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				<title level="a" type="main">Toward Benchmarking Group Explanations: Evaluating the Effect of Aggregation Strategies versus Explanation</title>
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							<persName><forename type="first">Francesco</forename><surname>Barile</surname></persName>
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							<persName><forename type="first">Shabnam</forename><surname>Najafian</surname></persName>
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							<persName><forename type="first">Tim</forename><surname>Draws</surname></persName>
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							<persName><forename type="first">Oana</forename><surname>Inel</surname></persName>
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							<persName><forename type="first">Alisa</forename><surname>Rieger</surname></persName>
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							<persName><forename type="first">Rishav</forename><surname>Hada</surname></persName>
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									<country key="NL">Netherlands</country>
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							<persName><forename type="first">Nava</forename><surname>Tintarev</surname></persName>
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						<title level="a" type="main">Toward Benchmarking Group Explanations: Evaluating the Effect of Aggregation Strategies versus Explanation</title>
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					<term>Social Choice-based Explanations</term>
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					<term>Explainable Recommender Systems</term>
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<div xmlns="http://www.tei-c.org/ns/1.0"><p>In the context of group recommendations, explanations have been claimed to be useful for finding a satisfactory choice for all the group members and helping them agree on a common decision, improving perceived fairness, perceived consensus, and satisfaction. In this work, we present a preregistered evaluation of the impact of using social choice-based explanations for group recommendations (i.e., explanations that intuitively describe the strategy used to generate the recommendation). Our objective is to conceptually replicate a previous study and investigate whether a) the used aggregation strategy or b) the explanation affected the most users' fairness perception, consensus perception, and satisfaction. Our results show that the participants are able to discriminate between the different strategies, assigning worse evaluations to the Most Pleasure strategy (which chooses the item with the highest of the individual evaluations). In addition to a condition with no (natural language) explanation, we introduce a more detailed social choice-based explanation, evaluating whether additional information about the strategy has a positive impact on the evaluation of the group recommendation. However, we surprisingly found no effect of level of explanations, either as a main effect or as an interaction effect with the aggregation strategy. Overall, our results suggest that users' perceptions of fairness, consensus, and satisfaction are primarily formed based on the social choice aggregation strategies for the studied group scenario. Our work also highlights the challenges of replication studies in recommender systems and discusses some of the design choices that may influence results when attempting to benchmark findings for the effectiveness of group explanations.</p></div>
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<div xmlns="http://www.tei-c.org/ns/1.0"><head n="1.">Introduction</head><p>In many domains, such as online communities <ref type="bibr" target="#b0">[1,</ref><ref type="bibr" target="#b1">2]</ref>, music, movies or TV programs <ref type="bibr" target="#b2">[3,</ref><ref type="bibr" target="#b3">4,</ref><ref type="bibr" target="#b4">5,</ref><ref type="bibr" target="#b5">6]</ref>, and tourism <ref type="bibr" target="#b5">[6,</ref><ref type="bibr" target="#b6">7]</ref>, people consume recommendations in groups rather than individually. Several approaches in the literature <ref type="bibr" target="#b3">[4,</ref><ref type="bibr" target="#b7">8,</ref><ref type="bibr" target="#b6">7]</ref> propose social choice strategies, which combine the individual preferences of all group members and predict an item that is suitable for everyone. Each such aggregation strategy, however, has its trade-offs. As stated by Arrow's theorem <ref type="bibr" target="#b8">[9]</ref>, the performance of an aggregation strategy depends on the evaluation context, meaning that it is unlikely for an aggregation strategy to outperform other strategies in all situations. Nevertheless, understanding why particular items are recommended is not a trivial task, especially for group recommendations <ref type="bibr" target="#b9">[10]</ref>. In general, explanations <ref type="bibr" target="#b10">[11,</ref><ref type="bibr" target="#b11">12]</ref> have been proposed as a means of describing why certain items are recommended. The adoption of explanations has proved to increase user acceptance of recommended items <ref type="bibr" target="#b12">[13,</ref><ref type="bibr" target="#b13">14]</ref>. In the context of group recommendations, however, the role of explanations is even more challenging. Multiple functions need to be met, besides explaining why certain items are recommended <ref type="bibr" target="#b14">[15,</ref><ref type="bibr" target="#b15">16]</ref> -to help users agree on a joint decision, as well as improve users' perceived fairness, perceived consensus, and satisfaction <ref type="bibr" target="#b14">[15,</ref><ref type="bibr" target="#b4">5,</ref><ref type="bibr" target="#b16">17]</ref>.