Simple Majority Rule Research Articles

Manipulations in Democracy?

Democracy is upheld through the principle of majority rule. To validate the application of democracy, it is imperative to assess the sincerity of voter decisions. When voter sincerity is compromised, manipulation may occur, thereby undermining the legitimacy of democratic processes. This paper presents a general version of a symmetric dichotomous choice model. Using simple majority rule, we show that when a voter receives one or more private signals, sincere voting is an equilibrium behavior. A slight change to this basic model may create an incentive to vote insincerely. We show that even in a more restricted model where every voter receives only one private signal whose level of precision is the same for all the voters but depends on the state of nature, voters may have an incentive to vote insincerely.

2023 Update to the American College of Clinical Pharmacy Pharmacotherapy Didactic Curriculum Toolkit.

The American College of Clinical Pharmacy (ACCP) Pharmacotherapy Didactic Curriculum Toolkit has been used by colleges and schools of pharmacy as a guide for curricular development and revisions since its inaugural publication in 2009. The toolkit was last revised and updated by the 2019 Publications Committee. The 2023 ACCP Publications Committee was charged with reviewing the 2019 Update to the ACCP Pharmacotherapy Didactic Curriculum Toolkit to determine any necessary revisions/updates. The committee revised tier classifications, shifting the focus of the 2023 toolkit to content within the Pharm.D. curriculum. Multiple literature sources were reviewed to assess conditions for inclusion in the 2023 toolkit, and external feedback was solicited from various practice disciplines. All topics were voted on by a simple majority rule during virtual meetings or by electronic votes. There are a total of 231 topics in the 2023 toolkit, a decrease of 77 (23.2%) from the 2019 edition. Topics in each tier are as follows: 68 as tier 1 (29%), 111 as tier 2 (48%), and 52 as tier 3 (23%). Although some topics were removed completely, others were combined with other line items or revised, which may further minimize curricular overload. Similar to the 2016 and 2019 toolkits, many tier 2 topics remain in the 2023 toolkit, emphasizing the continued need for additional training through postgraduate residencies or fellowships (or "on-the-job" equivalent experiences), board certifications, and various certificate training programs. The 2023 ACCP Pharmacotherapy Didactic Curriculum Toolkit is designed to assist individual faculty and colleges and schools of pharmacy with curricular development and revisions. It will continue to be reviewed every 3 years to identify needed revisions on the basis of the pharmacist's evolving role, advances in therapeutics and pharmacy practice, and changes to accreditation standards and recognized professional competencies.

Sparse Affine Sampling: Ambiguity-Free and Efficient Sparse Phase Retrieval

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine measurements to achieve ambiguity-free signal reconstruction. The proposed method relies on two-stage approach that consists of support identification followed by the exact recovery of nonzero signal entries. In the noise-free case, perfect support identification using a simple counting rule is guaranteed subject to a mild condition on the signal sparsity, and subsequent exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed approach is then extended to two noisy scenarios, namely, sparse noise (or outliers) and non-sparse bounded noise. For both cases, perfect support identification is still ensured under mild conditions on the noise model, namely, the support size for sparse outliers and the power of the bounded noise. Under perfect support identification, exact signal recovery can be achieved using a simple majority rule for the sparse noise scenario, and reconstruction up to a bounded error can be achieved using linear least-squares (LS) estimation for the non-sparse bounded noise scenario. The obtained analytic performance guarantee for the latter case also sheds light on the construction of the sensing matrix and bias vector. In fact, we show that a near optimal performance can be achieved with high probability by the random generation of the nonzero entries of the sparse sensing matrix and bias vector according to the uniform distribution over a circle. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme.

Condorcet Method, Independence of Irrelevant Alternatives, and the Size of the Bundestag

ABSTRACT How should an excessively large parliament be effectively reduced in size without violating constitutional principles? This is a question that the German Bundestag has discussed since the introduction of the 2013 electoral reform measure. Facing a Bundestag consisting of 709 members and some public dissatisfaction, a reform measure to decrease the parliament’s size was adopted in 2020. However, the 20 Bundestag, elected in September 2021, again increased in size to 735 members. The newly adopted electoral law still uses plurality voting to select the directly elected lawmakers. It is widely known that selection using the plurality rule is flawed because it violates the principle of majority decision. Aside from this aspect, this paper demonstrates that the plurality rule itself contributes to the excessive size of the parliament. By removing the flaws caused by the plurality rule and replacing this voting scheme with a Condorcet method (simple-majority rule), the targeted reduction of the size of the Bundestag can be achieved.

