<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Probabilistic Game Theoretic Algorithms for Group Recommender Systems</article-title>
      </title-group>
      <contrib-group>
        <aff id="aff0">
          <label>0</label>
          <institution>Categories and Subject Descriptors H1.2 [User/Machine Systems]: human factors; H5.2 [User Interfaces]: evaluation/methodology</institution>
          ,
          <addr-line>user-centered design</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>General terms Experimentation</institution>
          ,
          <addr-line>Human factors</addr-line>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>George Popescu EPFL - HCI Group IC IIF Station 14</institution>
          <addr-line>1015 Lausanne</addr-line>
          ,
          <country country="CH">Switzerland</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Aggregating users' individual preference and recommending a common set of items for a group has become a challenging topic in group recommender systems and social websites. This issue is mainly concerned with the following three objectives: eliciting individual users' preferences, suggesting outcomes that maximize the overall satisfaction for all users and ensuring that the aggregation mechanism is resistant to individual users' manipulation. Firstly we show how our proposed probabilistic weighted-sum algorithm (PWS) works and emphasize on its advantages. Then we compare PWS with related approaches implemented in similar systems using the case of our music recommender, GroupFun. We describe an experiment design to study users' perceptions of the algorithms, their perceived fairness and incentives to manipulate the final recommendation outcome. We expect our results to show that PWS will be perceived as fair and diversity- and discovery-driven, thus enhancing the group's satisfaction. Our future work will focus on the actual evaluation of GroupFun using the experiment design presented here.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Quality measurement</kwd>
        <kwd>usability evaluation</kwd>
        <kwd>recommender systems</kwd>
        <kwd>quality of user experience</kwd>
        <kwd>post-study questionnaire</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. INTRODUCTION</title>
      <p>Group recommender systems use various aggregation strategies to
suggest a common list of items to a group of users. These
strategies aim at increasing the group’s welfare and are based on
users’ votes on items. The social welfare is an aggregate of
individual utilities of all group members. Most common used
deterministic strategies are: plurality voting, utilitarian, approval
voting, least misery, most pleasure, average without misery,
fairness, most respected person, Borda count, Copeland rule or
Kemeny scores (Masthoff, 2005). One can easily create other
WOMRAD 2011 2ndWorkshop on Music Recommendation and
Discovery, colocated with ACM RecSys 2011 (Chicago, US)
Copyright ©. This is an open-access article distributed under the terms
of the Creative Commons Attribution License 3.0 Unported, which
permits unrestricted use, distribution, and reproduction in any medium,
provided the original author and source are credited.</p>
      <p>Pearl Pu
EPFL - HCI Group</p>
      <p>IC IIF Station 14
1015 Lausanne, Switzerland</p>
      <p>+41 21 693 6081
distinct strategies based on these. Social choice theory aims to
offer an answer to “which strategy is most effective and will be
most liked by a group of users?” (Hastie and Kameda, 2005).
With the purpose of determining what strategy people actually
use, Masthoff (2004) found that individuals use computationally
simple strategies mentioned above, particularly the average
strategy, the average without misery and the least misery strategy.
However, there is no dominant strategy as people switch between
them given a different context. Fairness plays an important role in
decision making but members do not have a clear strategy for
applying it.</p>
      <p>Our main research question is to determine “which group
satisfaction rule best satisfy users expectations”. We propose 4
algorithms and investigate upon: “which algorithm is best suited
to meet users’ expectations” for our music recommender system,
GroupFun and “how users perceive the algorithms’ accuracy”.
Next we present related work, then considered algorithms together
with our implementation and future experiment design.</p>
    </sec>
    <sec id="sec-2">
      <title>2. BASELINE AND RELATED WORK</title>
    </sec>
    <sec id="sec-3">
      <title>2.1 MusicFX</title>
      <p>
        MusicFX is a music system offering best music match to
employees working out in a fitness center (McCarthy and
Anagnost, 1998). The algorithm aims at selecting the most
preferred music genre that maximizes members’ listening
pleasure. For this it computes a group preference index and sums
squared individual preferences. Then it lists the most popular
categories. The system also saves events in its history such as:
member entrance, member exit, individual preference update,
system parameter adjustment and maximum station play time
elapsed. Since some individual preference filters may not change,
the system opts for a different music configuration according to
two criteria: playing more the music which members like most
and playing less the music which members like least. The
weighted random selection operator is one strategy used to reduce
the likelihood of starvation. Another strategy is limiting the period
of time for one genre to be played – regardless of how popular it
is – before the selection algorithm is invoked in order to select a
new station. MusicFX has two important advantages: (
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) it
increases the variety of music and (
        <xref ref-type="bibr" rid="ref2">2</xref>
        ) it democratizes the music
selection process. Thus it is adaptive to changing preferences of
its users also proposing new songs for them. One drawback of the
system is that it changes music stations abruptly in the middle of
the songs.