</p><p>To the best of our knowledge, however, only a few studies <ref type="bibr" target="#b16">[17]</ref> have focused on generating and evaluating explanations based on social choice aggregation strategies to increase fairness and consensus perception of users or their satisfaction. We have identified several limitations in the current literature on group recommendation explanations that we address in this paper. First, social choice-based aggregation strategies and their explanations are not evaluated in isolation. Hence, it is unclear to what extent users' fairness perception, consensus perception, and satisfaction evaluations depend on a) the explanations or b) simply the social choice aggregation strategies. Furthermore, while we agree that the field of group recommendation explanations is a young one, there is no precedent of replication studies, let alone benchmarks and baselines to compare explanations against. The challenges the replication crises have posed in the social sciences and medicine suggest that similar difficulties would be present in other fields involving user studies <ref type="bibr" target="#b17">[18,</ref><ref type="bibr" target="#b18">19]</ref>.</p><p>In this paper, thus, we address the aforementioned limitations by taking the first steps toward an explanation benchmark for group explanations. We conduct a preregistered between-subjects user study with 400 participants, where each participant evaluates one aggregation strategy and one explanation type in terms of perceived fairness, perceived consensus, and satisfaction regarding the group recommendations <ref type="foot" target="#foot_0">1</ref> . In addition, we also test for interaction effects between aggregation strategies and explanation types. Thus, we address the following research questions: RQ1: Are there differences between social choice-based aggregation strategies in group recommendation settings regarding users' fairness perception, consensus perception, or satisfaction?</p><p>RQ2: Do explanations that are based on the group recommendation aggregation strategy at hand increase users' fairness perception, consensus perception, or satisfaction?</p><p>RQ3: Does the effectiveness of explanations (w.r.t. users' fairness perception, consensus perception, or satisfaction) vary depending on the aggregation strategies at hand? RQ4: Are users' levels of perceived fairness or perceived consensus related to their satisfaction concerning the group recommendations?</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.">Related Work and Hypotheses</head><p>In this section, we introduce the social choice-based aggregation strategies used to generate recommendations for groups. Then, we illustrate the relevant literature on the explanations for group recommender systems. Motivated by relevant literature, we also present the hypotheses that we verify in our study.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.1.">Social Choice-based Aggregation Strategies</head><p>There are two main approaches to generate group recommendations: (i) aggregated models: aggregate individual preferences (e.g., existing ratings) into a group model, generating then the group recommendations based on such a group model; and (ii) aggregated predictions or strategies: aggregate individual item-ratings predictions and recommend items with the highest aggregated scores to the group <ref type="bibr" target="#b14">[15]</ref>. Several aggregation strategies inspired by Social Choice Theory have been proposed to aggregate individuals' information <ref type="bibr" target="#b7">[8]</ref>. An overview of these strategies, known as social choice-based aggregation strategies, can be found in Masthoff <ref type="bibr" target="#b3">[4]</ref>. Following, we describe six of the most utilized social choice-based aggregation strategies: (i) Additive Utilitarian (ADD) is a consensus-based strategy <ref type="bibr" target="#b19">[20]</ref>, so it takes into account the preferences of all group members, recommending the item with the highest sum of all group members ratings; (ii) Fairness (FAI) is a consensus-based strategy <ref type="bibr" target="#b7">[8]</ref> well suited in the context of repeated decisions, in which the items are ranked as the individuals are choosing them in turn;</p><p>(iii) Approval Voting (APP) is a majority-based strategy <ref type="bibr" target="#b19">[20]</ref>, so it focuses on the most popular items among group members, recommending the item which has the highest number of ratings greater than a predefined threshold; (iv) Least Misery (LMS) is a borderline strategy <ref type="bibr" target="#b19">[20]</ref>, so it takes into account only a subset of group members preferences and recommends the item which has the highest of all lowest ratings; (v) Majority (MAJ) is a borderline strategy <ref type="bibr" target="#b19">[20]</ref> which recommends the item with the highest number of all ratings representing the majority of itemspecific ratings; (vi) Most Pleasure (MPL) is a borderline strategy <ref type="bibr" target="#b19">[20]</ref> which recommends the item with the highest of all individual group members ratings. Social choice-based aggregation strategies are widely used in the group recommenders literature <ref type="bibr" target="#b7">[8]</ref>. In Masthoff <ref type="bibr" target="#b7">[8]</ref>, several experiments are presented to identify the best strategy in terms of perceived group satisfaction. The results, however, show that there is no winning strategy -different strategies perform well in different scenarios. This consideration leads us to the following hypotheses related to RQ1<ref type="foot" target="#foot_1">2</ref> :</p><p>• H1a: There is a difference between social choice-based aggregation strategies in group recommendation settings regarding users' fairness perception.</p><p>• H1b: There is a difference between social choice-based aggregation strategies in group recommendation settings regarding users' consensus perception.</p><p>• H1c: There is a difference between social choice-based aggregation strategies in group recommendation settings regarding user satisfaction.