct" answers,
we have to rely on the users to verify answers from others.
We call this kind of mutual verification of users' answers
"social verification."
In this paper, we propose formal models for two fundamental social verification
mechanisms, simultaneous verification and sequential verification, in human
computation systems. By adopting a game-theoretic approach, we perform an
equilibrium analysis which explains the effect of each verification mechanism
on a system's outcome. Our analysis results show that
sequential verification leads to a more diverse and descriptive set of outcomes
than simultaneous verification, though the latter is stronger in ensuring the
correctness of verified answers. Our experiments on Amazon Mechanical
Turk, which asked users to input textual terms related to a word, confirmed
our analysis results. We believe that our formal models for social
verification mechanisms will provide a basis for the design of future human
computation systems.
1 Introduction
Despite the impressive advancements in the computer technology, tasks that are
trivial for humans, such as image labeling and commonsense reasoning, still
challenge the most advanced computers. Human computation tackles these tasks
by treating humans as intelligent systems to solve
computationally intractable problems. A number of works have shown that, by
providing proper incentives, people can collectively solve computationally-hard
problems. For example, Amazon Mechanical
Turk^{2} provides a financial
marketplace that coordinates workers and developers in solving human
intelligence tasks. Games with a purpose [1], proposed by Luis von Ahn,
demonstrate that "having fun" can be a strong incentive to gather humans
together in solving computationally-challenging problems.
Although human computation has been adopted in many applications for solving
a variety of problems, little is known regarding a human computation
system's behavior and outputs, e.g., if a system produces desired outcomes as
expected. For example, ESP Game [2], one of the best-known human computation
applications, is designed as a two-player guessing game for image labeling.
While ESP Game has successfully collected an enormous number of image
annotations, it suffers from the drawback that players tend to guess more
general and simpler words. Weber et al [3] showed that, players tend to use
colors, synonyms, and generic words when they play an ESP Game. Moreover, the
authors designed a bot that plays the game based on a language model of
collected image annotations. Even without looking at the image, the bot can
guess labels that have 81% agreement rate with a human player
given at least one taboo word. Motivated by this example, we
consider the importance of modeling social verification mechanisms in human computation
systems.
In this paper, we provide formal models for two fundamental social verification
mechanisms and apply game theory to analyze the systems' outcomes if either
mechanism is applied. By social verification, we denote the mechanism which
arranges the questions for users and determines the "correctness" of
users' inputs based on their correlations. The two social verification
mechanisms we modeled are:
Simultaneous verification: In this mechanism, users are given the same
question and asked to provide their own answers. If some or all of the users
agree on an answer, their answers are considered "correct." In our
analysis, we model this mechanism in the form of coordination game.
Sequential verification: This mechanism is like a popular game
"Charade". In its two-player case, a user A first gets a question and
responses with a set of descriptions about the question. Then another user
B will receive the descriptions from A as the hints, and B is asked to guess
what the original question is. If B's answer matches the original
question, then A's descriptions about the question are considered
"correct." We model this mechanism by an extensive game with imperfect
information.
Based on the equilibrium analysis in the proposed game-theoretic models, we
analyze the effects of the two social verification mechanisms and discuss how
the systems' outcomes would be like if either mechanism is applied. Our
analysis results show that sequential verification leads to a more diverse and
descriptive set of outcomes than simultaneous verification, though the latter
is stronger in ensuring the correctness of the verified answers. Our experiments on
Amazon Mechanical Turk, which asked users to input textual terms related to a
word, confirmed our analysis results. We believe that our formal models for
social verification mechanisms will provide a basis for the design of future
human computation systems.
The rest of this paper is organized as follows. After reviewing related work in
Section 2, we introduce the relevant game theoretic models and
solution concepts in Section 3.
In Section 4, we give a formal definition of the social verification
mechanisms and then model the two mechanisms as two types of two-player game models.
Equilibrium analysis and existing application reviews are also explained.
Section 5 compares the two social verifications
and describes the experiments conducted on Amazon Mechanical Turk.
Section 6 contains come concluding remarks.
2 Related Work
Most research projects on human computation focus on developing
applications to solve problems that are intractable for computers.