      </p>
    </sec>
    <sec id="sec-4">
      <title>2.2 PolyLens</title>
      <p>PolyLens is a collaborative filtering recommender system which
recommends movies to groups of people based on their individual
preferences (O’Connor et al. 2001). It represents a group
outcomes are songs si that are selected in the common playlist.
We let each user a j submit a numerical vote score(si , a j ) for
each song si that reflects their preference for that song. These
votes are given as ratings on a 5-point Likert scale and normalized
so that the scores given by each user sum to 1:
We then assign a joint score to each song that is computed as the
sum of the scores given by the individual users:
To choose the songs to be included in a playlist of length k, a
deterministic method is to choose the k songs with the highest
joint rating: weighted sum (DWS):
The probabilistic weighted sum (PWS) iteratively selects each of
the k songs randomly according to the probability distribution:
extension of the MovieLens recommender system with over
80,000 users and their ratings for more than 3,500 movies (with a
total of nearly 5 million votes). Users can create and manage
groups, access individual and group recommendations and receive
notification alerts for group invitation. The algorithm uses the
least misery strategy given that the groups formed to watch a
movie together tend to be small. As such the group is as happy as
its least happy member. The authors mention that “the social
value function and algorithm are unlikely to work well for large
groups”. They further note that “it is still an open research
question to understand the types of social value functions that best
satisfy large groups and to implement them algorithmically”.</p>
    </sec>
    <sec id="sec-5">
      <title>2.3 Voting strategies</title>
      <p>An extensive study on a group of television viewers aiming at
finding which strategy people use was realized by Masthoff
(2005). In the experiment 10 deterministic group voting rules are
compared: plurality voting, utilitarian strategy, Borda count,
Copeland rule, approval voting, least misery strategy, most
pleasure strategy, average without misery strategy, fairness
strategy and most respected person strategy. The experiment
shows that individuals do not use a clear dominant strategy, but
average, average without misery, and least misery are all plausible
candidates for implementation. In a different experiment
addressing how people judge the recommendation results
multiplicative utilitarian strategy is the most promising strategy,
but the other strategies received close scores. In the study of
television viewers the hypothesis that social status influences
selection has no statistical dominance. Non-linear utility suits
better users’ expectations than a linear one. For instance quadratic
rating scale is appropriate for implementation. Furthermore, there
is strong evidence that human subjects use a series of simple
strategies in different judgment contexts they face. For instance, if
one takes the satisfaction of the group to be the average of the
satisfaction of the individuals, then the average strategy performs
best. Taking the minimum better corresponds to the predictions
which are made by individuals assessing their own needs.</p>
    </sec>
    <sec id="sec-6">
      <title>3. ALGORITHMS</title>
      <p>In the music domain many users usually form many groups and
listen to many songs. Given the fact that the length of one song is
of 3 to 4 minutes users usually select a playlist containing several
to lots of songs. This is not the case of movies selection when
users need to agree on only one or few movie(s) they would like
to consume given their limited time and the length of a movie:
~2h. Thus, the music domain presents both opportunities and
challenges since the recommendation needs to focus on both
diversity and accuracy.</p>
      <p>We propose the following 4 algorithms for comparison:
• PS (Probabilistic Sum): select the common playlist’
songs probabilistically, each of them having the same
probability to be selected
• LM (Least Misery): select songs with the highest
minimum individual ratings
•
•</p>
      <p>DWS (Deterministic Weighted Sum): deterministically
select songs with the highest score
PWS (Probabilistic Weighted Sum): compute weighted
sum and select songs based on their score probabilities.</p>
    </sec>
    <sec id="sec-7">
      <title>3.1 General framework</title>
      <p>Let A be the set of all users and S the set of all possible outcomes
that can be rated. In our group music recommendation setting, the
By comparison, the probabilistic sum (PS) method chooses the k
songs with equal probability:
The least misery (LM) method takes into account the minimum of
ratings for each user:
min &amp;
,
' , ∀
∈ )</p>
    </sec>
    <sec id="sec-8">
      <title>3.2 Example</title>