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.2.">Explaining to Groups</head><p>In general, explanations can be seen as additional information that is associated with the recommendations to achieve several goals, such as increasing the transparency (explaining how the recommendation system works), effectiveness (helping the user in making good decisions), and usability of the system, as well as user satisfaction <ref type="bibr" target="#b20">[21]</ref>. Several studies in different domains showed the benefits of using explanations for recommendations in increasing users acceptance rate and satisfaction <ref type="bibr" target="#b21">[22]</ref>, or trust in the system <ref type="bibr" target="#b22">[23]</ref>. In group recommendations, explanations can achieve further goals: fairness (consider all group members' preference as much as possible); consensus (help group members to agree on the decision) <ref type="bibr" target="#b14">[15]</ref>; privacypreserving (preserve group members' confidential data, to avoid concerns about a possible loss of privacy by, e.g., disclosing the preference information of individual group members in the explanation) <ref type="bibr" target="#b23">[24,</ref><ref type="bibr" target="#b24">25,</ref><ref type="bibr" target="#b25">26]</ref>. However, most of the research on explanations for recommender systems focus on single-user scenarios, while only a few studies investigate the problem of generating explanations for groups. Typically, such explanations are related to the underlying mechanism of the employed social choice-based aggregation strategy <ref type="bibr" target="#b4">[5,</ref><ref type="bibr" target="#b26">27,</ref><ref type="bibr" target="#b16">17]</ref>. Natural language explanation styles based on the underlying social choice aggregation strategies were introduced in Najafian and Tintarev <ref type="bibr" target="#b4">[5]</ref>, while Kapcak et al. <ref type="bibr" target="#b26">[27]</ref> extended this work using the wisdom of the crowd to improve the quality of the initially proposed explanations. Quijano-Sanchez et al. <ref type="bibr" target="#b27">[28]</ref> introduced explanations including the social factors of personality and tie strength between group members to generate tactful explanations (e.g., explanations that avoid damaging friendships). In a more extensive study, Tran et al. <ref type="bibr" target="#b16">[17]</ref> propose three types of explanations for six social choice-based aggregation strategies (ADD, FAI, APP, LMS, MAJ, and MPL), by considering: (1) the aggregation strategy itself -Type 1, (2) the aggregation strategy itself and the decision history -Type 2, and (3) the aggregation strategy itself and the future decision plan -Type3. In a user study, they evaluated these explanations and showed that explanations related to the ADD and MAJ strategies help the most to increase the fairness and consensus perception, and satisfaction regarding the group recommendation. They also found that users' perceived fairness or consensus correlates with their satisfaction. Although these works present valuable ways to generate explanations for the most used benchmark aggregation strategies in group recommender systems research, it is unclear whether the effects attributed to the explanations might not, in fact, depend on the aggregation strategies themselves. Starting from this consideration, we formulated a second set of hypotheses that we intend to validate, related to RQ2:</p><p>• H2a: Explanations based on the aggregation strategy at hand increase users' fairness perception concerning group recommendations.</p><p>• H2b: Explanations based on the aggregation strategy at hand increase users' consensus perception concerning group recommendations.</p><p>• H2c: Explanations based on the aggregation strategy at hand increase users' satisfaction concerning group recommendations.</p><p>Furthermore, an aspect that has not been investigated is the level of detail that the explanation can achieve concerning the aggregation strategy used and whether this affects the users' fairness perception, consensus perception, and satisfaction. To this end, we introduce a third set of hypotheses which we intend to test, related to RQ3:</p><p>• H3a: The effect of aggregation strategy-based explanations on users' fairness perception concerning group recommendations is moderated by the type of aggregation strategy at hand.</p><p>• H3b: The effect of aggregation strategy-based explanations on users' consensus perception concerning group recommendations is moderated by the type of aggregation strategy at hand.</p><p>• H3c: The effect of aggregation strategy-based explanations on user satisfaction concerning group recommendations is moderated by the type of aggregation strategy at hand.</p><p>Finally, we also validate the correlation between user satisfaction and perceived fairness and consensus, c.f., <ref type="bibr" target="#b16">[17]</ref>:</p><p>• H4a: Users' perceived fairness is positively related to user satisfaction concerning group recommendations.</p><p>• H4b: Users' perceived consensus is positively related to user satisfaction concerning group recommendations.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.">Method</head><p>We conducted an online between-subjects user study to test our hypotheses. <ref type="foot" target="#foot_2">3</ref> We presented users with scenarios that reflected one of five different social choice-based aggregation strategies for group recommender systems and that included either no explanation or one of two different explanation types. This section outlines the materials, variables, procedure, participant sample, and statistical analyses related to our user study.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.1.">Materials Aggregation Strategies</head><p>Our study considered five different social choice-based aggregation strategies for group recommender systems, that have been evaluated in prior work <ref type="bibr" target="#b16">[17]</ref>. Each of these strategies aggregates the preferences of several users to obtain a recommendation for the group as a whole <ref type="bibr" target="#b19">[20]</ref>. Differently than in <ref type="bibr" target="#b16">[17]</ref>, we do not consider the Fairness aggregation strategy because the explanation types that we propose can not be generated for this strategy. Each aggregation strategy is applied to the rating scenario presented in Table <ref type="table" target="#tab_0">1</ref>, where each item (i.e., the three restaurants, Rest A, Rest B, and Rest C) is rated on a 5-star rating scale (i.e., 1 -the worst and 5 -the best). Specifically, we consider the following aggregation strategies, from Section 2.1: Additive Utilitarian (ADD); Approval Voting (APP) considering a threshold equal to 3, as in <ref type="bibr" target="#b16">[17]</ref>; Least Misery (LMS); Majority (MAJ); Most Pleasure (MPL).