The best-known example is the ESP Game [2], a two-player online
game, which motivates players to contribute their cognitive skills
in annotating images. While playing the game, a player attempts to label a given
image, presented by the system, to match labels given by his online partner.
Inspired by the ESP Game,
many applications have been designed as games to solve a variety of
computationally hard problems, such as locating objects within an
image [4], collecting commonsense
knowledge [5], and annotating music [6].
The concept of turning games into productive tools is called "Games With A
Purpose" (GWAP) [1].
Despite the impressive progress in human computation,
there have been relatively few studies of the
general design principles and the theoretic foundation.
In a review article [7], Luis von Ahn proposed three
game-structure templates, which generalize instances of human computation games
based on their successful experiences in deploying GWAP.
The templates, namely output-agreement games, inversion-problem games,
and input-agreement games, describe the game structures and suggest possible
implementations in solving human computation tasks.
The difference between the templates and our proposed social verifications
is that we focus on user behavior and resulting outcomes of the social interactions.
From this point of view, we reduce the three game-structure templates to
two social verification mechanisms.
Since we are considering user interaction in human computation, game
theory seems to be an appropriate approach to better understand the incentive structure
and user behavior behind the system.
To the best of our knowledge, the PhotoSlap game [8] was the first to apply game
theoretic analysis in human computation games. A multi-player game, PhotoSlap,
has been developed to accomplish the task of face recognition. By showing that the desired
player strategies lie in the subgame perfect equilibrium, the game design is shown to
motivate users to contribute useful output.
Jain and Parkes [9] proposed a game theoretic analysis of the ESP Game and
conducted equilibrium analysis under two preference settings, namely the
match-early preference and rare-word-first preference.
However, these projects all focused on analyzing specific applications.
In contrast to previous works, this paper models the abstractions of human
computations, i.e., the social verification mechanisms.
Modeling the abstractions instead of the specific game makes the analysis results
applicable to other human computation applications.
3 Preliminaries
In this section, we introduce the relevant game models and
solution concepts in game theory [10].
3.1 Game Models
Definition 1(Normal-form game)
A game in normal form can be defined as a tuple
Γ = (N, (A_{i})_{i ∈ N}, (u_{i})_{i ∈ N}), where
N is the set of players; and for each player i ∈ N, A_{i} is the set of
available actions for player i, and u_{i}:(×_{i ∈ N}A_{i}) → \mathbbR
is the utility function mapping each action profile of a game into a real-valued
payoff for player i.
A two-player normal-form game can be described conveniently by a table, where
one player's actions are represented by the rows and the other player's actions
are represented by the columns. In this paper, we focus on a specific class of normal-form
game, called coordination game. In a two-player coordination game, players can
gain optimal payoff by performing the same action.
Player 1
a_{1}
a_{2}
a_{3}
a_{1}
(1,1)
(0,0)
(0,0)
a_{2}
(0,0)
(1,1)
(0,0)
a_{3}
(0,0)
(0,0)
(1,1)
Table 1: An example of coordination game represented in a table form.
Definition 2(Extensive game with imperfect information)
An extensive game with imperfect information can be defined as a tuple
Γ = (N,H,P,(I_{i})_{i ∈ N},(u_{i})_{i ∈ N}), where
N is the finite set of players,
H is the set of action history taken by players, and A(h) is the
set of actions available after the nonterminal history h,
P is the player function that assigns each nonterminal history to a
member of N, where P(h)=k means it is player k's turn
after history h,
(I_{i}) is the information partition of {h ∈ H:P(h)=i} for each
player i with the property that A(h)=A(h′) whenever h and
h′ are in the same partition,
u_{i} is the payoff function of player i associated with every
terminal history.
An extensive game with imperfect information can be described by a game tree,
as shown in Figure 2. In the game tree, each node represents a player
i; nodes connected by the dotted line are in the same
information partition; the paths from the root to the nodes is the set of
history H; and the payoff is shown after every terminal node. For example,
the meaning of the leftmost path is: if player 2 takes strategy y_{1} after
player 1 takes strategy x_{1}, they both get payoff 1.
Figure 1: An example of an extensive game with imperfect information in the form
of game tree.
3.2 Solution Concepts
A solution concept is a formal rule representing the game model's prediction,
indicating how players in the game perform their actions. The most
commonly-used solution concepts are equilibrium concepts. In this section, we give a formal
definition of the Nash equilibrium and the sequential equilibrium.
