We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of @math items that maximize the total derived utility of all the agents (i.e., in our example we are to pick @math movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases.
@cite_34 define rank-dependent scoring rules. Under standard positional scoring rules, the score of a candidate is the sum of the scores it obtains from all the voters, where the score that a candidate obtains from a given voter depends only on his or her rank in this voter's preference order. Rank-dependent scoring rules generalize this idea as follows. Instead of simply summing up the scores of a given candidate, they apply an OWA operator to the list of the scores that he or she got from the voters. Thus a rank-dependent scoring rule is defined by a scoring vector (a function mapping ranks to scores) and an OWA operator. Here, OWAs replace the sum operator for aggregating the scores coming from different agents , while in our setting they aggregate the scores of different object for a fixed agent.
@cite_34
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Positional scoring rules in voting compute the score of an alternative by summing the scores for the alternative induced by every vote. This summation principle ensures that all votes contribute equally to the score of an alternative. We relax this assumption and, instead, aggregate scores by taking into account the rank of a score in the ordered list of scores obtained from the votes. This defines a new family of voting rules, rank-dependent scoring rules (RDSRs), based on ordered weighted average (OWA) operators, which, include all scoring rules, and many others, most of which of new. We study some properties of these rules, and show, empirically, that certain RDSRs are less manipulable than Borda voting, across a variety of statistical cultures.