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Explanations</head><p>Each explanation is presented after showing the scenario in Table <ref type="table" target="#tab_0">1</ref> and a recommendation generated with one of the aggregation strategies considered (see Section 3.2 for more details). We evaluate three types of explanations (see Table <ref type="table">4</ref>): (i) Basic explanations, which explain the aggregation strategy at hand. These explanations have been adopted from Tran et al. <ref type="bibr" target="#b16">[17]</ref>, and refer to Type 1; (ii) Detailed explanations, that explain the aggregation strategy in greater detail by describing the specific reason why a given item has been recommended; additionally, we included a condition no explanation, where the aggregation strategy is applied, but no explanation is given. Participants did, however, see the ratings of the other group members in this condition.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.2.">Procedure</head><p>Our study consisted of two subsequent steps. During the first step (after participants had agreed to informed consent), we introduced participants to the study and asked them for their gender and age. The second step of our study started with the following scenario (taken from Tran et al. <ref type="bibr" target="#b16">[17]</ref>): "Assume, there is a group of four friends (Alex, Anna, Sam, and Leo). Every month, a group decision is made by these friends to decide on a restaurant to have dinner together. To select a restaurant for the dinner next month, the group again has to take the same decision. In this decision, each group member explicitly rated three restaurants (Rest A, Rest B, and Rest C) using a 5-star rating scale (1: the worst, 5: the best). The ratings given by group members are shown in the table below:" After that, Table <ref type="table" target="#tab_0">1</ref> was shown. Participants saw a group recommendation either with or without an explanation depending on which aggregation strategy and explanation type they had been assigned to (see Table <ref type="table">4</ref>). We then measured perceived fairness, perceived consensus, and satisfaction (see Section 3.3). We also included an attention check where we specifically instructed participants on what option to select. Finally, participants could explain their answers in a text field. The study had been approved by the ethics committee of our institution.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.3.">Variables Independent Variables</head><p>(i) Aggregation strategy (categorical, between-subjects). Each participant was exposed to a scenario that reflected one of the five aggregation strategies (i.e., ADD, APP, LMS, MAJ, or MPL; see Section 3.1). (ii) Explanation type (categorical, between-subjects). Each participant saw either no explanation, a basic explanation, or a detailed explanation (see Section 3.1).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Dependent Variables</head><p>We measured each of our three dependent variables by asking participants to respond to a statement on a seven-point Likert scale ranging from "strongly agree" (scored as −3) to "strongly disagree" (scored as 3). We have: (i) Perceived fairness (ordinal): "The group recommendation is fair to all group members"; (ii) Perceived Consensus (ordinal): "The group members will agree on the group recommendation"; (iii) Satisfaction (ordinal): "The group members will be satisfied with regard to the group recommendation".</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Descriptive Variables</head><p>We collected data on two demographic variables: (i) Age (categorical), participants could select one of the options 18-25, 26-35, 36-45, 46-55, &gt;55; (ii) Gender (categorical). Participants could select one of the options female, male, or other. Participants could also select a "prefer not to say" option for these variables.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.4.">Participants</head><p>Before data collection, we computed the required sample size for our study in a power analysis for a between-subjects ANOVA (Fixed effects, special, main effects, and interactions; see Section 3.5) using G*Power <ref type="bibr" target="#b28">[29]</ref>. Here, we specified the default effect size f = 0.25, a significance threshold 𝛼 = 0.05 11 = 0.005 (due to testing multiple hypotheses; see Section 3.5), a power of (1 − 𝛽) = 0.8, and that we will test 5 × 3 = 15 groups (i.e., 5 different aggregation strategies for 3 different explanation scenarios). We performed this computation for each hypothesis using their respective degrees of freedom. This resulted in a total required sample size of at least 378 participants. We thus recruited 400 participants from the online participant pool Prolific 4 , all of whom were proficient English speakers above 18 years of age. To maintain high-quality answers, we selected only participants that had an approval rate of at least 90% and participated in at least 10 prior studies. Each participant was allowed to participate in our study only once and received £0.63 as a reward for participation. We excluded one participant from data analysis because they did not pass the attention check we included in the experiment. The resulting sample of 399 participants was composed of 61% female, 38% male, and 1% other participants. They represented a diverse range of age groups: 28% were between 18 and 25, 29% between 26 and 35, 17% between 36 and 45, 14% between 46 and 55, and 13% were above 55 years of age. We randomly distributed participants over the 15 conditions (i.e., exposing them to 1/5 aggregation strategies and 1/3 explanation types).