Definition 3(Nash equilibrium)
The Nash equilibrium of a normal-form game (N, (A_{i})_{i ∈ N},(u_{i})_{i ∈ N})
is an action profile a^{*} ∈ (×A_{i}) of actions with the property that
for every player i ∈ N, we have
The Nash equilibrium is a commonly used equilibrium, whereby no player can increase
his payoff by changing his action when he believes no other players would
change. In the definition, a is the combination of actions of all players
and a_{−i} is the set of actions of all players except player i.
A sequential equilibrium is a refinement of the Nash equilibrium for extensive games
with imperfect information. In addition to specifying a strategy for each
player, a belief system for each player stating which history has occurred
in each information partition is needed. The pair of a strategy profile and a
belief system is called an assessment, defined as follows.
Definition 4(Assessment)
An assessment in an extensive game
(N,H,P,(I_{i})_{i ∈ N},(u_{i})) is a pair (β,μ), where
β is a profile of behavioral strategies and μ is a function that
assigns to every information set a probability measure on the set of
histories in the information set.
In the definition, β is the behavioral strategy where β(h)(a)
denotes the probability that action a will be taken after history h, and
μ is the belief system, where μ(I)(h) denotes the player's belief that
to history h is in partition I.
Definition 5(Sequential rationality)
An assessment (β, μ) is sequential rational in information set I
if the players get their optimal payoff by adopting
the strategy specified in β given their subsequent beliefs
and others' subsequent strategies, as specified in the assessment.
Definition 6(Consistency)
An assessment (β, μ) is consistent if
there exists a sequence of completed mixed strategy profiles {β_{k}}
such that lim_{k → ∞}(β_{k},μ_{k}) = (β,μ), where
μ_{k} is derived from β_{k} using Bayes'
rule.
Definition 7(Sequential equilibrium)
An assessment is a sequential equilibrium of an extensive game with perfect
recall if it is sequential rational and consistent.
4 Social Verification Models
In this paper, we model human computation as the process of finding the
descriptions of questions, i.e. given a question q from the question
space Q, we want to find the appropriate description d from the
description space D. For example, in the image annotation problem,
the questions Q are images, and the descriptions D are labeling words.
In the problem of locating objects in images, Q is the set of object names,
and D is the set of relevant image parts.
To guarantee the quality of the outputs produced by human computation, social
verification is commonly used since it is inherent with
two desired properties. First, it can encourage
users to perform the desired computation by rewarding users whose output
matches with other users'. Moreover, verifications guarantee
a high probability of correct output under the condition that more people behave
correctly than those that do not.
In this paper, we model two two-player social verification
mechanisms: simultaneous verification and sequential verification.
We give the formal definitions and analysis in the following section.
4.1 Simultaneous Verification
4.1.1 Definition
Simultaneous verification describes the structure whereby users give descriptions
of a question simultaneously.
The descriptions are considered to be valid
if two users agree on the same description.
Formally, given the question q ∈ Q, each player
i ∈ {1,2} can choose a description d_{i} ∈ D. When the two descriptions
d_{1} and d_{2} match, users are rewarded and the system produces an output.
Figure 2: Simultaneous verification mechanism in human computation.
4.1.2 Game theoretic modeling
In a simultaneous-verification game, each player makes his decision without
knowing the other player's decision. This kind of game can be defined as a
normal-form game.
In addition, simultaneous verification is characterized by three properties:
(1) every player in the game is identical with respect to the game rules,
i.e., changing the identity of the players would not change their payoffs;
(2) both players get the same payoff; and
(3) players get the optimal payoff when they perform the same actions.
Based on these characteristics, simultaneous verification games can be modeled
as a normal-form game.
Definition 8(Simultaneous verification game)
Given a question q and a set of possible descriptions D,
a human computation game with simultaneous verification can be modeled
as a normal-form game, represented by a tuple
Γ = (N,(D_{i})_{i ∈ N}, (u_{i})_{i ∈ N}), where N={1,2},
D_{1} = D_{2} = D is the set of descriptions available for players,
and (u_{i}) is the utility function of
player i that satisfies the following three conditions:
u_{1} = u_{2} = u,
u(d_{1}, d_{2}) = u(d_{2},d_{1}),
u(d_{i},d_{i}) > u(d_{i}, d_{j}) for all i ≠ j.
