Where are the hard manipulation problems

Standard voting rules usually assume that the preferences of voters are provided in the form of complete rankings over a fixed set of alternatives. This assumption does not hold in applications like recommendation systems where the set of alternatives is extremely large and only partial preferences can be elicited. In this paper, we study the problem of strategic manipulation of voting rules that aggregate voter preferences provided in the form of pairwise comparisons between alternatives. Our contributions are twofold: first, we show that any onto pairwise voting rule is manipulable in principle. Next, we analyze how the computational complexity of manipulation of such rules varies with the structure of the graph induced by the pairs of alternatives that the manipulator is allowed to vote over and the type of the preference relation. Building on natural connections between the pairwise manipulation and sports elimination problems (including a mixed-elimination variant that we introduce in this paper), we show that manipulating pairwise voting rules can be computationally hard even in the single-manipulator setting, a setting where most standard voting rules are known to be easy to manipulate.

Classical results in voting theory show that strategic manipulation by voters is inevitable if a voting rule simultaneously satisfies certain desirable properties. Motivated by this, we study the relevant question of how often a voting rule is manipulable. It is well known that elections with a large number of voters are rarely manipulable under impartial culture (IC) assumption. However, the manipulability of voting rules when the number of candidates is large has hardly been addressed in the literature and our article focuses on this problem. First, we propose two properties: (i) asymptotic strategy-proofness and (ii) asymptotic collusion-proofness, with respect to new voters, which makes the two notions more relevant from the perspective of computational problem of manipulation. In addition to IC, we explore a new culture of society where all score vectors of the candidates are equally likely. This new notion has its motivation in computational social choice and we call it impartial scores culture (ISC) assumption. We study asymptotic strategy-proofness and asymptotic collusion-proofness for plurality, veto and [Formula: see text]-approval, and Borda voting rules under IC as well as ISC assumptions. Specifically, we prove bounds for the fraction of manipulable profiles when the number of candidates is large. Our results show that the size of the coalition and the tie-breaking rule play a crucial role in determining whether or not a voting rule satisfies the above two properties.

The logic of bringing-it-about (BIAT) aims to capture a notion of agency in which actions are analysed in terms of their results: ‘An agent does something’ means that the agent brings it about that something takes place. Our starting point is the basic BIAT logic as introduced by Elgesem in the ‘90s: this logic contains only a modal operator to express BIAT statements by single agents. Several extensions have been proposed by Elgesem himself and others, notably with the capability operator, coalitions of agents and means-end BIAT statements (i.e. of the form ‘the agent does B by doing A’). We first propose a variant of the neighbourhood semantics, called bi-neighbourhood semantics, for the basic BIAT logic and the mentioned extensions, in which a world is equipped by a set of pairs or neighbourhoods. Differently from the semantics defined in the literature, this reformulation is well suited for countermodel construction. We then introduce modular hypersequent calculi for all logics considered in this work. Our calculi enjoy the fundamental property of cut admissibility, from which it follows their completeness with respect to the axiomatization. Moreover, our calculi provide at the same time a decision procedure, as well as the first practical countermodel extraction procedure: from a single failed proof it is possible to build directly a finite countermodel of the formula under verification in the bi-neighbourhood semantics. By this last result, we obtain constructive proofs of the semantic completeness of the calculi and consequently of the finite model property for all logics.

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p263.pdf **Abstract:** We simulate voting rules for multiwinner elections in a model of judgment aggregation that distinguishes between rationality and feasibility constraints. These constraints restrict the structure of the individual judgments and of the collective outcome computed by the rule, respectively. We extend known results regarding the simulation of single-winner voting rules to the multiwinner setting, both for elections with ordinal preferences and for elections with approval-based preferences. This not only provides us with a new tool to analyse multiwinner elections, but it also suggests the definition of new judgment aggregation rules, by generalising some of the principles at the core of well-known multiwinner voting rules to this richer setting. We explore this opportunity with regards to the principle of proportionality. Finally, in view of the computational difficulty associated with many judgment aggregation rules, we investigate the computational complexity of our embeddings and of the new judgment aggregation rules we put forward.

