Learning to Explain Voting Rules

The concept of distance rationalizability has several applications within social choice. In the context of voting, it allows one to define (rationalize) voting rules via a consensus class (roughly, a set of elections in which it is obvious who should win) and a distance function: namely, a candidate is said to be an election winner if it is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be represented in this manner. In this paper, we provide new results on distance rationalizability of several well-known voting rules such as all scoring rules, Approval, Young's rule and Maximin. We also show that a previously published proof of distance rationalizability of Young's rule is incorrect: the consensus notion and the distance function used in that proof give rise to a voting rule that is similar to---but distinct from---the Young's rule. Finally, we demonstrate that some voting rules cannot be rationalized via certain notions of consensus. To the best of our knowledge, these are the first non-distance-rationalizability results for voting rules.

The concept of distance rationalizability of voting rules has been explored in recent years by several authors. Roughly speaking, we first choose a consensus set of elections (defined via preferences of voters over candidates) for which the result is specified a priori (intuitively, these are elections on which all voters can easily agree on the result). We also choose a measure of distance between elections. The result of an election outside the consensus set is defined to be the result of the closest consensual election under the distance measure. Most previous work has dealt with a definition in terms of preference profiles. However, most voting rules in common use are anonymous and homogeneous. In this case there is a much more succinct representation (using the voting simplex) of the inputs to the rule. This representation has been widely used in the voting literature, but rarely in the context of distance rationalizability. We show exactly how to connect distance rationalizability on profiles for anonymous and homogeneous rules to geometry in the simplex. We develop the connection for the important special case of votewise distances, recently introduced and studied by Elkind, Faliszewski and Slinko in several papers. This yields a direct interpretation in terms of well-developed mathematical concepts not seen before in the voting literature, namely Kantorovich (also called Wasserstein) distances and the geometry of Minkowski spaces. As an application of this approach, we prove some positive and some negative results about the decisiveness of distance rationalizable anonymous and homogeneous rules. The positive results connect with the recent theory of hyperplane rules, while the negative ones deal with distances that are not metrics, controversial notions of consensus, and the fact that the $\ell^1$-norm is not strictly convex.

When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.

The student graduation level is the number of student graduations, whether the graduation is categorized on time or overdue. The level of student graduation is very influential on an accreditation of the department and the accreditation of the University. The prediction of the graduation duration of students to finish his study is used by the university as reference to make policies and measures how to reduce the level of inhibition of students and graduate not on time. So, the prediction of the level of student graduation in the university needs to be determined. Students graduation level are collected from several data in the academic system and need a further processed to obtain the predicted value of future student graduation level. A method that can be used as a data processes to produce a benefit is data mining. The method used in this analysis are C4.5 Decision Tree algorithm, which is one method of classification using decision tree structure. The result of this research is a 69.79% accuracy rate value and the error rate is 30.21.

Energy spectra unfolding of fast neutron sources using the group method of data handling and decision tree algorithms

Various voting rules (or social choice procedures) have been proposed to select a winner from the preferences of an entire population: Plurality, veto, Borda, Minimax, Copeland, etc. Although in theory, these rules may yield drastically different outcomes, for real-world datasets, behavioral social choice analyses have found that the rules are often in perfect agreement with each other! This work attempts to give a mathematical explanation of this phenomenon. We quantify the gap between the outcomes of two voting rules by the pairwise margin between their winners. We show that for many common voting rules, the gap between them can be almost as large as 1 when the votes are unrestricted. As a counter, we study the behavior of voting rules when the vote distribution is a uniform mixture of a small number of multinomial logit distributions. This scenario corresponds to a population consisting of a small number of groups, each voting according to a latent preference ranking. We show that for any such voting profile on g groups, at least 1/2g fraction of the population prefers the winner of a Borda election to any other candidate.