      <p>To illustrate how each algorithm works, we consider the following
example. In the next table, user1, user2, and user 3 represent
group members. The score distribution normalized to 1 for each of
the users is displayed in the respective row, and the joint scores
are shown in the table below.</p>
      <p>,</p>
      <p>
        ∑ ∈
=
∑ ∈
=
|"|
,
,
,
(
        <xref ref-type="bibr" rid="ref1">1</xref>
        )
(
        <xref ref-type="bibr" rid="ref2">2</xref>
        )
(
        <xref ref-type="bibr" rid="ref3">3</xref>
        )
(
        <xref ref-type="bibr" rid="ref4">4</xref>
        )
(
        <xref ref-type="bibr" rid="ref5">5</xref>
        )
(
        <xref ref-type="bibr" rid="ref6">6</xref>
        )
Considering the probability as the final score, the deterministic
weighted sum (DWS) will chose songs 4, 2, 1 and 3. Probabilistic
weighted sum (PWS) will choose one song after another using this
probabilistic distribution. Compared to other social choice based
algorithms, PWS is incentive compatible. That is, it is to the best
interest of the individual to reveal his/her preferences truthfully. It
is in fact equivalent to a random dictator method, where the
dictator will choose a song randomly with the probabilities given
by its degree of preference – a reasonable method since nobody
wants to hear the same song over and over again. This is because
the probability of a song si to be chosen can be written as:
or, in other words, the probability of choosing user a j times the
normalized score that user a j has given to song si . Indeed,
User3’s preference for song 1 yields a significant probability that
this song will be included in the playlist, relative to other songs.
      </p>
    </sec>
    <sec id="sec-9">
      <title>3.3 Discussion</title>
      <p>The contribution of the PWS algorithm in the paper stands out
with respect to group satisfaction. We expect users to be more
satisfied using PWS than other algorithms given their expectations
to discover the music of other members.</p>
      <p>Advantages of PWS compared with the other algorithms:</p>
      <sec id="sec-9-1">
        <title>Users are free to choose the number of songs</title>
      </sec>
      <sec id="sec-9-2">
        <title>Ratings are updated permanently</title>
      </sec>
      <sec id="sec-9-3">
        <title>The algorithm is computationally simple</title>
      </sec>
      <sec id="sec-9-4">
        <title>Users can negotiate their ratings and trade utility</title>
      </sec>
      <sec id="sec-9-5">
        <title>Incentive-compatible truthful property is observed</title>
      </sec>
      <sec id="sec-9-6">
        <title>The algorithm favors music diversity</title>
      </sec>
      <sec id="sec-9-7">
        <title>The disadvantages of PWS are:</title>
        <p>It is difficult to quantify rating differences between distinct
users. The weights given by each user cannot be compared
with the ones given by another since users have different
estimations of their utility.</p>
        <p>Self-selection effect: most popular songs will receive most
votes - not ideal if long tail distribution is desired.</p>
        <p>Since PWS can be interpreted as similar to the random scheme
users have to test it in more recommendation rounds to understand
its inner logic. PWS can be further developed to include the group
dynamics. One solution is to consider trust and other members’
comments on the songs rated by one user (e.g. “like”/”dislike”).
The PWS algorithm stands out with respect to allowing users to
engage in trustful individual preference elicitation and music
discovery. By returning to the recommendation list the group will
find a different playlist every-time they are would like to listen to
group music. By considering the probabilistic distribution of
ratings and an extensive music library the algorithm will mostly
suggest songs strongly liked by most others. Sometimes it will
recommend unexpected, rating-wise, serendipitous items
facilitating music discovery and group enjoyment.</p>
      </sec>
    </sec>
    <sec id="sec-10">
      <title>4. GROUPFUN</title>
      <p>GroupFun is a web application that helps a group of friends to
agree on a common music playlist for a given event they will
attend, e.g. a birthday party or a graduation ceremony. Firstly, it is
implemented as a Facebook plugin connecting users to their
friends. Secondly, it is a music application that helps individuals
to manage and share their favorite music with groups. In
GroupFun users can listen to their own collection of songs as well
as their friends’ music. With the collective music database, the
application integrates friends’ music tastes and recommends a
common playlists to them. Therefore, the application aims at
satisfying music tastes of the whole group by aggregating
individual preferences through the use of previously presented
algorithms.