Majority-approval social choice

This note axiomatically proposes a social choice rule called majority approval, which coincides with the simple majority rule when the latter is decisive (i.e., contains no top cycles), and otherwise coincides with approval voting (Brams and Fishburn, 1978) defined on the top cycle set. We compare our rule to other social choice rules that prioritize preference information over approval information, and show that it stands out for its appealing properties. In addition, we provide axiomatization for a version of majority approval that satisfies the Pareto criterion.

On the probability of the Condorcet Jury Theorem or the Miracle of Aggregation

The Condorcet Jury Theorem or the Miracle of Aggregation are frequently invoked to ensure the competence of some aggregate decision-making processes. In this article we explore the probability of the thesis predicted by the theorem (if there are enough voters, majority rule is a competent decision procedure) in different settings. We use tools from measure theory to conclude that it will happen almost surely or almost never, depending on the probability measure. In particular, it will fail almost surely for measures estimating the prior probability. To update this prior either more evidence in favor of competence would be needed (so that a large likelihood term compensates a small prior term in Bayes’ Theorem) or a modification of the decision rule. The former includes the case of (rational) agents reversing their vote if its probability of voting the right option is less than 1/2. Following the latter, we investigate how to obtain an almost sure competent information aggregation mechanism for almost any evidence on voter competence (including the less favorable ones). To do so, we substitute simple majority rule by weighted majority rule based on some stochastic weights correlated with epistemic rationality such that every voter is guaranteed a minimal weight equal to one. We also explore how to obtain these weights in a real setting.

Instance-based learning using the half-space proximal graph

• We propose a parameter-free instance-based classifier , the HSP classifier. • Our accuracy outperforms kNN while keeping its simplicity and complexity. • We also present a probabilistic and asymptotic versions of the HSP improving both the time and the original proposal’s accuracy. • The same weigthing methods that improves kNN, also improves the HSP and its asymptotic variants The primary example of instance-based learning is the k -nearest neighbor rule (kNN), praised for its simplicity and the capacity to adapt to new unseen data and toss away old data. The main disadvantages often mentioned are the classification complexity , which is O ( n ) , and the estimation of the parameter k , the number of nearest neighbors to be used. The use of indexes at classification time lifts the former disadvantage, while there is no conclusive method for the latter. This paper presents a parameter-free instance-based learning algorithm using the Half-Space Proximal (HSP) graph. The HSP neighbors simultaneously possess proximity and variety concerning the center node. To classify a given query, we compute its HSP neighbors and apply a simple majority rule over them. In our experiments, the resulting classifier bettered K N N for any k in a battery of datasets. This improvement sticks even when applying weighted majority rules to both kNN and HSP classifiers. Surprisingly, when using a probabilistic index to approximate the HSP graph and consequently speeding-up the classification task , our method could improve its accuracy in stark contrast with the kNN classifier, which worsens with a probabilistic index.

An application of simple majority rule to a group with an even number of voters

An application of simple majority rule to a group with an even number of voters

Preference–Approval Structures in Group Decision Making: Axiomatic Distance and Aggregation

Preference–approval structure combines the preference information of both ranking and approval, which extends the ordinal preference model by incorporating two categories of choice alternatives, that is, acceptable (good) and unacceptable (bad), in the preference modeling process. In this study, we present some axioms that imply the existence of a unique distance function of preference–approval structures. Based on theoretical analysis and simulation experiments, we further study a preferences aggregation model in the group decision-making context based on the proposed axiomatic distance function. In this model, the group preference is defined as a preference–approval structure that minimizes the sum of its distances to all preference–approval structures of individuals in the group under consideration. Particularly, we show that the group preference defined by the axiomatic distance–based aggregation model has close relationships with the simple majority rule and Cook and Seiford’s ranking.