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.5.">Statistical Analyses</head><p>For each of the three dependent variables in our study (i.e., fairness perception, consensus perception, and satisfaction), we conducted a two-way analysis of variance (ANOVA) using aggregation strategy and explanation type as between-subjects factors. These three ANOVAs were used to test nine hypotheses (i.e., H1a -H3c). Specifically, each of them tested main effects of aggregation strategy (H1a -H1c) and explanation type (H2a -H2c) as well as the interaction between these two variables in affecting the dependent variables (H3a -H3c). We chose this type of analysis despite the anticipation that our data may not be normally distributed (i.e., violating an ANOVA assumption) because ANOVAs are usually robust to Likert-type ordinal data <ref type="bibr" target="#b29">[30]</ref>. We additionally performed two Spearman correlation analyses to test hypotheses H4a and H4b.</p><p>We thus tested 11 different hypotheses. Applying a Bonferroni correction <ref type="bibr" target="#b30">[31]</ref>, we lowered the significance threshold to 𝛼 = 0.05 11 = 0.0046. Since we found significant main effects related to our first six hypotheses (H1a -H2c; see Section 4), we conducted Tukey posthoc analyses to investigate specific differences between the aggregation strategies and explanation types. The p-values from these posthoc analyses were adjusted to correct for multiple testing (i.e., written as 𝑝 adj ).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.">Results</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Descriptive Statistics</head><p>Participants' distribution over the 15 different conditions (i.e., all possible combinations between the five aggregation strategies and the three explanation types) was balanced: each condition Table <ref type="table">2</ref> Results of three two-way ANOVAs for the dependent variables (DVs) fairness perception (left), consensus perception (center), and satisfaction (right). Per effect, we report the 𝐹 -statistic, 𝑝-value, and 𝜂 2 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 effect size. The terms "aggr" and "expl" represent the independent variables aggregation strategy and explanation type. Colons indicate interaction effects, asterisks statistical significance. was shown to 6% to 7% of participants. On average, participants spent 2.9 (sd = 2.2; no notable difference between conditions) minutes on the task. Qualitative feedback from participants suggested that the scenario and task were understandable. Participants had a slight overall tendency to perceive fairness, consensus, and satisfaction in the scenarios, as 51%, 51%, and 56% at least somewhat agreed to these three items, respectively. Figure <ref type="figure" target="#fig_0">1</ref> shows participants' mean fairness perception, consensus perception, and satisfaction across explanation types and split by aggregation strategies.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>RQ1: differences between social-choice based aggregation strategies regarding explanation effectiveness.</head><p>We found significant differences between the five aggregation strategies concerning all three dependent variables fairness perception, consensus perception, and satisfaction (H1a -H1c; 𝐹 = <ref type="bibr">[36.19, 49</ref>.57], all 𝑝 &lt; 0.001, 𝜂 2 𝑝 = [0.27, 0.34]; see Table <ref type="table">2</ref>). So, overall, participants expressed different levels regarding these three variables based on which aggregation strategy they were exposed to. Posthoc analyses revealed that MPL led to lower levels on all three variables compared to all other aggregation strategies (all 𝑝 adj &lt; 0.001). The only other significant differences we found between aggregation strategies was that APP (𝑝 adj = 0.004) and MAJ (𝑝 adj = 0.005) each led to lower fairness perception compared to LMS. In sum, participants -irrespective of which explanation type they saw -viewed MPL as significantly less fair, consensual, and satisfying compared to other strategies, and judged MAJ as well as APP as less fair compared to LMS. RQ2: differences between explanation types (i.e., no explanation, basic explanation, or detailed explanation). We found no significant differences between the three explanation types regarding all three dependent variables (H2a -H2c; 𝐹 = [0.14, 0.35], 𝑝 = [0.71, 0.86], all 𝜂 2 𝑝 = 0.00; see Table <ref type="table">2</ref>). So, our results contain no evidence for a difference between explanation types concerning our three dependent variables.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>RQ3: interactions between aggregation strategies and explanation types regarding explanation effectiveness.</head><p>There were no significant interaction effects between the five aggregation strategies and the three explanation types (H3a -H3c; 𝐹 = [0.65, 1.25], 𝑝 = [0.27, 0.71], 𝜂 2 𝑝 = [0.01, 0.03]; see Table <ref type="table">2</ref>). The effect of explanation types on participants' fairness perception, consensus perception, and satisfaction thus did not significantly differ based on which aggregation strategy was applied.</p><p>RQ4: associations between explanation effectiveness measures. In line with the findings of Tran et al. <ref type="bibr" target="#b16">[17]</ref>, Spearman correlation analyses revealed significant positive relationships between fairness perception and satisfaction (𝜌 = 0.71, 𝑝 &lt; 0.001) as well as between consensus perception and satisfaction (𝜌 = 0.76, 𝑝 &lt; 0.001). This means that, as participants' fairness and consensus perception increased, satisfaction also increased.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.">Discussion</head><p>In the following sections, we look closer at our results and their implications. We discuss the difference between aggregation strategies, the difference between different explanation levels, and the effect of the chosen scenario. We conclude with lessons learned for future benchmarking studies in explanations research and limitations of our study.