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@@ -191,7 +191,7 @@ This section gives an overview over the hypothesis tested during data analysis.
\begin{hypothesis}
\begin{itshape}
\label{hyp:Evaluation:MaximumMinimum} Highest improvements with group recommendation are when the amount of people satisfied with the dictator's decision is slightly lower than two and the highest reduction in dissatisfied group members can be seen with around two group members dissatisfied respectively.
\label{hyp:Evaluation:MaximumMinimum} Highest improvements with group recommendation are when the amount of people satisfied with the dictator's decision is slightly lower than two and the highest reduction in dissatisfied group members can be seen at around two group members dissatisfied respectively.
\end{itshape} \medskip \\*
This expectation is made because the assumption is made that in a real situation a group of four with having a few less than two satisfied members on average (with a dictator's decision) has enough room for improvement so that potentially three group members can be satisfied after the use of the recommender. Meaning that at least one more person is satisfied with the compromise. Potentially in some groups it might even be possible to then lift the last person from dissatisfaction towards a neutral attitude. A higher base satisfaction is assumed to reduce the possibility to make an additional group member satisfied.
\end{hypothesis}
@@ -236,7 +236,7 @@ This section gives an overview over the hypothesis tested during data analysis.
\begin{itshape}
\label{hyp:Evaluation:AggregationStrategies} Multiplication and best average aggregation strategies perform better than least misery across the board.
\end{itshape} \medskip \\
Best average and multiplication are strategies that are performing best in some of the, by \citeauthor{Masthoff2015} \cite[p. 755f]{Masthoff2015}, listed online experiments. Therefore it is reasonable to assume that they perform well here too. Least misery was listed in some studies as performing worst. Therefore there is an expectation of it faring less good than other group aggregation strategies.
Best average and multiplication are strategies that are performing best in some of the, by \citeauthor{Masthoff2015} \cite[p. 755f]{Masthoff2015}, listed online experiments. Therefore it is reasonable to assume that they perform well here, too. Least misery was listed in some studies as performing worst. Therefore there is an expectation of it faring less good than other group aggregation strategies.
\end{hypothesis}
\section{Results}
@@ -244,7 +244,8 @@ This section gives an overview over the hypothesis tested during data analysis.
\subsection{Threshold Center}
To get an understanding of the data all parameters except the $tc$ will be fixed. The preference aggregation strategy looked at is multiplication. The configuration database is used with all possible solutions (which is 148 in total). This results in a bigger visible effect as the recommender has access to all possible configurations. \autoref{fig:Evaluation:tcChange} shows the satisfaction change based on choice of $tc$. Of note is that the maxima of satisfaction change precedes the minima of dissatisfaction change for all group types. Maxima and minima occur at different tc values depending on the group type. Heterogeneous groups peek earliest while homogenous groups only show a peek towards the maximum $tc$ value. Changes in dissatisfaction are minimal even with $tc$ close to its maximum value. \autoref{fig:Evaluation:tcCount} shows the amount of group members satisfied and dissatisfied with a decision. The number of satisfied people decreases with an increasing $tc$ and its downward movement accelerates. The dissatisfaction curve shows a similar trend but in contrast here the number of dissatisfied group members increases with an increase in $tc$. The curve accelerates its growth analogues to the acceleration of the satisfaction curve. The behaviour of heterogeneous groups and random groups is similar but the curve for heterogeneous groups show less satisfaction and more dissatisfaction for a given tc. Also both curves have a negative satisfaction change when $tc$ reaches a certain height. Homogeneous groups only have happy group members for most $tc$ values but they decrease rapidly for values greater $85$. Dissatisfied group members are at zero for the whole value range of $tc$ except a very slight upward tick at the end that is barely noticeable.