In the “Home” page users see 4 playlists: one from a recent event,
one containing popular songs, one from a party and the last one
from an older event. They can listen to each song in each of the
playlists.
In the “My Group” page users can create groups, upload and rate
their music, invite friends and hear the group’s songs. Finally, in
the “My Music” page users see their contribution to GroupFun:
for each song is displayed the associated group, the rating and its
name and artist. Users can also listen to their individual
preferences in the same interface. One of the most important
characteristics of GroupFun is that it combines music, friends and
groups together. In other words, GroupFun serves as a platform
allowing users to conveniently organize their individual music
library, effectively communicate with friends and actively
participate in social activities.</p>
    </sec>
    <sec id="sec-11">
      <title>5. EXPERIMENT DESIGN</title>
      <p>To compare how users perceive the 4 algorithms, we plan to carry
on a between-groups user study. With the results of the
experiment we will be able to make a judgment of the influence of
both the algorithms and the design on users’ satisfaction. We plan
to collect solid user feedback regarding how an algorithm should
allow group members to arrive at a common decision in a music
recommendation setting.</p>
      <p>
        Our hypotheses are that: (
        <xref ref-type="bibr" rid="ref1">1</xref>
        ) users will not reveal their preferences
strategically as to influence the algorithm’s outcome; (
        <xref ref-type="bibr" rid="ref2">2</xref>
        ) they will
prefer more PWS than DWS given the increased diversity of the
recommendations they receive and (
        <xref ref-type="bibr" rid="ref3">3</xref>
        ) the group will perceive
more overall satisfaction but less diversity using the LM
algorithm compared with PWS.
      </p>
    </sec>
    <sec id="sec-12">
      <title>5.1 Procedure</title>
      <p>First we recruit university students, friends who have Facebook
accounts and other users on the Amazon Mechanical Turk
platform. All of them will use their own computers in order to
connect to the GroupFun application. We consider 4 algorithms
implemented for 4 groups of 40 users together with 1 interface.
Each of the algorithms displays a common list of 10 songs to all
group members. Users are asked to contribute their music to only
one of the groups and fill in an online post-study questionnaire
assessing their satisfaction. The final music outcome is shown to
all group members after they have finished their tasks. Users can
interact with the system in diverse ways such as: upload more or
less songs, change their ratings, see and hear to their friends’
playlists, etc.</p>
      <sec id="sec-12-1">
        <title>Interface/Algorithm</title>
      </sec>
      <sec id="sec-12-2">
        <title>Interface</title>
        <p>40
40
LM
40
PS
40</p>
      </sec>
    </sec>
    <sec id="sec-13">
      <title>5.2 Measurements</title>
      <p>The first 40 users see the results of the probabilistic weighted sum
algorithm, the next those of deterministic weighted sum and so on.
Since individuals who upload more songs expect to see their song
names more often in the final list they would prefer to know a
priori the computation rule of the algorithm so that they would
adjust the number of songs they upload. Given users’ known
selfratings and group ratings computed by the algorithms we expected
our subjects to identify some differences between the 4
approaches. Some of the questions from the post-study
questionnaire are presented in the table below. They were
extracted from a well-known user evaluation model, named
ResQue [7], that our group has developed.</p>
      <sec id="sec-13-1">
        <title>Measurements</title>
        <sec id="sec-13-1-1">
          <title>Perceived</title>
          <p>attractiveness</p>
        </sec>
        <sec id="sec-13-1-2">
          <title>Perceived satisfaction</title>
        </sec>
        <sec id="sec-13-1-3">
          <title>Perceived helpfulness</title>
        </sec>
      </sec>
      <sec id="sec-13-2">
        <title>Questions</title>
        <p>The layout of the system's interface is
attractive.</p>
        <p>The items recommended to
matched my interest.</p>
        <sec id="sec-13-2-1">
          <title>Outcome</title>
          <p>intention
change</p>
        </sec>
        <sec id="sec-13-2-2">
          <title>I was interested in changing the outcome of the algorithm.</title>
        </sec>
      </sec>
    </sec>
    <sec id="sec-14">
      <title>6. CONCLUSIONS AND FUTURE WORK</title>
      <p>In this paper we presented our research work on the algorithmic
development and evaluation of our music recommender system
and Facebook application, GroupFun. The major contribution of
this paper is the demonstration of the applicability of the PWS
algorithm for group recommendation strategies and negotiation. In
this context, we analyzed different group recommendation
approaches w.r.t. group satisfaction and discussed key satisfaction
issues to be taken into account. The PWS algorithm we proposed
calculates probabilities for songs to appear in groups’ playlists
favoring music diversity and discovery. Using PWS users state
