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. In this paper, we propose a rank minimization method to fuse the predicted confidence scores of multiple models, each of which is obtained based on a certain kind of feature. Specifically, we convert each confidence score vector obtained from one model into a pairwise relationship matrix, in which each entry characterizes the comparative relationship of scores of two test samples. Our hypothesis is that the relative score relations are consistent among component models up to certain sparse deviations, despite the large variations that may exist in the absolute values of the raw scores. Then we formulate the score fusion problem as seeking a shared rank-2 pairwise relationship matrix based on which each original score matrix from individual model can be decomposed into the common rank-2 matrix and sparse deviation errors. A robust score vector is then extracted to fit the recovered low rank score relation matrix. We formulate the problem as a nuclear norm and l 1 norm optimization objective function and employ the Augmented Lagrange Multiplier (ALM) method for the optimization. Our method is isotonic (i.e., scale invariant) to the numeric scales of the scores originated from different models. We experimentally show that the proposed method achieves significant performance gains on various tasks including object categorization and video event detection. The author is primarily concerned with the problem of aggregating multicriteria to form an overall decision function. He introduces a type of operator for aggregation called an ordered weighted aggregation (OWA) operator and investigates the properties of this operator. The OWA's performance is found to be between those obtained using the AND operator, which requires all criteria to be satisfied, and the OR operator, which requires at least one criteria to be satisfied. > We consider a classic social choice problem in an online setting. In each round, a decision maker observes a single agent's preferences over a set of m candidates, and must choose whether to irrevocably add a candidate to a selection set of limited cardinality k. Each agent's (positional) score depends on the candidates in the set when he arrives, and the decisionmaker's goal is to maximize average (over all agents) score. We prove that no algorithm (even randomized) can achieve an approximation factor better than O(log logm logm). In contrast, if the agents arrive in random order, we present a (1-1 e-o(1))- approximate algorithm, matching a lower bound for the offline problem. We show that improved performance is possible for natural input distributions or scoring rules. Finally, if the algorithm is permitted to revoke decisions at a fixed cost, we apply regret-minimization techniques to achieve approximation 1- 1 e-o(1) even for arbitrary inputs.