To get an understanding of the data \todo{konkreter werden!
hier geht es darum, einen sinnvollen Wert für tc für die weiteren Auswertungen zu finden} all parameters except the $tc$ will be fixed. The preference aggregation strategy looked at is multiplication \todo{warum?}. The configuration database is used with all possible solutions (which is 148 in total). This results in a bigger visible \todo{von was?} effect as the recommender has access to all possible configurations. \autoref{fig:Evaluation:tcChange} shows the satisfaction change based on choice of $tc$. Of note is that the maxima of satisfaction change precedes the minima of dissatisfaction change for all group types. Maxima and minima occur at different tc values depending on the group type. Heterogeneous groups peek earliest while homogenous groups only show a peek towards the maximum $tc$ value. Changes in dissatisfaction are minimal even with $tc$ close to its maximum value for homogeneous groups. \autoref{fig:Evaluation:tcCount} shows the amount of group members satisfied and dissatisfied with the dictator's decision. The number of satisfied people decreases with an increasing $tc$ and its downward movement accelerates. The dissatisfaction curve shows a similar trend in reverse. Here the number of dissatisfied group members increases with an increase in $tc$. The curve accelerates its growth analogous to the acceleration of the satisfaction curve. The behaviour of heterogeneous groups and random groups is similar but the curve for heterogeneous groups show less satisfaction and more dissatisfaction for a given tc. Also both curves have a negative satisfaction change when $tc$ reaches a certain height. Homogeneous groups only have happy group members for most $tc$ values but they decrease rapidly \todo[]{warum} for values greater $85$. Dissatisfied group members are at zero for the whole value range of $tc$ except a very slight upward tick at the end that is barely noticeable.
\begin{figure}
\centering
@@ -253,7 +254,7 @@ To get an understanding of the data all parameters except the $tc$ will be fixed
\label{fig:Evaluation:tcChange}
\end{figure}
\autoref{hyp:Evaluation:MaximumMinimum} states that the highest satisfaction change is expected at places where the overall satisfaction with the dictator's decision is close to two. However the data shows a slightly different result. This hypothesis does not hold true. When looking at the data we see peeks in satisfaction change when values are equal to $2.81, 2.51$ and $3$ (heterogeneous, random, homogenous). Therefore the expectation does not hold up. Moreover, valleys for dissatisfaction change are also not at the expected value of \textit{two}. They are instead at $1.19, 1.49, 0.04$ (heterogeneous, random, homogenous). Here the valleys are lower than expected. However the data from homogenous groups seems to be cut of. Therefore, it is not possible to say if there would be a potentially bigger decrease with a use case with more possible solutions.
\autoref{hyp:Evaluation:MaximumMinimum} states that the highest satisfaction change is expected at places where the overall satisfaction with the dictator's decision is close to two. However, the data shows a slightly different result. This hypothesis does not hold true. When looking at the data we see peeks in satisfaction change when values are equal to $2.81, 2.51$ and $3$ (heterogeneous, random, homogenous). Therefore the expectation does not hold up \todo[inline]{dieser Absatz sollte mit einer kurzen DIskussion enden, warum die Hypothese wider Erwarten nicht zutrifft}. Moreover, valleys for dissatisfaction change are also not at the expected value of \textit{two}. They are instead at $1.19, 1.49, 0.04$ (heterogeneous, random, homogenous). Here the valleys are lower than expected. However, the data from homogenous groups seems to be cut of. Therefore, it is not possible to say if there would be a potentially bigger decrease with a use case with more possible solutions \todo[inline]{wie hängt die Anzahl der gespeicherten Lösungen mit dieser Hypothese zusammen?}.
\begin{figure}
\centering
@@ -262,13 +263,16 @@ To get an understanding of the data all parameters except the $tc$ will be fixed
\label{fig:Evaluation:tcCount}
\end{figure}
The predicted trend that a higher $tc$ results in a lower satisfaction and a higher dissatisfaction, with the dictator's decision, as predicted by \autoref{hyp:Evaluation:HigherTcLessSatisfied} can be clearly seen in \autoref{fig:Evaluation:tcCount} and has been described in this section already.
The predicted trend that a higher $tc$ results in a lower satisfaction and a higher dissatisfaction with the dictator's decision, as predicted by \autoref{hyp:Evaluation:HigherTcLessSatisfied}, can be clearly seen in \autoref{fig:Evaluation:tcCount} and has been described in this section already \todo[inline]{discussion: was bedeutet das für die Hypothese bzw deine Evaluation?
Verhalten ist wie erwartet und auch so, wie es wahrscheinlich im realen Setting wäre}.