4.1.3 Equilibrium analysis
The game models in which players receive an optimal payoff when they choose the same
strategy are called coordination games. The equilibrium analysis
is straightforward.
Theorem 1
A simultaneous-verification game has n = |D| pure Nash equilibria,
represented by the set S where
S = {(d,d):d ∈ D}.
The proof of the Nash equilibrium analysis is trivial since a rational player
would not change his strategy if he takes the same strategy as the other player.
However, the result of equilibrium analysis does not provide
much useful information. We still do not know how a rational player would act
since there are n equilibria that players can choose.
Player 1
a_{1}
a_{2}
a_{3}
a_{1}
(1,1)
(0,0)
(0,0)
a_{2}
(0,0)
(1,1)
(0,0)
a_{3}
(0,0)
(0,0)
(1,1)
Table 2: An example of a simultaneous verification game.
The grey region marks the Nash equilibria of the game.
In traditional game theoretic analysis, the optimal strategy of the
coordination game is a mixed strategy that randomly chooses one of the
strategies in the n pure Nash equilibria. However, as the ESP Game
shows, people can do much better than randomly choose their actions.
Players in a game may coordinate to choose some preferred equilibria,
which are called the focal points (a.k.a Schelling points).
Originally introduced by Schelling [11], focal points are the
"prominent" or "salient" solutions to the game. For example, consider two
players who are both required to choose an element from the set Z,
and they only get a payoff when they choose the same element.
Suppose each player differentiates the elements in terms of frequency, which means
"how many times he/she has heard them mentioned."
For instance, if each element is a single word, the frequency of the element is
the times players have seen them in books and newspapers for some period of time.
A natural focal point would be to choose the element with the
highest frequency [12]. Intuitively, players would choose the
element with higher frequency since the element is more "prominent"
than others.
Returning to the simultaneous verification game,
players try to choose an element d from the description set D given
the question q. For simplicity, assume that all players have the same private
description of the frequency function f(d|q), which denotes how many times d
appears when q is given.
In this case, a natural focal point would be to choose the description d maximizing f(d|q).
Since the frequency is the statistic of the times of
occurrence in a certain period, we will rewrite it in the form of probability p(d|q)
by normalization. Following the formula of conditional probability,
p(d|q) =
p(d,q)
p(q)
=
p(d) ×p(q) ×r(d,q)
p(q)
= p(d) ×r(d,q),
where p(d,q) is the joint probability that elements d and q will co-occur, and
r(d,q) = [p(d,q)/(p(d) ×p(q))] is
defined to represent the relevance of the description d to the question
q. When d and q are irrelevant, i.e., totally independent, r(d|q) = 1.
Since the focal point of the game is to maximize f(d|q), i.e., p(d|q),
we can conduct the following lemma.
Lemma 1
In a human computation game with simultaneous verification
Γ = (N, (D_{i})_{i ∈ N}, (u_{i})_{i ∈ N}),
where each player's payoff is equal in every Nash equilibrium,
players would choose description d ∈ D satisfying
d = argmax_{d ∈ D} p(d) ×r(d,q),
where p(d) is the frequency of description d, and r(d,q) is the relevance
function indicating the relationship between description d and question q.
Intuitively, the player strategy in the focal points would be to choose the
description d that maximizes the frequency of d and the relevance of
description d to question q.
4.1.4 Analysis of human computation games with simultaneous verifications
(a) The ESP Game. Players are given the image and required to give annotation words.
(b) Matchin. Players are given a pair of images and required to answer which one the partner prefers.
(c) Squigl. Players are given a word-image pair and required to give the locations of the word in the image.
Figure 3: Human computation games with simultaneous verifications.
In this section, we review some human computation games with
simultaneous verifications and show how to apply our model and analysis
to these games.
The ESP Game. The typical example of simultaneous verification game
is the ESP Game [2], in which the question space D is the
set of images, the description space D is the set of labeling words,
and the match condition occurs when two provided labels, d_{1} and d_{2}, are the same.
According to the analysis, player would choose the description d which maximizes
p(d) ×r(d,q), where r(d,q) is the relevance relation between the
image with taboo words q and the label d, and p(d) is the properties of the label.