Brexit: A comparison of dynamic voting games with irreversible options

A large polarized electorate decides repeatedly between a reversible alternative (REMAIN) and an irreversible alternative (LEAVE) in an environment where the aggregate short-term effects of the decision vary from period to period. Decisions by simple majority or by a too low supermajority may perform poorly under circumstances where it is socially optimal to never LEAVE, as they can exhibit equilibria where LEAVE is chosen quickly. In general, a too low supermajority rule can have much higher welfare costs than a too high supermajority rule. If REMAIN also becomes permanent when it wins by a large enough margin, and if a new vote is triggered otherwise, particularly poor performances of the simple majority rule are avoided. The large asymmetry in potential welfare costs disappears, and the majority requirement becomes a relatively less important instrument.

Simple majority rule and integer programming

In this paper, we use the integer programming approach to mechanism design, first introduced by Sethuraman et al. (2003), and then systematized by Vohra (2011), to reformulate issues concerning the simple majority rule. Our main result consists in showing that, when the number of agents is even, a necessary and sufficient condition for the simple majority rule to be an Arrovian social welfare function is that it is defined on a domain which is echoic with antagonistic preferences. This result is an integer programming simplified version of Theorems 2, 3, and 4 in Inada (1969).

Democratizing the Senate from Within

This article proposes that the U.S. Senate adopt a “popular-majoritarian cloture rule,” under which a motion to close debate and proceed to a final vote would carry if but only if supported by a majority of Senators who collectively represent a larger share of the population than those Senators in opposition. This rule, which would be a constitutional exercise of the Senate’s power to set the rules of its proceedings, would make the body more democratic and more functional, and would be preferable both to the current filibuster rule and to simple majority rule.

Democratizing the Senate from Within

AbstractThis article proposes that the U.S. Senate adopt a “popular-majoritarian cloture rule,” under which a motion to close debate and proceed to a final vote would carry if but only if supported by a majority of Senators who collectively represent a larger share of the population than those Senators in opposition. This rule, which would be a constitutional exercise of the Senate’s power to set the rules of its proceedings, would make the body more democratic and more functional, and would be preferable both to the current filibuster rule and to simple majority rule.

Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom

This paper considers voting rules for two alternatives, viz. the simple majority rule of K.O. May, the majority rule with bias of Fishburn and others, and the majority rule by difference of votes of Goodin and List, and of Llamazares. These all have been characterized axiomatically for profiles of fixed length, that is, for a fixed population. The aim of this paper is to study analogs of these results in the situation where various populations are considered and disjoint populations can be combined into one population. The effect of this shift of focus is that now the domain of the rule consists of all finite nonempty sequences of votes. Young (1974) introduced the axiom of consistency, by which two populations can be combined into one as long as they agree on the output of the voting rule. We use a version of this axiom as given by Roberts (1991). Our paper can be seen as making a strong case for this simple, and natural axiom.In the simple majority rule as well as the majority rule by difference of votes, the outcome of a tie is undecided, that is, both alternatives are in the output. In the majority rule with bias, ties are broken. In our case of profiles of variable lengths there are reasons to distinguish between strong bias (a tie is always broken) and weak bias (in certain cases a tie is not yet broken). The case of weak bias fits nicely in the context of a new characterization of simple majority rule that follows from previous results of the authors.

Information acquisition and voting with heterogeneous experts

AbstractA social planner selects heterogeneously biased experts to (either sequentially or simultaneously) acquire costly signals, and then agents vote between two alternatives. To maximize social welfare, the social planner adopts an alternating mechanism—choosing extremely biased experts whose preferences oppose the pivotal voter's current preference—in the optimal sequential mechanism, whereas she chooses mildly biased experts in the optimal simultaneous mechanism. Despite the flexibility of a sequential mechanism, the optimal simultaneous mechanism can achieve strictly higher social welfare when information cost is low. Supermajority rules can dominate simple majority rule in terms of both information acquisition and social welfare.

The wisdom of stalemates: consensus and clustering as filtering mechanisms for improving collective accuracy.