\autoref{hyp:Evaluation:OnlyOneSatisfied} predicts that the satisfaction with the individual decision eventually reaches one and that no one is satisfied with the group recommender decision. This means the satisfaction change should reach minus one. \autoref{fig:Evaluation:tcCount} shows a downward trend that comes close to one for heterogeneous and random groups. Therefore, the trend suggests that the hypothesis holds in regards to heterogeneous and random groups but as the drop for homogenous groups just reaches below $2.8$ suggesting that the hypothesis does not hold for homogenous groups. Also, satisfaction change in heterogeneous groups reaches close to minus one but this value is neither reached by random groups, nor by homogenous groups. The hypothesis therefore should not be seen as confirmed in that regard as well and further investigation is needed.
\autoref{hyp:Evaluation:OnlyOneSatisfied} predicts that the satisfaction with the individual decision eventually reaches one and that no one is satisfied with the group recommender decision. This means the satisfaction change should reach minus one. \autoref{fig:Evaluation:tcCount} shows a downward trend that comes close to one for heterogeneous and random groups. Therefore, the trend suggests that the hypothesis holds with regard to heterogeneous and random groups but as the drop for homogenous groups just reaches below $2.8$ suggesting that the hypothesis does not hold for homogenous groups. Also, satisfaction change in heterogeneous groups reaches close to minus one but this value is neither reached by random groups, nor by homogenous groups. The hypothesis therefore should not be seen as confirmed in that regard as well and further investigation is needed \todo[inline]{besser: auf heterogene Gruppen trifft die Hypothese zu. Hier auch wieder: was bedeutet das?
Diskussion, warum die Hyp bei den anderen zwei Gruppen nicht zutreffend ist}.
During a group decision it is better to make one less person dissatisfied opposed to one more person satisfied. Therefore, this thesis uses $tc$ values that are closer to the minima of dissatisfaction change than to the maxima of satisfaction change. The minima for heterogeneous groups is at $tc = 70\%$ therefore this is the chosen value for the evaluation of other aspects. For random groups the minima of dissatisfaction change can be found at $tc = 85\%$ which is the value used for all following analysis of random groups. For homogenous group dissatisfaction change is decreasing until the highest possible value of $tc$ is reached. Because of that $tc = 94\%$ is used for analysis.
During \todo[inline]{hier oder am Anfang der Analyse nochmal eine Erklärung warum mit genau dieser gewählten Parametereinstellung Werte für tc bestimmt wurden
--maximale \# config ist am solidesten, bei einer groben betrachtung der Daten (eyeballing) hat sich multiplication als am besten herausgestellt, o.ä.} a group decision it is better to make one less person dissatisfied opposed to one more person satisfied. Therefore, this thesis uses $tc$ values that are closer to the minima of dissatisfaction change than to the maxima of satisfaction change. The minima for heterogeneous groups is at $tc = 70\%$ therefore this is the chosen value for evaluation of the remaining hypotheses. This is needed because otherwise analysis would be infeasible due to the parameter space being too large. For random groups the minima of dissatisfaction change can be found at $tc = 85\%$ which is the value used for all following analysis of random groups. For homogenous group dissatisfaction change is decreasing until the highest possible value of $tc$ is reached. Because of that $tc = 94\%$ is used for analysis.
\subsection{Data Analysis}
\subsection{Recommender Performance Analysis}
\begin{figure}[p]
\centering
@@ -291,19 +295,15 @@ During a group decision it is better to make one less person dissatisfied oppose
\label{fig:Evaluation:HomoSatisfaction}
\end{figure}
This subsection holds fixed parameters of $tc$. It describes the satisfaction change and the total amount of satisfied people with the recommenders decision dependent on the amount of stored configurations. For clarity reasons not all graphs of the data are included. The missing graphs can be found in the appendix and have references to them.
This subsection holds fixed parameters of $tc$. In it the satisfaction change and the total amount of satisfied people with the recommenders decision dependent on the amount of stored configurations. For clarity reasons not all graphs of the data are included. The missing graphs can be found in the appendix and have references to them.
