Paradox Of Voting Research Articles

On status quo bias and the existence of Condorcet cycles in binary voting situations

On status quo bias and the existence of Condorcet cycles in binary voting situations

Geoff Brennan on the Ethics and Rationality of Voting

Geoff Brennan made a wide range of important contributions to the literature on the ethics and rationality of voting. This article begins by situating these contributions in the broader debate over rational choice theory and the so-called paradox of voting. It then introduces Geoff’s expressive theory of voter behaviour, as developed in conjunction with Loren Lomasky, and considers its significance for the justification of democracy and the ethics of voting. The final section engages critically with Geoff’s view that citizens do not have moral duties to vote, developing a novel argument in defence of such duties that appeals to the importance of the social norms that undergird the processes of representative democracy.

VERICONDOR: End-to-End Verifiable Condorcet Voting with support for Strict Preference and Indifference

Condorcet voting is widely regarded as one of the most important voting systems in social choice theory. However, it has seen little adoption in practice, due to complex tallying and the need to break ties when there is a Condorcet cycle. Several online Condorcet voting systems have been developed to perform digital tallying and tie-breaking procedures, but they require voters to completely trust the server. Additionally, many end-to-end (E2E) verifiable e-voting systems require trustworthy authorities to perform complex decryption and tallying operations. We propose VERICONDOR, the first E2E verifiable Condorcet e-voting system without tallying authorities. VERICONDOR allows a voter to fully verify the tallying integrity by themselves while providing strong protection of ballot secrecy. We present novel zero-knowledge proof techniques to prove the well-formedness of an encrypted ballot with exceptional efficiency. VERICONDOR supports ranking candidates with strict preference, as well as indifference. The computational cost is exceptionally efficient for strict preferences at \(\mathcal{O}(n^{2})\) per ballot for \(n\) candidates, whilst remaining practical for indifferences at \(\mathcal{O}(n^{3})\) . In the case of ties, we show how to apply known Condorcet methods to break them in a publicly verifiable manner. Finally, we present a proof of concept implementation and evaluate its performance.

Algebraic analysis of pairwise comparisons with non-reciprocal property

The law of comparative judgement usually implies the reciprocal property of pairwise comparisons. But time error and position preference could yield some judgements that contradict this identity assumption. This paper proposes an algebraic approach to dealing with the challenge of non-reciprocal property in pairwise comparisons. The concept of non-reciprocal pairwise comparison matrix (NrPCM) is used to characterize the situation of non-reciprocal property. Algebraic analysis of NrPCMs is carried out, where a linear space is constructed by proposing a set of basis. Then the linear space is decomposed into the direct sum of some subspaces. The properties of the space are analyzed such as inner product, decomposition and coordinate. Finally, we apply the algebraic method to investigate the Condorcet paradox under the impact of indifferent voters. A novel transformation formula of non-reciprocal pairwise comparisons is proposed, where the non-reciprocal property holds. It is revealed that the occurrence of voting paradox can be understood clearly according to the transitivity property of NrPCMs.

Paradox of Voting: Extra-Urban Voters in the Late Roman Republic

Summary It is almost universally supposed on general principles that Roman citizens who did not live near the city of Rome were effectively disenfranchised by the logistical difficulty of traveling to the capital to vote, and thus that citizen participation in state decision-making was derisively small; this poses a difficulty for the ‘popular’ model of the functioning of the Roman Republic that has won considerable adherence in recent years. However, a systematic review of evidence for voting by citizens who lived around the peninsula and even for non-citizens’ travel to Rome before 90 BC to apply direct pressure on major votes, shows that distance did not present an insurmountable obstacle to meaningful participation in Roman political life by Italians and extra-urban citizens. It also demonstrates the great importance citizens attached to the vote (suffragium) – a guarantee of their freedom, and the key mechanism by which they influenced their political leaders. This in turn helps to clarify why many Italians, including those of modest means, would have desired Roman citizenship in the run-up to the ‘Social War.’

A Theory of Best Choice Selection through Objective Arguments Grounded in Linear Response Theory Concepts

In this study, we propose how to use objective arguments grounded in statistical mechanics concepts in order to obtain a single number, obtained after aggregation, which would allow for the ranking of “agents”, “opinions”, etc., all defined in a very broad sense. We aim toward any process which should a priori demand or lead to some consensus in order to attain the presumably best choice among many possibilities. In order to specify the framework, we discuss previous attempts, recalling trivial means of scores—weighted or not—Condorcet paradox, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), etc. We demonstrate, through geometrical arguments on a toy example and with four criteria, that the pre-selected order of criteria in previous attempts makes a difference in the final result. However, it might be unjustified. Thus, we base our “best choice theory” on the linear response theory in statistical physics: we indicate that one should be calculating correlations functions between all possible choice evaluations, thereby avoiding an arbitrarily ordered set of criteria. We justify the point through an example with six possible criteria. Applications in many fields are suggested. Furthermore, two toy models, serving as practical examples and illustrative arguments are discussed.