This explains why players would tend to guess easier words, which maximize p(d),
and related words, which maximize the relevance relation r(d,q) between
the taboo word and the labels.
Matchin [13] and Squigl^{3}.
In Matchin, Q is the set of image pairs, and D = {left, right} indicates the
preference of images. The player would choose the description d ∈ D which
maximize p(d) ×r(q,d), where p(d) is the frequency of choosing right
or left, and r(q, d) is the value of how preferred it is to choose the preference d
given the image-pair q.
Assuming players have the same frequency value
in choosing right or left, Matchin is able to obtain the true preference relations
between the image pair since players would maximize r(q,d), i.e., choose the preference.
In Squigl, Q is the set of image-word pairs, and D
is the set of possible traces. Following the same analysis, players would
choose to draw a rough sketch, i.e., maximizing p(d), around the specified object, i.e.,
maximizing r(q, d).
Voting and PhotoSlap. The traditional majority-based (voting) mechanism
can also be modeled as a simultaneous verification game.
A n-player voting game can be regarded as C^{n}_{2} two-player
simultaneous verification games, and the descriptions with the highest
number of matchings are treated as the output.
Moreover, users in a simultaneous verification game do not have to describe
the question at the same time.
In PhotoSlap [8], users are required to answer if two face photos are
of the same person in two different stages of the game. Though the players do not answer
the question together, PhotoSlap still can be modeled as a simultaneous
verification because player performs their actions without knowing what the other
players are doing.
4.2 Sequential Verification
4.2.1 Definition
The structure of sequential verification is similar to the popular game "Charade".
The process can be split into two phases: the description phase and the guessing phase.
In the description phase, the first player is required to provide descriptions
to the given question. In the guessing phase, the second player tries to guess
the original question given the descriptions. If the second player guesses
correctly, both players will be rewarded and the system treats the descriptions
as the output.
Formally, given q_{1} ∈ Q, player 1 can choose description d ∈ D,
and player 2 can choose q_{2} ∈ Q, which is his guess about the
original question.
Players are rewarded and system produces output when q_{1} and q_{2} match.
Figure 4: Sequential verification mechanisms in human computation.
4.2.2 Game theoretic modeling
Besides the two players described above, we consider the system as a third
player. First, the system player chooses a question q_{1} from the question space Q.
Then, player 1 chooses the description d from the description space D.
Finally, player 2, who is not aware of question q_{1}, makes his
guess of the original question q_{2} from the question space Q.
If the guess q_{2} matches q_{1}, then both players are rewarded.
This process can be modeled as a three-player extensive game with imperfect
information.
Definition 9(Sequential verification game)
Given a question space Q and a description space D, a
sequential-verification game can be modeled as a three-player extensive
game with imperfect information, represented by a tuple
Γ = (N,H,P,(I_{i})_{i ∈ N},(u_{i})_{i ∈ N}), where
where δ_{ij} equals to 1 if i=j, and 0 otherwise.
By limiting the size of the question space Q and the size of the description space D to
2, the sequential verification game can be represented in the form of game
tree, as shown in Figure 5. For the simplicity, we
omit the payoff for the system player.
Figure 5: An example of sequential verification modeling in human computation.
The payoff for the system player is omitted.
4.2.3 Equilibrium analysis
Similar to the analysis in simultaneous-verification game, we define a
frequency function f in the following sequential equilibrium analysis.
Given question space Q and the description space D, f(q|d)_{q ∈ Q, d ∈ D}
denotes the private description of the players on "how many times question q
appears when given description d". We also rewrite it in the form of
probability p(q|d).
Players get optimal payoffs when player 2 guesses correctly about the original
question q given description d. The behavior of player 2
is similar to that of players in simultaneous verification games, i.e. player
2 would guess the question q maximizing p(q|d).
However, the information we really care about is the behavior of player 1, since it
directly relates to the system outputs.
Under the belief that player 2 chooses question q maximizing p(q|d),
player 1 would choose the description d, such that
p(q|d) ≥ p(q_{i}|d) for all q_{i} ∈ Q, i.e., q is the most frequent element
co-occurring with d than any other questions. Player 2 would guess correctly if
both players adopt these strategies.