\autoref{fig:Evaluation:HeteroSatisfaction} shows the relationship between the change in satisfaction and dissatisfaction and the stored number of configurations. There are three graphs each. One for multiplication, one for least misery and one for best average. The graphs for satisfaction look similar to a logarithmic curve. The increase in change of satisfaction decelerates with a higher number of stored configurations. The change in satisfaction is always above zero and a satisfaction increase of more than three quarters of the maximum can already be seen with around 25 stored configurations. Moreover, the curve for multiplication is greater than all other curves for all parameters. Least misery reaches the lowest amount of change across all values. The minimum number of satisfaction change is $0$ for least misery, and $0.1$ for best average and multiplications. The highest number is around $0.3$ for least misery, $0.4$ for best average and $0.5$ for multiplication
\autoref{fig:Evaluation:HeteroSatisfaction} \todo[]{auch hier: erkläre genauer, wie die Graphen aufgebaut sind und gib dem Leser eine Interpretationshilfe an die hand (links sind hohe Werte gut, rechts niedrige)} shows the relationship between the change in satisfaction and dissatisfaction and the number of stored configurations. There are three graphs each. One for multiplication, one for least misery and one for best average. The graphs for satisfaction are similar to a logarithmic curve. The increase in change of satisfaction decelerates with a higher number of stored configurations. The change in satisfaction is always above zero and a satisfaction increase of more than three quarters of the maximum can already be seen at around 25 stored configurations. Moreover, the curve for multiplication is greater than all other curves for all parameters. Least misery reaches the lowest amount of change across all values. The minimum number of satisfaction change is $0$ for least misery, and $0.1$ for best average and multiplications. The highest number is around $0.3$ for least misery, $0.4$ for best average and $0.5$ for multiplication
When looking at dissatisfaction change the graphs are all in the negative number range. Multiplication reaches the lowest number and best average the highest. The gap between all three functions is less than that of satisfaction increase. And overall the curves are flatter meaning the change with 25 stored configurations already reaches close to five sixth of the minimum value. The highest number of satisfaction change is $-0.4$ for all strategies meanwhile the lowest number is around $-0.57$ for least misery, $-0.53$ for best average and $-0.63$ for multiplication.
The figures for homogenous (\autoref{fig:Evaluation:HomoSatisfaction}) and random groups (\autoref{fig:Evaluation:RandomSatisfaction}) have a similar shape but their values and slope vary. The satisfaction change for homogenous groups is mostly negative, starting at $-2$, and only reaches a positive level for more than $100$ stored configurations with a value of $0.04$. Multiplication and best average have higher values than least misery here too. Moreover the dissatisfaction change is positive across the bored with a value range of $[0,1]$.
Random groups as seen in \autoref{fig:Evaluation:RandomSatisfaction} mostly have a positive change in satisfaction. Values range here from $-0.55$ to $0.27$ for least misery, from $-0.27$ and $-0.28$ to $0.74$ for best average and multiplication. The change is higher than the change for heterogeneous groups. dissatisfaction also changes similarly to heterogeneous groups. Here the values for random groups reach a lower level. They range from $0$ to $-0.59$ for least misery. Multiplication and best average both have as minimum value around $-0.21$ and behave similarly. The range goes down to $-0.84$ for best average and $-0.86$ for multiplication.
The figures for homogenous (\autoref{fig:Evaluation:HomoSatisfaction}) and random groups (\autoref{fig:Evaluation:RandomSatisfaction}) have a similar shape but their values and slope vary. The satisfaction change for homogenous groups is mostly negative, starting at $-2$, and only reaches a positive level for more than $100$ stored configurations with a value of $0.04$. Multiplication and best average have higher values than least misery here, too. Moreover the dissatisfaction change is always positive with a value range of $[0,1]$, except it slightly falls below zero after more than $75$ configurations are stored.
Random groups as seen in \autoref{fig:Evaluation:RandomSatisfaction} mostly have a positive change in satisfaction. Values range here from $-0.55$ to $0.27$ for least misery, from $-0.27$ and $-0.28$ to $0.74$ for best average and multiplication. The change is higher than the change for heterogeneous groups. Dissatisfaction also changes similarly to heterogeneous groups. Here the values for random groups reach a lower level. They range from $0$ to $-0.59$ for least misery. Multiplication and best average both have as minimum value around $-0.21$ and behave similarly. The range goes down to $-0.84$ for best average and $-0.86$ for multiplication.
\autoref{fig:Evaluation:HeteroSatisfaction} also shows the total number of group members satisfied and dissatisfied with the recommender's decision. Satisfaction with the recommender's decision starts at $2.4$ and quickly reaches $2.65$ for least misery and $2.8$ for best average and multiplication. The highest value for multiplication is at $2.89$. Dissatisfaction also quickly plateaus. Here values for different recommenders are closer together. They start at $0.74$ (least misery) to $0.78$ (best average) and go as low as $0.62$ for least misery, $0.66$ for best average and $0.56$ for multiplication.
