Condorcet efficiency of two stage constant scoring rules

A discussion is presented regarding the single-stage election procedures Plurality, Negative Plurality, and Borda Rules; with an emphasis on their Condorcet Efficiency, which measures their propensity to elect the Condorcet Winner. A theoretical analysis shows how the Condorcet Efficiency of these voting rules change as the various measures of group mutual coherence change. Both Plurality and Negative Plurality Rules are found to perform very poorly over identifiable ranges of the defined measures of group mutual coherence. While Borda Rule is not always found to be the most Condorcet Efficient single-stage rule in all scenarios, it never performs poorly under any scenario. These theoretical results are then reinforced by empirically-based analysis to show very solid support for using Borda Rule, despite some concerns that have been expressed that Borda Rule requires voters to rank candidates, while Plurality and Negative Plurality Rules do not.

We compare the Condorcet Efficiencies of the plurality rule, the negative plurality rule, and the Borda rule to examine what might be gained by using a voting rule that requires candidate rankings. Previous analyses have considered (1) voting situations for which the three rules determine different candidates as winners (and the Condorcet Efficiencies might actually differ across the three rules) as well as (2) refined measures of Group Mutual Coherence that assess the presence of underlying models of rational behavior that governs voter preferences. In this paper, we present the final step of this particular line of analysis by analyzing (1) and (2) simultaneously. We conclude that there is a considerable benefit on the basis of Condorcet Efficiency from asking voters to submit candidate rankings in three-candidate elections.

Let P(n, 4) denote the probability that there is a pairwise simple majority rule winner on four candidates with n voters under the impartial anonymous culture condition. Similarly, let Pt(n, 4) denote the probability that the complete ranking obtained by pairwise simple majority voting on four candidates with n voters is transitive under the impartial anonymous culture condition. We obtain representations for P(n, 4) and Pt(n, 4), and computed values for each for odd n with 3 ≤ n ≤ 19.

The standard two-stage voting rules Plurality Elimination and Negative Plurality Elimination are evaluated relative to Borda Rule on the basis of Condorcet Efficiency. Theoretical analysis shows that the Condorcet Efficiency of these two-stage voting rules consistently marginally dominate Borda Rule as the various measures of group mutual coherence change. However, it is also found that the probability that either of the two-stage rules will elect a different candidate than the winner by Borda Rule is quite small. Empirically-based analysis reinforces this observation to lead to the general conclusion that the additional effort that is required to use a two-stage voting rule, rather than simply using Borda Rule, is not likely to be worthwhile. Other benefits are considered that result from using Borda Rule rather than a two-stage voting rule.

Image compression frequently supports reduced storage requirement in a computer system, as well as enhancement of effective channel bandwidth in a communication system, by decreasing the source bit rate through reduction of source redundancy. The majority of image compression techniques emphasize pixel-level operations, such as matching rectangular or elliptical sampling blocks taken from the source data stream, with exemplars stored in a database (e.g., a codebook in vector quantization or VQ). Alternatively, one can represent a source block via transformation, coefficient quantization, and selection of coefficients deemed significant for source content approximation in the decompressed image. This approach, called transform coding (TC), has predominated for several decades in the signal and image processing communities. A further technique that has been employed is the deduction of affine relationships from source properties such as local self-similarity, which supports the construction of adaptive codebooks in a self-VQ paradigm that has been called <i>iterated function systems </i>(IFS). Although VQ, TC, and IFS based compression algorithms have enjoyed varying levels of success for different types of applications, bit rate requirements, and image quality constraints, few of these algorithms examine the higher-level spatial structure of an image, and fewer still exploit this structure to enhance compression ratio. In this paper, we discuss a fourth type of compression algorithm, called <i>object-based compression</i>, which is based on research in joint segmentaton and compression, as well as previous research in the extraction of sketch-like representations from digital imagery. Here, large image regions that correspond to contiguous recognizeable objects or parts of objects are segmented from the source, then represented compactly in the compressed image. Segmentation is facilitated by source properties such as size, shape, texture, statistical properties, and spectral signature. In particular, discussion addresses issues such as efficient boundary representation, variance assessment and representation, as well as a texture classification and replacement algorithms that can decrease compression overhead and increase reconstruction fidelity in the decompressed image. Contextual extraction of motion patterns in digital video sequences, using a frequency-domain pattern recognition technique based on interframe correlation, is described in a companion paper. This technique can also be extended to multidimensional image domains, to support joint spectral, spatial, and temporal compression.

In a large electorate it is natural to consider voters’ preference profiles as frequency distributions over the set of all possible preferences. We assume coherence in voters’ preferences resulting in accumulation of voters preferences. We show that such distributions can be studied via superpositions of simpler so called unimodal distributions. At these, it is shown that all well-known rules choose the mode as the outcome. We provide a set of sufficient conditions for a rule to have this trait of choosing the mode under unimodal distributions. Further we show that Condorcet consistent rules, Borda rule, plurality rule are robust under tail-perturbations of unimodal distributions.

The margin of victory of an election, defined as the smallest number k such that k voters can change the winner by voting differently, is an important measurement for robustness of the election outcome. It also plays an important role in implementing efficient post-election audits, which has been widely used in the United States to detect errors or fraud caused by malfunctions of electronic voting machines.

