Preferences Single-Peaked on a Tree: Multiwinner Elections and Structural Results

A preference profile is single-peaked on a tree if the candidate set can be equipped with a tree structure so that the preferences of each voter are decreasing from their top candidate along all paths in the tree. This notion was introduced by Demange (1982), and subsequently Trick (1989b) described an efficient algorithm for deciding if a given profile is single-peaked on a tree. We study the complexity of multiwinner elections under several variants of the Chamberlin–Courant rule for preferences single-peaked on trees. We show that in this setting the egalitarian version of this rule admits a polynomial-time winner determination algorithm. For the utilitarian version, we prove that winner determination remains NP-hard for the Borda scoring function; indeed, this hardness results extends to a large family of scoring functions. However, a winning committee can be found in polynomial time if either the number of leaves or the number of internal vertices of the underlying tree is bounded by a constant. To benefit from these positive results, we need a procedure that can determine whether a given profile is single-peaked on a tree that has additional desirable properties (such as, e.g., a small number of leaves). To address this challenge, we develop a structural approach that enables us to compactly represent all trees with respect to which a given profile is single-peaked. We show how to use this representation to efficiently find the best tree for a given profile for use with our winner determination algorithms: Given a profile, we can efficiently find a tree with the minimum number of leaves, or a tree with the minimum number of internal vertices among trees on which the profile is single-peaked. We then explore the power and limitations of this framework: we develop polynomial-time algorithms to find trees with the smallest maximum degree, diameter, or pathwidth, but show that it is NP-hard to check whether a given profile is single-peaked on a tree that is isomorphic to a given tree, or on a regular tree.

EFFECTIVENESS OF GOVERNMENT GOODS AND SERVICES PROCUREMENT SYSTEMS (CASE STUDY IN SEBELAS MARET UNIVERSITY)

<p>This study aims to determine the effectiveness of the procurement of goods and services at Sebelas Maret University. To find out the effectiveness of the system of procurement of goods and services seen from their suitability with the principle of procurement of goods / services and the Standard Operating Procedure (SOP) specified. The principles of procurement of government goods / services include: 1) efficient, 2) effective, 3) transparent, 4) open, 5) competing, 6) fair, and 7) accountable. This study uses a quantitative descriptive approach. The types of data in this study are information or information, both oral, written and actions related to the research variables. The main data from this study are in the form of written questionnaires and field documentation. The population in this study were officers in the procurement of goods and services. The research sample was 30 people and the sampling technique was purposive sampling. The results of the study indicate that the stages of the procurement process of goods and services have been effectively implemented. This is indicated by the process of auction announcements with a score of 87%, 88% auction registration, 88% job description, 89% income and bid opening, 90% bid and qualification evaluation, and 90% winner determination and announcement. Overall, the process of procurement of goods and services gets a score of 89% and is included in very suitable / implemented criteria.</p>

A Graph-Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions

Iterative combinatorial auctions are known to resolve bidder preference elicitation problems. However, winner determination is a known key bottleneck that has prevented widespread adoption of such auctions, and adding a time-bound to winner determination further complicates the mechanism. As a result, heuristic-based methods have enjoyed an increase in applicability. We add to the growing body of work in heuristic-based winner determination by proposing an ant colony metaheuristic–based anytime algorithm that produces optimal or near-optimal winner determination results within specified time. Our proposed algorithm resolves the speed versus accuracy problem and displays superior performance compared with 20 past state-of-the-art heuristics and two exact algorithms, for 94 open test auction instances that display a wide variety in bid-bundle composition. Furthermore, we contribute to the literature in two predominant ways: first, we represent the winner determination problem as one of finding the maximum weighted path on a directed cyclic graph; second, we improve upon existing ant colony heuristic–based exploration methods by implementing randomized pheromone updating and randomized graph pruning. Finally, to aid auction designers, we implement the anytime property of the algorithm, which allows auctioneers to stop the algorithm and return a valid solution to the winner determination problem even if it is interrupted before computation ends.

Learning Within an Instance for Designing High-Revenue Combinatorial Auctions

We develop a new framework for designing truthful, high-revenue (combinatorial) auctions for limited supply. Our mechanism learns within an instance. It generalizes and improves over previously-studied random-sampling mechanisms. It first samples a participatory group of bidders, then samples several learning groups of bidders from the remaining pool of bidders, learns a high-revenue auction from the learning groups, and finally runs that auction on the participatory group. Previous work on random-sampling mechanisms focused primarily on unlimited supply. Limited supply poses additional significant technical challenges, since allocations of items to bidders must be feasible. We prove guarantees on the performance of our mechanism based on a market-shrinkage term and a new complexity measure we coin partition discrepancy. Partition discrepancy simultaneously measures the intrinsic complexity of the mechanism class and the uniformity of the set of bidders. We then introduce new auction classes that can be parameterized in a way that does not depend on the number of bidders participating, and prove strong guarantees for these classes. We show how our mechanism can be implemented efficiently by leveraging practically-efficient routines for solving winner determination. Finally, we show how to use structural revenue maximization to decide what auction class to use with our framework when there is a constraint on the number of learning groups.

Winner Determination and Strategic Control in Conditional Approval Voting

Our work focuses on a generalization of the classic Minisum approval voting rule, introduced by Barrot and Lang (2016), and referred to as Conditional Minisum (CMS), for multi-issue elections. Although the CMS rule provides much higher levels of expressiveness, this comes at the expense of increased computational complexity. In this work, we study further the issue of efficient algorithms for CMS, and we identify the condition of bounded treewidth (of an appropriate graph that emerges from the provided ballots), as the necessary and sufficient condition for polynomial algorithms, under common complexity assumptions. Additionally we investigate the complexity of problems related to the strategic control of such elections by the possibility of adding or deleting either voters or alternatives. We exhibit that in most variants of these problems, CMS is resistant against control.