\autoref{fig:Evaluation:HeteroSatisfaction} also shows the average number of group members satisfied and dissatisfied with the recommender's decision. Satisfaction with the recommender's decision starts at $2.4$ and quickly reaches $2.65$ for least misery and $2.8$ for best average and multiplication. The highest value for multiplication is at $2.89$. Dissatisfaction also quickly plateaus. Here values for different recommenders are closer together. They start at $0.74$ (least misery) to $0.78$ (best average) and go as low as $0.62$ for least misery, $0.66$ for best average and $0.56$ for multiplication.
As shown in \autoref{fig:Evaluation:HomoSatisfaction} when looking at the total numbers the value range for homogenous groups is much larger but the overall shape stays the same. Here satisfaction numbers go from $0.55$ to $2.95$. Least misery performs visibly worse than multiplication and best average reaching only $2.7$. Dissatisfaction values range from $1.21$ to $0.01$ and the values are not really visibly distinguishable besides that in the range $[25,50]$ least misery seems to have the highest number of dissatisfied group members.
@@ -311,15 +311,15 @@ Random groups have less overall satisfaction with $tc = 85\%$ as seen in \autore
\subsection{Discussion}
After description of the data now the focus shifts to the hypotheses left that have not been evaluated.
\autoref{hyp:Evaluation:HomogenousMoreSatisfied} states that homogenous groups have more satisfied member's with regards to the dictator's and the group recommender's decision. \autoref{fig:Evaluation:tcCount} shows that this holds true for dictator's decision as for every instance satisfaction in homogeneous groups is higher than that of other groups. However \autoref{fig:Evaluation:HeteroSatisfaction}, \autoref{fig:Evaluation:HomoSatisfaction} and \autoref{fig:Evaluation:RandomSatisfaction} show that for satisfaction with the recommender's decision this does not hold when looking at $tc$ values where the recommender performs best for each segment. In those places the homogenous group only reaches the highest amount of satisfaction when the recommender has access to all stored configurations. With a decreasing number of stored configurations both random groups and heterogeneous groups perform better. It is important to note, when the same $tc$ values are used homogenous groups have a higher amount of satisfied people across the board.
After description of the data the remaining hypotheses are discussed.
\autoref{hyp:Evaluation:HomogenousMoreSatisfied} states that homogenous groups have more satisfied member's with regards to the dictator's and the group recommender's decision. \autoref{fig:Evaluation:tcCount} shows that this holds true for dictator's decision as for every instance satisfaction in homogeneous groups is higher than that of other groups. However, \autoref{fig:Evaluation:HeteroSatisfaction}, \autoref{fig:Evaluation:HomoSatisfaction} and \autoref{fig:Evaluation:RandomSatisfaction} show that for satisfaction with the recommender's decision this does not hold when looking at $tc$ values where the recommender performs best for each segment. In those places the homogenous group only reaches the highest amount of satisfaction when the recommender has access to all stored configurations. With a decreasing number of stored configurations both random groups and heterogeneous groups achieve a higher satisfaction \todo[]{Interpretation: warum ist das so?}. It is important to note, when the same $tc$ values are used homogenous groups have a higher amount of satisfied people across the board.
\autoref{hyp:Evaluation:HeterogenousBiggerSatisfactionIncrease} states that the increase in satisfaction should be bigger for more heterogeneous groups. However \autoref{fig:Evaluation:HeteroSatisfaction}, \autoref{fig:Evaluation:HomoSatisfaction} and \autoref{fig:Evaluation:RandomSatisfaction} show this to be not true. The recommendations for heterogeneous groups indeed cause a larger change in satisfaction compared to homogeneous groups but random groups cause a positive change of higher magnitude. Also the decrease in dissatisfaction is higher among random groups.
\autoref{hyp:Evaluation:HeterogenousBiggerSatisfactionIncrease} states that the increase in satisfaction should be bigger for more heterogeneous groups. However, \autoref{fig:Evaluation:HeteroSatisfaction}, \autoref{fig:Evaluation:HomoSatisfaction} and \autoref{fig:Evaluation:RandomSatisfaction} show this to be not true. The recommendations for heterogeneous groups indeed cause a larger change in satisfaction compared to homogeneous groups but random groups cause a positive change of higher magnitude. Also the decrease in dissatisfaction is higher among random groups \todo[]{Interpretation: warum ist das so? Warum trifft die Hypothese nicht zu?}.
