Abstract
We tackle the practical problem of finding a good rule to recommend a collective set of news items to a group of media consumers with possibly very disparate individual interest in the available items. For our analysis, we adapt a formal framework from voting theory in Computational Social Choice to the media setting in order to compare the performance of five recommendation rules with respect to several desirable properties of recommendation sets. Through simulations, we find that polarization of the audience limits how well these rules can perform in general. On the other hand, greater diversity or universality can be achieved at only low cost in utility.
We would like to thank Ulle Endriss for guidance and very helpful suggestions. We are also grateful to anonymous reviewers for detailed and constructive feedback. At the time at which this work was carried out, all authors were affiliated with the Institute for Logic, Language and Computation, University of Amsterdam.
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Notes
- 1.
A strict, total order is a transitive, antisymmetric and irreflexive, connected relation.
- 2.
An anonymous reviewer has pointed out to us that this assumption may be too strict: reading one article may reduce the effort it takes to read another one on the same topic. Thus the cost of reading both articles may well be less than the sum of their individual costs. It would indeed be interesting to generalize the cost function in this way in future investigations.
- 3.
They are pseudo-utilities in that they are distinct from the consumers’ true utilities that form the input of the upstream recommender system.
- 4.
One might wonder at this point whether another utility-related measure, Pareto-efificiency, would be of use in our setting. In the budgeted context, a winner set W, is Pareto-efficient if there is no combination of items \(V=\{v_1,...,v_n\}\) such that there is \(w\in W\) and \(i\in N\) with \(u_i(V)>u_i(w)\), \(u_j(V)\ge u_j(w)\) for all \(j\ne i\) and \(C(V)\le C(w)\). In other words, there is no way to replace an item in W such that nobody is worse off, at least one consumer is better off and still fit the budget. To answer this question, one should recall that the utilities employed here are pseudo-utilities: the preference orders on which they are based do not contain information on whether some combination of lower ranked items would actually be preferred over a single higher ranked item. Utilities in our setting merely serve as a way to obtain an aggregate measure of the popularity of a winner set. They do not contain information that would allow one to make between-item or between-consumer comparisons. For these kind of comparisons we need to fall back to the preference orderings. In social choice, the notion corresponding to Pareto-efficiency is called unanimity. Studying unanimity in our multi-winner, budgeted setting would require an adaptation of the usual axiom. We leave this as an interesting avenue for future research.
- 5.
One might ask why we did not consider a rule that minimizes the Gini-coefficient. The reason is that usually even proponents of egalitarianism don’t aspire to minimize inequality (in all domains) but rather put side constraints on utility maximization, as in the famous Maximin-principle [12]. The Maximin-principle would correspond to the rule \(F(\mathcal {R},C^m(A),B)=\mathop {\arg \max }\nolimits _{W\in \mathcal { W_B}} \min _{i\in N} u_i(W)\) in our setting.
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Hungerbühler, S., Jóhnsson, H.P., Lisowski, G., Rapp, M. (2019). Social Choice and the Problem of Recommending Essential Readings. In: Sikos, J., Pacuit, E. (eds) At the Intersection of Language, Logic, and Information. ESSLLI 2018. Lecture Notes in Computer Science(), vol 11667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59620-3_4
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