Decision procedures aggregating the preferences of multiple agents can\nproduce cycles and hence outcomes which have been described heuristically as\n`chaotic'. We make this description precise by constructing an explicit\ndynamical system from the agents' preferences and a voting rule. The dynamics\nform a one dimensional statistical mechanics model; this suggests the use of\nthe topological entropy to quantify the complexity of the system. We formulate\nnatural political/social questions about the expected complexity of a voting\nrule and degree of cohesion/diversity among agents in terms of random matrix\nmodels---ensembles of statistical mechanics models---and compute quantitative\nanswers in some representative cases.\n

The problem of electing a committee which satisfies voters is one for which good solutions are scarce. Extending single-winner voting rules to the multi-winner case works well only when voters have no preferential dependencies among candidates for the committee. (Our motivating example is a voter who believes that Alice and Bob are the best candidates, but also that the worst possible committee is one with both Alice and Bob.) In order to tackle the interdependence problem, we propose a voting rule called the Goalbase Summation Rule (GSR), which uses goalbases (sets of weighted propositional formulas) as ballots. Using goalbases as ballots lets voters express complex preferences in a compact fashion, while the computational complexity of finding winning committees remains reasonable when the number of seats is fixed. Additionally, the GSR is able to simulate and extend many existing voting rules.

In many real world elections, agents are not required to rank all candidates. We study three of the most common methods used to modify voting rules to deal with such partial votes. These methods modify scoring rules (like the Borda count), elimination style rules (like single transferable vote) and rules based on the tournament graph (like Copeland) respectively. We argue that with an elimination style voting rule like single transferable vote, partial voting does not change the situations where strategic voting is possible. However, with scoring rules and rules based on the tournament graph, partial voting can increase the situations where strategic voting is possible. As a consequence, the computational complexity of computing a strategic vote can change. For example, with Borda count, the complexity of computing a strategic vote can decrease or stay the same depending on how we score partial votes.

Approval ballots provide an opportunity for agents to make a comment about every candidate, without incurring the overhead of determining a full ranking on the set of candidates; they are very natural for many practical settings. We study the computational complexity of the committee selection problem for several approval-based voting rules in the presence of outliers. Our first result shows that outliers render the committee selection problem intractable for approval, net approval, and minisum approval voting rules. We next study the parameterized complexity of this problem with five natural parameters, namely the target score, the size of the committee (and its dual parameter namely the number of candidates outside the committee); and the number of outliers (and its dual parameter namely the number of non-outliers). For approval, net approval, and minisum approval voting rules, we provide a dichotomous result, which resolves the parameterized complexity of this problem for all subsets of the above five natural parameters considered (by showing either fixed parameter tractability or W[1]-hardness for all subsets of parameters).

Vulnerability of Voting Paradoxes As a Criteria For Voting Procedure Selection

One approach to voting on several interrelated issues consists in using a language for compact preference representation, from which the voters’ preferences are elicited and aggregated. A language usually comes with a domain restriction. We consider a well-known restriction, namely, conditionally lexicographic preferences, where both the relative importance between issues and the preference between values of an issue may depend on the values taken by more important issues. The naturally associated language consists in describing conditional importance and conditional preference by trees together with conditional preference tables. In this paper, we study the aggregation of conditionally lexicographic preferences, for several voting rules and several restrictions of the framework. We characterize computational complexity for some popular cases, and show that in many of them, computing the winner reduces in a very natural way to a maxsat problem.

First-line chemotherapy for ovarian cancer during the past decade has evolved toward the use of carboplatin and paclitaxel combinations. This has been based on randomized trials showing that combinations of these two drugs lead to a outcome similar to that obtained using cisplatin and paclitaxel (that had, in turn, proven superior in progression-free survival and overall survival to cisplatin and cyclophosphamide) but with less toxicity. Surprisingly, taxane–platinum combinations were not superior to control arms in two studies (ICON3 and GOG-132) utilizing carboplatin or cisplatin as the comparators. This has renewed interest in the role of single agents in first-line chemotherapy – a concept also supported by a number of prior clinical trials with single-agent platinum compounds yielding results not inferior to combinations. Early ‘pre-emptive’ crossover (prior to the stipulated clinical progression) to paclitaxel or a paclitaxel-containing regimen, however, occurred in 24% of patients initially treated with cisplatin on GOG-132. This has led to the interpretation of this trial as a combination versus sequential design. Although not subscribing to this interpretation, the results of GOG-132 and ICON3 not only raise doubts over a clear superiority of combinations over single agents but also lead to a consideration of sequential treatment designs for first line. Advantages of such designs are: (a) ability to provide ‘dose-dense’ platinums followed by ‘dose-dense’ paclitaxel and, perhaps, other drugs; and (b) the potential of acquiring biological data linked to the antitumor effects of a specific drug. Mathematical modeling and recent positive results in breast cancer adjuvant therapy support the use of ‘dose-dense’ strategies, and these should be considered in the design of future trials in ovarian cancer.