their preference truthfully. They align their decision to that of the
group. Furthermore, our current development of GroupFun allows
users to create groups, rate and share their music profiles with
their friends.</p>
      <p>To understand how users’ perceive our algorithms and current
interface, we plan to conduct an experiment to compare the 4
algorithms in a between-subjects study. As such we will evaluate
user satisfaction for music group recommendations. Furthermore,
to learn more about the perceived ease of use and perceived
usefulness of our system we plan to invite more members and
analyze user feedback in terms of design and functionality. We
also intend to develop a new version of the algorithm which will
better match users’ behavior and expectations.</p>
    </sec>
    <sec id="sec-15">
      <title>7. ACKNOWLEDGMENTS</title>
      <p>This research was supported by EPFL and the Swiss National
Science Foundation. We thank Elsa Friscira and Laurentiu
Dascalu for their important contribution to the development of
GroupFun and GroupFun users for their answers and involvement
in the evaluation of our algorithms.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <surname>Hastie</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          and
          <string-name>
            <surname>Kameda</surname>
            ,
            <given-names>T.</given-names>
          </string-name>
          <year>2005</year>
          .
          <article-title>The robust beauty of majority rules in group decisions</article-title>
          .
          <source>In Psychological Review</source>
          , Vol.
          <volume>112</volume>
          , no.
          <issue>2</issue>
          ,
          <fpage>494</fpage>
          -
          <lpage>508</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <surname>Masthoff</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <year>2004</year>
          . Group modeling:
          <article-title>Selecting a sequence of television items to suit a group of viewers. User Modeling</article-title>
          and
          <string-name>
            <surname>User-Adapted</surname>
            <given-names>Interaction</given-names>
          </string-name>
          , Vol.
          <volume>14</volume>
          , no.
          <issue>1</issue>
          ,
          <fpage>37</fpage>
          -
          <lpage>85</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <surname>Masthoff</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          <year>2005</year>
          .
          <article-title>The pursuit of satisfaction: affective state in group recommender systems</article-title>
          .
          <source>In Computer Science</source>
          , Vol.
          <volume>3538</volume>
          ,
          <fpage>297</fpage>
          -
          <lpage>306</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <surname>McCarthy</surname>
            <given-names>J.F.</given-names>
          </string-name>
          and
          <string-name>
            <surname>Anagnost</surname>
            ,
            <given-names>T.D.</given-names>
          </string-name>
          <year>1998</year>
          .
          <article-title>MusicFX: an arbiter of group preferences for computer supported collaborative workouts</article-title>
          .
          <source>Proc. ACM Computer Supported Cooperative Work</source>
          ,
          <fpage>363</fpage>
          -
          <lpage>372</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>O</given-names>
            <surname>'Connor</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            ,
            <surname>Cosley</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            ,
            <surname>Konstan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.A.</given-names>
            ,
            <surname>Riedl</surname>
          </string-name>
          ,
          <string-name>
            <surname>J.</surname>
          </string-name>
          <year>2001</year>
          .
          <article-title>PolyLens: A recommender system for groups of users</article-title>
          .
          <source>Proc. ACM European Conference on Computer Supported Cooperative Work.</source>
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <surname>Popescu</surname>
            <given-names>G.</given-names>
          </string-name>
          and
          <string-name>
            <surname>Pu</surname>
            <given-names>P.</given-names>
          </string-name>
          <year>2010</year>
          .
          <article-title>Group Recommender Systems as a Voting Problem</article-title>
          .
          <source>EPFL Technical report.</source>
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <surname>Pu</surname>
            <given-names>P.</given-names>
          </string-name>
          and
          <string-name>
            <surname>Chen</surname>
            <given-names>L.</given-names>
          </string-name>
          <year>2010</year>
          .
          <article-title>A User-Centric Evaluation Framework of Recommender Systems</article-title>
          .
          <source>In the 3rd ACM Conference on Recommender Systems</source>
          , Barcelona, Spain
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>