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.1.">The Differences Between Aggregation Strategies</head><p>As shown in Section 4, there are differences between the aggregation strategies in terms of perceived fairness, perceived consensus, and satisfaction. The MLP strategy obtains the lowest scores, regardless of the type of explanation received. Furthermore, MAJ and APP are perceived to be less fair than LMS. We discuss how these results may have interacted with the presented scenario in Section 5.5. However, these results are in contrast with the findings of Tran et al. <ref type="bibr" target="#b16">[17]</ref>, where the same scenario was used. In such work, the MAJ and ADD strategies scored better than the LMS strategy. An explanation of this difference can be the different design of our experiment: we implemented a between-subject design to guarantee the independence between the conditions; on the contrary, in <ref type="bibr" target="#b16">[17]</ref> each user evaluated six strategies and was exposed to different explanation types. Although the strategies were presented in a randomized order to reduce biases, it is possible that the user used an explanation type seen first as a reference point to compare with, in the following evaluations, which introduced noise in the users' evaluations. Furthermore, to evaluate the effect of the aggregation strategy separately from the explanation, we asked participants to evaluate the recommendation. In contrast, Tran et al. <ref type="bibr" target="#b16">[17]</ref> asked the participants to evaluate the explanation provided, hence the evaluation of the explanation was influenced by the evaluation of the aggregation strategy.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.2.">The Role of Explanations</head><p>The results presented showed no significant difference between the different types of explanations. Furthermore, no interaction effects between the explanations and the aggregations regarding the measured dependent variables (perceived fairness, perceived consensus, and satisfaction) were found. However, these results are not enough to claim that the explanations are not useful for group recommender systems. First, it must be considered that the used scenario was particularly simple to evaluate. More complex scenarios might involve a more balanced situation between subgroups with different preferences, or a greater number of options to choose from: such factors might complicate the assessment; in such cases, an explanation of the approach used might have an impact. Moreover, the strategies presented here represent baselines for group recommenders. Therefore, it is necessary to formalise the explanations for these strategies, as they serve as a reference against which more articulated strategies can be compared. The most recent lines of research in group recommenders, however, try to integrate into the recommendation generation process personal factors (experience in the domain <ref type="bibr" target="#b31">[32]</ref> or personality <ref type="bibr" target="#b32">[33,</ref><ref type="bibr" target="#b27">28,</ref><ref type="bibr" target="#b33">34]</ref>), as well as social factors (tie strength <ref type="bibr" target="#b34">[35]</ref>, centrality of group members in the group social network <ref type="bibr" target="#b35">[36]</ref>, group diversity <ref type="bibr" target="#b36">[37]</ref>). In such cases, an explanation may have an impact on the transparency and comprehensibility of the system and result in different evaluations regarding fairness perception, consensus perception, and satisfaction. This, of course, also leads to privacy issues, concerning which personal information of one or more individuals can be mentioned in an explanation.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.3.">The Link Between Fairness, Consensus, and Satisfaction</head><p>The correlation between fairness perception (or consensus perception) and satisfaction, already reported in Tran et al. <ref type="bibr" target="#b16">[17]</ref>, and also showed in our results, confirms the close connection between these concepts. A solution perceived as less fair is also perceived as less satisfactory, and a less satisfactory solution is unlikely to be accepted by the group. This confirms that these aspects, sometimes considered secondary, are crucial and that a group recommendation system must take them into account, both in the generation of recommendations and in their evaluation.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.4.">Lessons Learned for Benchmarking</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Report on Participant Recruitment</head><p>Numerous platforms can be used to outsource user studies <ref type="bibr" target="#b37">[38]</ref>, such as Prolific and Amazon Mechanical Turk. Recruitment might also focus on particular users, such as students or staff members. Filtering conditions, such as those for quality control also affect which demographics take part in a study. More generally, any selection of study participants can influence the outcome of the evaluation, which should not be generalized outside the scope of the scenario <ref type="bibr" target="#b38">[39]</ref>. Therefore, we recommend a thorough reporting on how participants were recruited.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Report Study Design and Statistical Analysis Rigorously</head><p>The choice of the quantitative study, between-subjects, within-subjects or mixed designs is also influencing the conclusions that can be drawn, as well as the statistical analysis that should be applied. In any case, randomizing participants to conditions is of paramount importance, regardless of study design. More personalized study designs, such as the one conducted by Tran et al. <ref type="bibr" target="#b16">[17]</ref>, should clearly specify how each scenario has been allocated to participants, to be able to replicate them. We, in particular, recommend more rigorous reporting of how randomization is performed, as well as sharing scripts to support replication and comparison.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Ensure consistency in measurement or motivate changes well</head><p>In separating the evaluation of explanations and aggregation strategy, we found it was no longer feasible to ask participants to evaluate the explanations rather than the resulting recommendation. In addition, compared to Tran et al. <ref type="bibr" target="#b16">[17]</ref>, we ask study participants to rate explanations' effectiveness on a 7-point Likert scale, instead of a 5-point Likert scale, since this ensures greater robustness in the use of ANOVA analysis, according to <ref type="bibr" target="#b29">[30]</ref>. While these changes may not have affected the results, such changes in the design must be described and motivated when attempting to benchmark such user studies.