We use preference data from the 2015 parliament election in the Austrian federal state of Styria to analyze different voting rules. An exit poll right after the election collected data on ordinal and cardinal preferences from approximately 1000 actual voters. Our analysis is threefold. First, we determine the hypothetical social outcomes under different voting rules; second, we investigate the stability of the outcomes under those rules. Finally, we provide a categorization of different types of parties and analyze the impact of certain voting rules (Plurality Rule, Plurality Run Off, Hare System, Condorcet Method, Approval Voting, Borda Rule, Evaluative Voting, and Majority Judgment) on the performances of parties in those scenarios.

In traditional decision (classification) tree algorithms, the label is assumed to be a categorical (class) variable. When the label is a continuous variable in the data, two possible approaches based on existing decision tree algorithms can be used to handle the situations. The first uses a data discretization method in the preprocessing stage to convert the continuous label into a class label defined by a finite set of nonoverlapping intervals and then applies a decision tree algorithm. The second simply applies a regression tree algorithm, using the continuous label directly. These approaches have their own drawbacks. We propose an algorithm that dynamically discretizes the continuous label at each node during the tree induction process. Extensive experiments show that the proposed method outperforms the preprocessing approach, the regression tree approach, and several nontree-based algorithms.

Recently, the River Method was introduced as novel refinement of the Split Cycle voting rule. The decision-making process of River is closely related to the well established Ranked Pairs Method. Both methods consider a margin graph computed from the voters' preferences and eliminate majority cycles in that graph to choose a winner. As ties can occur in the margin graph, a tiebreaker is required along with the preferences. While such a tiebreaker makes the computation efficient, it compromises the fundamental property of neutrality: the voting rule should not favor alternatives in advance. One way to reintroduce neutrality is to use Parallel-Universe Tiebreaking (PUT), where each alternative is a winner if it wins according to any possible tiebreaker. Unfortunately, computing the winners selected by Ranked Pairs with PUT is NP-complete. Given the similarity of River to Ranked Pairs, one might expect River to suffer from the same complexity. Surprisingly, we show the opposite: We present a polynomial-time algorithm for computing River winners with PUT, highlighting significant structural advantages of River over Ranked Pairs. Our Fused-Universe (FUN) algorithm simulates River for every possible tiebreaking in one pass. From the resulting FUN diagram one can then directly read off both the set of winners and, for each winner, a certificate that explains how this alternative dominates the others.

Various conditions from social choice theory are discussed as they apply to actual voting procedures. It is found that none of these conditions makes a very interesting distinction among actual voting rules. Further, many of these conditions are argued to be not universally acceptable. It is then shown that, especially in cases in which there are more than two candidates, strategies are an essential part of voting, and particularly strategies of the type associated with ‘coordination problems’ as studied by Thomas C. Schelling. Some tentative acceptability conditions for voting rules are set forth which attempt to take coordination strategies into account. These are also found to be not universally acceptable.

Aim: Chronic kidney disease (CKD) is among the main 20 reasons for death worldwide and influences around 10% of the world grown-up populace. CKD is an issue that upsets typical kidney work. The main objective of this study aims to find the best-suited algorithm that will give us the most ideal prediction. We will be comparing Novel Decision Tree with Linear Regression to find out which of these can give us the best accuracy. Material and Methods: The study used 322 samples with Novel Decision Tree and Linear Regression is executed with varying training and testing splits for predicting the accuracy for kidney disease prediction with the G-power value of 80% and the kidney datasets were collected from various web sources with recent study findings and threshold 0.05%, confidence interval 95% mean and standard deviation. The performance of the classifiers are evaluated based on their accuracy rate using the chronic kidney disease dataset. Results: The accuracy of predicting kidney disease in Novel Decision Tree (96.66%) and Linear Regression (85.25%) is obtained. There is a statistical 2-tailed significant difference in accuracy for two algorithms is 0.000 (p<0.05) by performing independent samples t-tests. Conclusion: This study concludes that the Prediction of Kidney disease using the Novel Decision Tree (DT) algorithm appears to be significantly better than the Linear Regression(LR) with improved accuracy.