We write these strategies in the form of sequential equilibrium in the
following lemma.
Lemma 2
Given a question space Q, a description space D, and a frequency function f
shared by all players,
an assessment (β,μ) is a sequential equilibrium of the
sequential-verification game (N,H,P,(I_{i})_{i ∈ N},(u_{i})_{i ∈ N})
if the following condition holds for all q_{i} ∈ Q:
β_{system}(ϕ)(q_{i}) = [1/(|q|)],
β_{2}(I(d))(q_{i}) = {
1,
if q_{i} = argmax_{q ∈ Q} p(q|d)
0,
otherwise.
β_{1}(q_{i})(d) = {
1/|D_{qi}|,
if d ∈ D_{qi}
0,
otherwise.
μ_{2}(I(d))(q_{i},d) = {
1/|D_{qi}|,
if d ∈ D_{qi}
0,
otherwise.
β_{i}(I)(d) is the probability to choose description d for player i in
information set I, and
D_{qi} is the set of d which satisfies q_{i} = argmax_{q ∈ Q}p(q|d) and d ∈ D.
Intuitively, D_{qi} is the set that contains all the descriptions that make question q "prominent".
Though the notations seem to be complicated, the results are intuitive.
The result of the sequential equilibrium analysis shows, for rational players:
(1) player 1 would describe the question q in the way that
q is more frequently seen than other questions given the description d.
While there are many possible descriptions satisfying the above condition,
player 1 would choose one of them in random.
(2) player 2 would choose the answer which best fits the description, i.e.
which has the highest frequency.
To prove the sequential equilibrium, the assessment should be examined if it
satisfies sequential rationality and consistency. The proof for sequential
rationality is trivial since both players cannot increase their payoff by
changing the strategies. The consistency of the assessment can be proved by
setting the elements of value 0 in β_{1} and μ_{2} to ϵ and
normalizing the value of the other elements.
4.2.4 Analysis of human computation games with sequential
verifications
Peekaboom [4], a web game for locating objects in images,
is an example demonstrating the sequential verification, where
Q is the set of the labels, D is the set of all possible combinations of
image portions, and the match condition occurs when the original question q_{1} equals to player 2's
prediction q_{2}.
The music annotation game TagATune [6] is another example,
which runs two sequential verification games simultaneously.
In each sequential verification, Q is the set of songs, and D is the set of
annotation words. However, instead of choosing q_{2} ∈ Q,
player 2 is given a hint question (song) q and only need to
choose whether the question song is the same as the hint song. (q or not q).
The players are rewarded and system produces
a output when the match condition occurs in both sequential verification
games.
According to the equilibrium analysis, player 1 would randomly choose
one of the descriptions that are able to make the question "prominent",
i.e., the chosen description d should satisfy p(q|d) ≥ p(q^{*}|d) ∀q^{*} ∈ Q given the question q.
While this strategy is more descriptive than
the strategy taken in the simultaneous verification game, there are more
uncertainties on the descriptions player may choose.
For example, when given the term "elephant" and an image containing an
elephant in Peekaboom, player could choose the description that reveals
(1) the image parts of the whole elephant, (2) the image parts of the nose,
(3) the image parts of the elephant head, or even (4) the image parts of
a portion of the elephant head.
The situation is similar in TagATune, in which player may describe
a song in various way. These results need further analysis in order to
represent useful information.
5 Evaluation
In the previous section, we give a game theoretic analysis of two social
verification mechanisms and demonstrate how to apply the modeling and analysis
in several human computation games. While the preliminary results support our
analysis, we do not compare the system output of two mechanisms directly since
the target problems and game designs are not the same.
Therefore, we conduct experiments on a simple scenario: give the descriptions
for the specified terms. The question space Q and the description space D
are both the set of words. Given the question space Q to be a set of 120 words,
we apply two proposed social verification mechanisms in this scenario and collect
their system outputs.
5.1 Experiment Setup
There are two stages in this task: the description stage and the guessing stage, as
shown in Figure 11.
In the description stage, players are given a word and are
required to give descriptions or any related terms.
In the guessing stage, players are given some descriptions and are required to
guess which word is being described.
This human intelligence task is implemented in two mechanisms in the form of
games and published on Amazon Mechanical Turk to collect user input.