The data shows that having a larger configuration database causes the amount of satisfied group members to be greater than recommendation's using a smaller database. With dissatisfaction the same is seen in inverse. A larger configuration database causes the number of dissatisfied group members to drop compared to a small database. However in some runs there have been instances of least misery that have seen a slight drop. This can be seen in \autoref{fig:Evaluation:HeteroSatisfaction} when comparing $74$ and $148$ as number of stored configurations. Why this happens is not entirely clear but a cause of that might be that least misery just takes into account the worst performing group member of the group. Therefore it is possible that there is a second slightly worse solution, when comparing least misery scores, which actually has a slight advantage in terms of dissatisfaction. Having this second best configuration can cause it to be in the second database partition therefore resulting in less dissatisfaction on average. \autoref{hyp:Evaluation:StoreSizeBetterResults} therefore is supported by the data but it does not fully hold up when looking at least misery.
The data shows that having a larger configuration database causes the amount of satisfied group members to be greater than recommendation's using a smaller database. With dissatisfaction the same is seen in inverse. A larger configuration database causes the number of dissatisfied group members to drop compared to a small database. However, in some runs there have been instances of least misery that have seen a slight drop. This can be seen in \autoref{fig:Evaluation:HeteroSatisfaction} when comparing $74$ and $148$ as number of stored configurations. Why this happens is not entirely clear but a cause of that might be that least misery just takes into account the worst performing group member of the group. Therefore it is possible that there is a second slightly worse solution, when comparing least misery scores, which actually has a slight advantage in terms of dissatisfaction. Having this second best configuration can cause it to be in the second database partition therefore resulting in less dissatisfaction on average. \autoref{hyp:Evaluation:StoreSizeBetterResults} therefore is supported by the data but it does not fully hold up when looking at least misery.
\autoref{hyp:Evaluation:AggregationStrategies} states least misery performs worse than multiplication. For a change in satisfaction this can be seen across the board however for dissatisfaction change this is not true everywhere. \autoref{fig:Evaluation:HeteroSatisfaction} shows that least misery performs better than best average in terms of dissatisfaction reduction. However in other cases it performs visibly worse. Also of note is multiplication performs best across the board. This supports the findings by \citeauthor{Masthoff2015} \cite[p. 755f]{Masthoff2015} and also shows that the satisfaction model does show some similar results to online evaluations.
\autoref{hyp:Evaluation:AggregationStrategies} states least misery performs worse than multiplication. For a change in satisfaction this can be seen across the board however for dissatisfaction change this is not true everywhere. \autoref{fig:Evaluation:HeteroSatisfaction} shows that least misery performs better than best average in terms of dissatisfaction reduction \todo[]{Warum könnte dieses Verhalten auftreten?}. However in other cases it performs visibly worse. Also of note is multiplication performs best across the board. This supports the findings by \citeauthor{Masthoff2015} \cite[p. 755f]{Masthoff2015} and also shows that the satisfaction model does show some similar results to online evaluations.
To go back to \autoref{sec:Evaluation:Questions} this section has shown that for random and heterogeneous groups the recommender performs better than a dictator. The average satisfaction depends on the chosen parameters but for the chosen value range average satisfaction with the recommender decision lies above two and can reach close to three satisfied group members for a high number of stored configurations and for some group types. The amount of stored finished configurations plays an important role in performance but with a fraction of stored configurations the recommender still yields good results.
To go back to in \autoref{sec:Evaluation:Questions} posed evaluation questions this section has shown that for random and heterogeneous groups the recommender performs better than a dictator. The average satisfaction depends on the chosen parameters but for the chosen value range average satisfaction with the recommender decision lies above two and can reach close to three satisfied group members for a high number of stored configurations and for some group types. The amount of stored finished configurations plays an important role in performance but with a fraction of stored configurations the recommender still yields good results. \todo[inline]{an dieser Stelle nochmal ausführlicher den Bogen schlagen zu deinem Recommender als sinnvolle Unterstützung bei der Entscheidungsfindung in Gruppen}