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Report on Completeness</head><p>We found that certain aggregation strategies can not be explained in certain instances or scenarios. In this paper, this was the case of the Fairness strategy, which is well-suited for repeated decisions, but less applicable for single decisions as in our case. We recommend that future work not only describes the cases where explanations can be generated but also describes the edge cases for which they cannot.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Consider the Effect of the Scenario</head><p>The proposed scenario in this work was selected to specifically study groups with heterogeneous preferences. However, this choice is likely to have affected our specific results. For example, the MPL strategy in this specific scenario recommends a solution that displeases at most three out of four group members (Rest C, see Table <ref type="table" target="#tab_0">1</ref>). It is not surprising, therefore, that it is identified as the least fair, least satisfactory strategy, and the one on which it is most difficult to reach an agreement. The result might have been different if it displeased fewer group members. We, therefore, recommend not only to clearly report on the scenario used, but also to discuss its implications.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Consider effects of the role of the participant in a group</head><p>The evaluations are given in this paper based on an external evaluator who may be more unbiased (than someone within the group). Users within the group may be influenced by their own preferences. Furthermore, the assessment of the fairness of a scenario will likely differ depending on whether it favors the user, e.g., if MLP displeases 2 users and whether the active user is one of them.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.5.">Limitations</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Recommendations and explanations are not evaluated by group members</head><p>As previously mentioned, in line with the evaluation approach in Tran et al. <ref type="bibr" target="#b16">[17]</ref>, our study participants were asked to evaluate the recommendations as external evaluators. This means that study participants were not members of the group. We hypothesize, however, that their evaluations could be different when part of the group. Deciding for an evaluator that is part of the group would entail controlling more cases, such as when the evaluator is in the majority preference, minority preference, or a tie preference.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>A. Appendix -Basic and Detailed Explanations</head><p>In this appendix, we specify how to generate the Basic and Detailed explanations used in this work, for each of the aggregation strategies considered (see section 3.1). Let 𝐺 = {𝑢 1 , ..., 𝑢 𝑛 } be a group of users, and 𝐼 = {𝑖 1 , ..., 𝑖 𝑚 } be a set of items. Also, let {𝑢 𝑗 1 , 𝑢 𝑗 2 , ..., 𝑢 𝑗𝑛 ¯} be a subset of group members who gave a specific rating 𝑟 to the item 𝑖 𝑘 selected by the considered strategy. Hence, we can define the explanations, for each aggregation strategy, as in the Table <ref type="table" target="#tab_2">3</ref>, while the Table <ref type="table">4</ref> shows the explanations obtained on the scenario used in the experiment (see the Table <ref type="table" target="#tab_0">1</ref>). </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Table 4</head><p>All possible explanation scenarios that participants saw in our study. The explanations describe a restaurant recommendation scenario that participants were exposed to (based on the scenario defined in Table <ref type="table" target="#tab_0">1</ref>). </p></div><figure xmlns="http://www.tei-c.org/ns/1.0" xml:id="fig_0"><head>Figure 1 :</head><label>1</label><figDesc>Figure 1: Participants' mean fairness perception, consensus perception, and satisfaction across explanation types on scales from −3 ("strongly disagree") to 3 ("strongly agree"; see Section 3.3). Colors indicate aggregation strategies: Additive Utilitarian (ADD), Approval Voting (APP), Least Misery (LMS), Majority (MAJ), Most Pleasure (MPL). Error bars represent the standard error of the mean.</figDesc></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_0"><head>Table 1 :</head><label>1</label><figDesc>Ratings</figDesc><table><row><cell></cell><cell></cell><cell cols="3">of group members for</cell></row><row><cell></cell><cell cols="4">the restaurants (1: the worst,</cell></row><row><cell></cell><cell cols="4">5: the best) from Tran et al.</cell></row><row><cell></cell><cell>[17].</cell><cell></cell><cell></cell><cell></cell></row><row><cell></cell><cell cols="4">Alex Anna Sam Leo</cell></row><row><cell>Rest A Rest B Rest C</cell><cell>2 1 5</cell><cell>2 4 1</cell><cell>4 4 1</cell><cell>4 4 1</cell></row></table></figure>
<figure xmlns="http://www.tei-c.org/ns/1.0" type="table" xml:id="tab_2"><head>Table 3</head><label>3</label><figDesc>Generic formulations for each aggregation strategy of the explanations used in this study. 𝑘 has been recommended to the group since no group members has a real problem with it (as 𝑢𝑗 1 , 𝑢𝑗 2 , ... and 𝑢𝑗 𝑛 ¯gave it a rating of 𝑟 which is the highest rating among the lowest ratings per item). " 𝑘 has been recommended to the group since it achieves the highest of all individual group members' ratings (as 𝑢𝑗 1 , 𝑢𝑗 2 , ... and 𝑢𝑗 𝑛 ¯gave it the rating 𝑟, which is the highest rating among all items' high ratings). "</figDesc><table><row><cell cols="2">Strat. No explanation</cell><cell>Basic explanation</cell><cell>Detailed explanation</cell></row><row><cell>ADD</cell><cell>"𝑖 𝑘 has been recom-</cell><cell>"𝑖 𝑘 has been recommended to</cell><cell>"𝑖 𝑘 has been recommended to the group since it</cell></row><row><cell></cell><cell>mended to the group. "</cell><cell>the group since it achieves the</cell><cell>achieves the highest total rating (as the sum of</cell></row><row><cell></cell><cell></cell><cell>highest total rating. "</cell><cell>the ratings of all members for 𝑖 𝑘 is 𝑟 which is</cell></row><row><cell></cell><cell></cell><cell></cell><cell>higher than other items). "</cell></row><row><cell>APP</cell><cell>"𝑖 𝑘 has been