Results in heart disease classification that are inaccurate and have low accuracy can endanger the patient's life. Some parameters in the algorithm model also influence classification. This study compares the Decision Tree and Random Forest algorithms for heart disease. The influence of maximum depth on heart disease classification also has significant implications. If the maximum depth is not set correctly, the classification results can be inaccurate and lead to incorrect diagnoses. This study uses five data split schemes, namely 60%: 40%, 70%: 30%, 75%: 25%, 80%: 20%, 90%: 10% and tested with different max depth parameters, namely max depth = 3, 4, 5, 6, and 7. This research produces the best accuracy using the 90%:10% scheme and max depth = 7 with the best accuracy result using the Random Forest algorithm of 99.29% while the Decision Tree algorithm is 98.05%. Then the precision and recall value of the Random Forest algorithm is 99% while the Decision Tree is 98%. The results of computation time using Decision Tree are faster than using Random Forest with a computation time for training data of 0.0075 s, while the testing data are 0.009 s. In future research, research can be conducted on the effect of other parameters by testing using several data sets.

Voting rules are powerful tools that allow multiple agents to aggregate their preferences in order to reach joint decisions. A common flaw of some voting rules, known as the no-show paradox, is that agents may obtain a more preferred outcome by abstaining an election. Whenever a rule does not suffer from this paradox, it is said to satisfy participation. In this paper, we initiate the study of participation in probabilistic social choice, i.e., for voting rules that yield probability distributions over alternatives. We consider three degrees of participation based on expected utility, the strongest of which even requires that an agent is strictly better off by participating at an election. While the latter condition is prohibitive in non-probabilistic social choice, we show that it can be met by reasonable probabilistic functions. More generally, we study to which extent participation and Pareto efficiency are compatible. To the best of our knowledge, this is the first work in this direction.

Classification is an important task in the field of machine learning. Decision tree algorithms are a popular choice for handling classification tasks due to their high accuracy, simple algorithmic process, and good interpretability. Traditional decision tree algorithms, such as ID3, C4.5, and CART, differ primarily in their criteria for splitting trees. Shannon entropy, Gini index, and mean squared error are all examples of measures that can be used as splitting criteria. However, their performance varies on different datasets, making it difficult to determine the optimal splitting criterion. As a result, the algorithms lack flexibility. In this paper, we introduce the concept of generalized entropy from information theory, which unifies many splitting criteria under one free parameter, as the split criterion for decision trees. We propose a new decision tree algorithm called RSE (RS-Entropy decision tree). Additionally, we improve upon a two-term information measure method by incorporating penalty terms and coefficients into the split criterion, leading to a new decision tree algorithm called RSEIM (RS-Entropy Information Method). In theory, the improved algorithms RSE and RSEIM are more flexible due to the presence of multiple free parameters. In experiments conducted on several datasets, using genetic algorithms to optimize the parameters, our proposed RSE and RSEIM methods significantly outperform traditional decision tree methods in terms of classification accuracy without increasing the complexity of the resulting trees.

Manufacturing industries facing problem in optimal selection of process parameters in machining process. Finding optimum process parameters for achieving maximum Material Removal Rate and minimum Surface Roughness is a challenging task and it requires lot of time and energy for experimentation trails or experience. It wastes lot of resources and money, sometimes ends up with negative results. To overcome the above issue, this paper presents an algorithm for prediction of Surface Roughness and Material Removal rate using Decision Tree Algorithm and Naive Bayes Algorithm without experimentation. Lot of resources and time can be saved using these machine learning algorithms. In this paper, Material removal rate and Surface roughness of EDM machining of Aluminum composites is predicted using Decision tree algorithm and Naive Bayes algorithm. Then the model can be used to predict the Material Removal Rate and Surface finish of any combination process parameters before machining process.