Groups of organisms, from bacteria to fish schools to human societies, depend on their ability to make accurate decisions in an uncertain world. Most models of collective decision-making assume that groups reach a consensus during a decision-making bout, often through simple majority rule. In many natural and sociological systems, however, groups may fail to reach consensus, resulting in stalemates. Here, we build on opinion dynamics and collective wisdom models to examine how stalemates may affect the wisdom of crowds. For simple environments, where individuals have access to independent sources of information, we find that stalemates improve collective accuracy by selectively filtering out incorrect decisions (an effect we call stalemate filtering). In complex environments, where individuals have access to both shared and independent information, this effect is even more pronounced, restoring the wisdom of crowds in regions of parameter space where large groups perform poorly when making decisions using majority rule. We identify network properties that tune the system between consensus and accuracy, providing mechanisms by which animals, or evolution, could dynamically adjust the collective decision-making process in response to the reward structure of the possible outcomes. Overall, these results highlight the adaptive potential of stalemate filtering for improving the decision-making abilities of group-living animals.

Using Truth Detection to Incentivize Workers in Mobile Crowdsourcing

Mobile crowdsourcing platforms often want to incentivize workers to finish tasks with high quality and truthfully report their solutions by providing proper rewards. Most existing incentive mechanisms reward workers based on the comparison among workers’ reported solutions. However, these mechanisms are vulnerable to worker collusion, i.e., workers coordinate to misreport their solutions. We address such an issue by proposing a novel rewarding mechanism based on a <inline-formula><tex-math notation="LaTeX">${truth detection}$</tex-math></inline-formula> technology, which relies on the independent verification of the correctness of each worker’s response to some question with an <i>imperfect</i> accuracy. We model the interactions between the platform and workers as a two-stage Stackelberg game. In Stage I, the platform optimizes the reward mechanism parameters associated with <i>truth detection</i> to maximize its payoff. In Stage II, the workers decide their effort levels and reporting strategies to maximize their payoffs (which depend on the output of the truth detector). We analyze the game’s equilibrium and show that our proposed mechanism can effectively mitigate worker collusion. We also propose a novel rule, named <i>filtered majority</i> , for the platform to more effectively aggregate the workers’ solutions. Our proposed aggregation rule utilizes truth detection and outperforms the conventional simple majority rule. We further characterize the impact of the truth detection accuracy on the platform’s decisions. Surprisingly, under the simple majority rule, we show that as the truth detection accuracy improves, the platform should always incentivize more workers to exert effort and truthfully report. However, under our proposed filtered majority rule, we show that as the truth detection accuracy improves, in some cases, the platform should incentivize fewer workers and save costs. We further examine the impact of the workers’ imperfect estimation of the truth detection accuracy on the platform’s decisions.

The wisdom of the crowd and prediction markets

Thanks to digital innovation, the wisdom of the crowd, which aims at gathering information (e.g. Wikipedia) and making a prediction (e.g. using prediction markets) from a group’s aggregated inputs, has been widely appreciated. An innovative survey design, based on a Bayesian learning framework, called the Bayesian truth serum (BTS), was proposed previously to reduce the bias in the simple majority rule by asking additional survey questions. A natural question is whether we can extend the BTS framework to prediction markets (not just polls). To do so, this paper proposes two estimators, one based on a prediction market alone and the other based on both the market and a poll question. We show that both estimators are consistent within the BTS framework, under different sets of regularity conditions. Simulations are conducted to examine the convergence of different estimators. A real data set of sports betting is used to demonstrate the effectiveness of one estimator.

Simple Majorities with Voice but No Vote

Oligarchic majority rules bring the voice but no vote principle into effect. We prove characterizations of the oligarchic majority rules for both fixed and unrestricted societies and a binary agenda. This is a general class of rules that includes the simple majority rule as well as dictatorships. Suitable sets of axioms identify a subsociety whose members have voice but no vote, and valid votes are aggregated by the majority rule.

On the merit of non-specialization in the context of majority voting

This study shows that independence between voters’ skills and states of nature improves the majority voting efficiency relative to the case when such independence does not exist. This implies that specialization (state of nature wise) is not advantageous under the simple majority rule.