<div>Abstract<p><b>Purpose:</b> Estrogen receptor–positive (ER<sup>+</sup>) breast cancers are typically treated with endocrine agents, and dependence on the ER pathway is often retained even after multiple rounds of antiestrogen therapy. Selective estrogen receptor degraders (SERD) are being developed as a strategy to more effectively target ER and exploit ER dependence in these cancers, which includes inhibiting both wild-type and mutant forms of ER. The purpose of this study was to evaluate the efficacy of a novel orally bioavailable SERD, elacestrant (RAD1901), in preclinical models of ER<sup>+</sup> breast cancer.</p><p><b>Experimental Design:</b> Elacestrant was evaluated as a single agent and in combination with palbociclib or everolimus in multiple ER<sup>+</sup> breast cancer models, including several patient-derived xenograft models.</p><p><b>Results:</b> Elacestrant induces the degradation of ER, inhibits ER-mediated signaling and growth of ER<sup>+</sup> breast cancer cell lines <i>in vitro</i> and <i>in vivo</i>, and significantly inhibits tumor growth of multiple PDX models. Furthermore, we demonstrate that elacestrant in combination with palbociclib or everolimus can lead to greater efficacy in certain contexts. Finally, elacestrant exhibits significant antitumor activity both as a single agent and in combination with palbociclib in two patient-derived breast cancer xenograft models harboring <i>ESR1</i> mutations.</p><p><b>Conclusions:</b> These data underscore the potential clinical utility of elacestrant as a single agent and as a combination therapy, for both early- and late-stage ER<sup>+</sup> disease. <i>Clin Cancer Res; 23(16); 4793–804. ©2017 AACR</i>.</p></div>

Hematopathology II, Abstract 99–107, Posters

Electric Power Profiles Contract via Probabilistic Optimization

BackgroundMulti-dimensional scaling (MDS) is aimed to represent high dimensional data in a low dimensional space with preservation of the similarities between data points. This reduction in dimensionality is crucial for analyzing and revealing the genuine structure hidden in the data. For noisy data, dimension reduction can effectively reduce the effect of noise on the embedded structure. For large data set, dimension reduction can effectively reduce information retrieval complexity. Thus, MDS techniques are used in many applications of data mining and gene network research. However, although there have been a number of studies that applied MDS techniques to genomics research, the number of analyzed data points was restricted by the high computational complexity of MDS. In general, a non-metric MDS method is faster than a metric MDS, but it does not preserve the true relationships. The computational complexity of most metric MDS methods is over O(N2), so that it is difficult to process a data set of a large number of genes N, such as in the case of whole genome microarray data.ResultsWe developed a new rapid metric MDS method with a low computational complexity, making metric MDS applicable for large data sets. Computer simulation showed that the new method of split-and-combine MDS (SC-MDS) is fast, accurate and efficient. Our empirical studies using microarray data on the yeast cell cycle showed that the performance of K-means in the reduced dimensional space is similar to or slightly better than that of K-means in the original space, but about three times faster to obtain the clustering results. Our clustering results using SC-MDS are more stable than those in the original space. Hence, the proposed SC-MDS is useful for analyzing whole genome data.ConclusionOur new method reduces the computational complexity from O(N3) to O(N) when the dimension of the feature space is far less than the number of genes N, and it successfully reconstructs the low dimensional representation as does the classical MDS. Its performance depends on the grouping method and the minimal number of the intersection points between groups. Feasible methods for grouping methods are suggested; each group must contain both neighboring and far apart data points. Our method can represent high dimensional large data set in a low dimensional space not only efficiently but also effectively.