Simultaneous verification game (SIM Game):
This is a two-player process. Similar to the ESP Game, players are given the
same term in the description stage. In each round, they have 30 seconds to
match with each other. Players get paid if they finish the game and match
descriptions at least 10 rounds in the 15 rounds of playing. Descriptions
that are matched by players are recorded.
Sequential verification game (SEQ Game):
This is a two-player process. In each round, one player is in the
description stage to describe the given term, and the other is in the
guessing stage to guess the term. Players win that round if the guessing
player guess correctly in 30 seconds. Players get paid if they finish the
game and win at least 10 round in the 15 rounds of playing.
(a) The description stage. Players describe the question given by systems.
(b) The guessing stage. Players guess the original question according
to the provided descriptions.
Figure 6: Snapshots of the evaluations conducted on Amazon Mechanical Turk.
5.2 Experiment Results
The simultaneous verification game (SIM Game) has been played for 154 times, whereby
1878 labels are generated, and the sequential verification game (SEQ Game)
has been played for 178 times, in which 4368 labels are generated.
In the 1878 labels collected by SIM Game, there are 384
distinct labels, and there are 2634 distinct labels out of 4368 total labels
in SEQ Game. The result demonstrates that SEQ Game leads
to a more diverse output than SIM Game. Moreover, the labels in SEQ Game is usually
more descriptive than that in SIM Game, as demonstrated in Table 3.
On average, each label contains 2.633 words in SEQ Game, and 1.002 words
in SIM Game. While more words represents for more descriptive powers,
we can implicitly infer that labels in SEQ Game is more descriptive.
Another interesting discovery is the ratio of the mis-spelling words.
There are 335 mis-spelling words in the 4368 labels of SEQ Game, and no
mis-spelling labels in SIM Game. This result may be dure to the stronger
verification in ensuring the correctness in SIM Game.
SIM Game
SEQ Game
add
science with numbers
class
adding, subtracting
calculus
subject in calculations
school course with numbers
Table 3: Labels collected for "Mathematics."
5.3 Discussion
This small-scale experiments have revealed some important properties of
the labels generated in two social verification mechanisms.
First, labels collected in sequential verification mechanism are more
descriptive and diverse than the labels in the simultaneous verification
mechanism. The result confirms the game theoretic analysis of player behavior
in the previous section.
Understanding player behavior and system outputs in different social
verification mechanisms is essential in designing human computation
applications. For example, adopting sequential verification mechanism might be
a better choice when description diversity is important in the application.
However, additional mechanisms, such as spell checking,
should be applied to ensure the data quality.
If the description space is limited, e.g., the two choices in Matchin,
or the output correctness is essential, simultaneous
verification mechanism would be a better fit.
6 Conclusions
In this paper, we propose formal models for two fundamental social verification
mechanisms, simultaneous verification and sequential verification, in a game
theoretic approach. Our contributions are summarized below:
We have shown that social verification mechanisms in human computation games
can be modeled by using game theory. Since simultaneous and sequential
verifications are fundamental, our models can be generally applied to human
computation systems.
We have shown that simultaneous and sequential verifications can lead to
different system outcomes. While sequential verification promotes a more
diverse and descriptive labeling, simultaneous verification is stronger in
ensuring the data correctness.
Real-world experiments involving two mechanisms have been conducted.
Through analyzing the data generated by the different mechanisms, we
summarize the properties of the system output and give suggestions for choosing
mechanisms when designing new human computation applications.
In our future work, we will identify other verification mechanisms and explore
the possibility of integrating competitive elements into human computation. In
addition, we will investigate other issues from a game theoretic perspective,
including the presence of malicious players and how to change the incentive
structure to achieve different system outcomes.
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Footnotes:
1.
This work was supported in part by Taiwan E-learning and Digital Archives
Programs (TELDAP) sponsored by the National Science Council of Taiwan under the
grants NSC98-2631-001-011 and NSC98-2631-001-013. It was also supported in
part by the National Science Council of Taiwan under the grants
NSC97-2221-E-001-009.
2. https://www.mturk.com/mturk/3. http://www.gwap.com/squigl-aSheng-Wei Chen (also known as Kuan-Ta Chen) http://www.iis.sinica.edu.tw/~swc
Last Update September 19, 2017