recom-</cell><cell>"𝑖 𝑘 has been recommended</cell><cell></cell></row><row><cell></cell><cell>mended to the group. "</cell><cell>to the group since it achieves</cell><cell></cell></row><row><cell></cell><cell></cell><cell>the highest number of ratings</cell><cell></cell></row><row><cell></cell><cell></cell><cell>which are above 𝜃. "</cell><cell></cell></row><row><cell>MAJ</cell><cell>"𝑖 𝑘 has been recom-</cell><cell>"𝑖 𝑘 has been recommended to</cell><cell>"𝑖 𝑘 has been recommended to the group since</cell></row><row><cell></cell><cell>mended to the group. "</cell><cell>the group since most group</cell><cell>most group members like it (as 𝑛 ¯out of 𝑛 group</cell></row><row><cell></cell><cell></cell><cell>members like it. "</cell><cell>members gave it a high rating). "</cell></row><row><cell>MPL</cell><cell>"𝑖 𝑘 has been recom-</cell><cell>"𝑖 𝑘 has been recommended to</cell><cell>"𝑖</cell></row><row><cell></cell><cell>mended to the group. "</cell><cell>the group since it achieves the</cell><cell></cell></row><row><cell></cell><cell></cell><cell>highest of all individual group</cell><cell></cell></row><row><cell></cell><cell></cell><cell>members. "</cell><cell></cell></row></table><note>"𝑖 𝑘 has been recommended to the group since it achieves the highest number of ratings which are above a threshold (as the 𝑛 ¯group members 𝑢𝑗 1 , 𝑢𝑗 2 , ... and 𝑢𝑗 𝑛 ¯gave it ratings higher than 𝜃). "LMS"𝑖 𝑘 has been recommended to the group. ""𝑖 𝑘 has been recommended to the group since no group members has a real problem with it. ""𝑖</note></figure>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" n="1" xml:id="foot_0">To preregister our study, we publicly determined our research questions, hypotheses, experimental setup, and data analysis plan before any data collection. The (time-stamped) preregistration can be found at https://osf.io/ ghbsq.</note>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" n="2" xml:id="foot_1">We note here that we slightly changed the preregistered hypotheses according to the change made to the research question. The intention is to compare all five aggregation strategies and not only the ones that are categorized as consensus-based.</note>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" n="3" xml:id="foot_2">All material for analyzing our results and replicating our user study, (i.e., document with preregistration of all the hypotheses tested, user study materials, data gathered in the user study and the analysis scripts) is publicly available -https://osf.io/5xbgf/.</note>
		</body>
		<back>
			<div type="annex">
<div xmlns="http://www.tei-c.org/ns/1.0"><head>We do not measure nor capture the reasoning process of the study participants regarding recommendations</head><p>In the condition with no explanations, we provide a mere description of the recommendation. However, we do not capture how study participants reflect on the recommendation or to what extent they understand it. Prior literature <ref type="bibr" target="#b39">[40,</ref><ref type="bibr" target="#b13">14,</ref><ref type="bibr" target="#b40">41]</ref>, however, provides several directions for measuring recommendation understandability, which could be investigated in future work. Nevertheless, our descriptive analysis in Section 4 shows that participants spent a similar amount of time to complete each explanation condition. This suggests that they spent a similar amount of effort analyzing their fairness and consensus perception, as well as satisfaction regarding the recommended restaurant.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head>Recommendations are provided for unnamed restaurants</head><p>We did not want to influence participants' decisions by providing real restaurant names as recommendations. This helped us control for the potential bias that could have been added while showing a real restaurant name. Such normalization, however, could potentially influence the assessments of the study participants, compared to a customized recommendation. Another limitation of our study is that all recommendations are in the restaurants' domain. Different recommendation domains could be differently perceived in terms of fairness, consensus, and satisfaction. In particular, the investment related to the domain considered has shown to have an impact on the evaluation of the recommendations <ref type="bibr" target="#b41">[42]</ref>; the restaurant domain is generally perceived as a medium-low investment, compared to other domains suitable for group recommendations, such as tourism.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="6.">Conclusions</head><p>We present a preregistered evaluation of the impact of using social choice-based explanations for group recommendations. Overall, our finding suggests that explanations are not necessarily helpful for improving perceptions of the recommendations. Participants' evaluations were not influenced by the presence of an explanation, and their perceptions of fairness, consensus, and satisfaction were primarily formed based on the social choice-based aggregation strategies. Participants evaluated the Least Misery (LMS) strategy as more fair than the Approval Voting (APP) and the Majority (MAJ), while the Most Pleasure (MPL) was considered the worst in terms of perceived fairness, perceived consensus, and satisfaction. We also discuss some of the challenges and decision points required to benchmark future studies of group explanations. In particular, we highlighted the importance of clarifying and motivating the recruitment process and properly choosing the experimental design, specifying how each condition is assigned to each participant. Furthermore, we discussed how the choice of the scenario to present for the evaluation can influence the results, and that, therefore, the results should always be discussed in relation to it. In future work, we plan to investigate the influence of internal vs. external evaluators. We plan to thoroughly study the reasoning process of evaluators and measure the level of understanding regarding the recommended item. To observe to what extent our results generalize, we also plan to replicate our study with other scenarios and domains.</p></div>			</div>
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