The most well-known approaches to decision rules are inspired by “majority-based” and “ranking-based” utilitarianism. The long lasting discussion on the appropriate collective decision mechanism is based on the merits of the rules consistent with these two approaches. Focusing on conformity with qualified majority, we propose single-approval multiple-rejection (SAMR) as a plausible flexible scoring rule narrowing the gap between the two approaches. Given k alternatives, such a mechanism permits approval of a single alternative and rejection of at most \((k-2)\) alternatives allowing any relative significance of the approved vs. the rejected alternatives. SAMR is the unique type of rule that spans the whole spectrum of the qualified majority-based utilitarian rules, independent of k. Our first characterization result exposes the relationship between its consistency with any predetermined \(\alpha \)-majority based rule, \(\alpha >1/2\), and the best/worst (approval/rejection) relative weight p. Our second result establishes that the plurality rule is the unique scoring rule consistent with any \(\alpha \)-majority, \(\alpha < 1/2\). These results imply the impossibility of universal scoring-rule consistency with any ideal or real \(\alpha \)-majority.

Constraint Satisfaction Problems (CSP) have been widely studied in several research areas like Artificial Intelligence or Operational Research due their complexity and industrial interest. From previous research areas, heuristic (informed) search methods have been particularly active looking for feasible approaches. One of the critical problems to work with CSP is related to the exponential growth of computational resources needed to solve even the simplest problems. This paper presents a new efficient CSP graph-based representation to solve CSP by using Ant Colony Optimization (ACO) algorithms. This paper presents also a new heuristic (called Oblivion Rate), that have been designed to improve the current state-of-the-art in the application of ACO algorithms on these domains. The presented graph construction provides a strong reduction in both, the number of connections and the number of nodes needed to model the CSP. Also, the new heuristic is used to reduce the number of pheromones in the system (allowing to solve problems with an increasing complexity). This new approach has been tested, as case study, using the classical N-Queens Problem. Experimental results show how the new approach works in both, reducing the complexity of the resulting CSP graph and solving problems with increasing complexity through the utilization of the Oblivion Rate.

Under approval voting (AV), each voter just distinguishes the candidates he approves of from those appearing as unacceptable. The preference approval voting (PAV) is a hybrid version of the approval voting first introduced by Brams and Sanver (in: Brams, Gehrlein, Roberts (eds) The mathematics of preference, choice and order. Springer, Berlin, pp 215–237, 2009). Under PAV, each voter ranks all the candidates and then indicates the ones he approves. In this paper, we provide an analytical representation of the limiting probability that PAV elects the Condorcet winner (resp. the Condorcet loser) when she exists in three-candidate elections. We perform our analysis by assuming the assumption of the Extended Impartial Culture. The aim is to measure at which extend PAV performs better than AV both on the propensity of electing the Condorcet winner and on that of the non-election of the Condorcet loser. For this purpose, we also provide an analytical representation of the limiting probability that AV elects the Condorcet winner (resp. the Condorcet loser) when she exists in three-candidate elections. Our representation of the limiting probability that AV elects the Condorcet winner is more general than that provided by Diss et al. (in: Laslier and Sanver (eds) Handbook on approval voting. Springer, Berlin, pp 255–283, 2010) and it leads to the same figures as the representation provided by Gehrlein and Lepelley (Group Decis Negot 24:243–269, 2015).

The paper proposes a general definition of positionalist voting rules. Unlike the commonly-employed scoring rules, our notion of positionalism allows for non-linear criteria to be included in the requisite class. We define a voting rule as positionalist if, for any profile of strict individual orderings, any two alternatives are compared collectively solely on the basis of their positional scores according to the individual rankings. In contrast to the class of scoring rules, however, we do not restrict attention to linear aggregation procedures. Two plausible unanimity properties are examined in the context of our new class of positionalist rules and, moreover, we characterize the lexicographic extensions that refine the plurality rule and its inverse counterpart.

Vegetative and sexual reproduction in Pfiesteria spp. (Dinophyceae) cultured with algal prey, and inferences for their classification

The Condorcet efficiency of Borda Rule with anonymous voters

The rapidly growing demand for energy and the environmental concerns about carbon dioxide emissions make the development of renewable biofuels more and more attractive. Tremendous academic and industrial efforts have been made to produce bioethanol, which is one major type of biofuel. The current production of bioethanol is limited for commercialization because of issues with food competition (from food-based biomass) or cost effectiveness (from lignocellulose-based biomass). In this report we applied a consolidated bioprocessing strategy to integrate photosynthetic biomass production and microbial conversion producing ethanol together into the photosynthetic bacterium, Synechocystis sp. PCC6803, which can directly convert carbon dioxide to ethanol in one single biological system. A Synechocystis sp. PCC6803 mutant strain with significantly higher ethanol-producing efficiency (5.50 g L−1, 212 mg L−1 day−1) compared to previous research was constructed by genetically introducing pyruvate decarboxylase from Zymomonas mobilis and overexpressing endogenous alcohol dehydrogenase through homologous recombination at two different sites of the chromosome, and disrupting the biosynthetic pathway of poly-β-hydroxybutyrate. In total, nine alcohol dehydrogenases from different cyanobacterial strains were cloned and expressed in E. coli to test ethanol-producing efficiency. The effects of different culturing conditions including tap water, metal ions, and anoxic aeration on ethanol production were evaluated.