The Paradoxes of Preferential Voting and the Possibility of Strengthening the Electoral Vote in the Slovak Republic

The purpose of this contribution is to generally highlight the power potential of the voter's voice in the elections to the National Council of the Slovak Republic (NR SR), resulting from the proportional electoral system. The specific focus is on selected determinants of the voting power, including the number of preferential votes, the established percentage threshold for preferential marking, the size, and the existence of a single electoral district. At the center of attention is the voter's voice with the attribute "preferential," and the examination of its potential and real impact on the composition of the parliament. By analyzing the central issue of preferential votes, we will gradually uncover weaknesses and imperfections arising from the electoral system setup. The purpose of this contribution is to present selected possible solutions and proposals that would strengthen the weight of preferential votes in the proportional electoral system. To achieve a comprehensive concept of the contribution, descriptive, comparative, and primarily the methods of analysis and synthesis of knowledge, as well as statistical data methods, were utilized. As it was not possible to obtain all the comprehensive data from the Statistical Office of the Slovak Republic within the researched problem, we formulated conclusions based on our own calculations derived from respecting the data of the 2020 parliamentary elections, through mathematical statistics, data collection, and analysis. The aim of this contribution is to contribute to the awareness of deeper connections between the electoral system setup and the actual impact of the voter's voice in the decision-making process in the elections to the NR SR. It also aims to demonstrate certain weaknesses arising from the electoral system setup and stimulate a professional discussion about possible proposals that would fundamentally contribute to increasing the weight of the voter's voice and reflecting the will of the voters to a higher degree in the composition of the parliament.

FACTORS OF ELECTORAL (NON) PARTICIPATION OF CITIZENS IN THE CONTEXT OF RATIONAL CHOICE THEORY

The article is devoted to the study of the factors of electoral (non)participation of citizens in the context of the theory of rational choice. The author pays the main attention to the variables that make it possible to calculate the potential effectiveness of voting for a particular citizen, including the probability of the decisive vote, benefits from voting, and losses from voting. The author emphasizes that, according to the theory of rational choice, citizens make simple calculations to determine whether it is appropriate to vote, taking into account the abovementioned variables. According to the model of rational choice, for the vast majority of citizens, voting is completely irrational, since the weight of one vote is insignificant, the benefits of voting are negligible, and the costs are quite significant. However, most voters spend the resources to show up at the polling station on polling day and cast their own single vote for their preferred candidate. In this case, the paradox of voting arises and the limitations of the theory of rational choice are revealed. The author highlights that several additions or variations of the theory have been presented by the scientific community. In particular, among them, the positive decision to vote is explained by the desire to support the functioning of democratic processes; a sense of civic duty; a desire to minimize maximum losses; faith in the decisive vote; mobilization efforts of politicians; minimal expenses for the voter; a conviction that calculations are impractical. Each amendment is characterized by both advantages for understanding electoral behavior in the context of the theory, and disadvantages, which often come down to ignoring the fundamental variables of the theory and giving the psycho-emotional factor an exceptionally prominent place. The author points out that a reassessment of the initial values of the theory, namely the probability that the single vote will become decisive and the cost of the spent voter`s resources, can lead to a completely new interpretation of the theory and scientific results.

Paradox of voting: peril of the vetoing to the perpetual peace

The permanent members of the Security Council of the United Nations possess veto power which was vested to them by the Charter of the United Nations to maintain global peace and security. As many, as well as recent events (Russia’s illegal aggression towards Ukraine in 2022) exhibit, in certain circumstances casting veto power, poses some perils to the global peace, per se, and they are twofold. First, all permanent members can exercise this power, according to their will, to block any resolution of the Security Council, including those that deplore their own illegal and illegit actions. The second challenge is the amendment of the UN Charter. The present wording of the UN Charter makes amending the Charter paradoxically onerous, if not impossible (by giving huge power to the permanent members again). Consequently, this situation has long triggered and urged politicians and legal scholars to explore possible solutions. This article will humbly contemplate the issue and explore the suggestions for the reinvigoration of the existing instruments to resolve the current legal and political quagmire.

A Novel Epoch-Based Transaction Consistency Sorting Protocol for DAG Distributed Ledger

Because of the characteristics of decentralization, immutability, and transparency, blockchain has gradually become a new and revolutionary technology, which has far-reaching significance for the development of modern technology. However, the traditional Bitcoin blockchain that supports synchronous consensus suffers from the fatal flaw of low throughput. To improve throughput, a number of DAG distributed ledgers have been proposed that support asynchronous consensus, all of which allow multiple nodes to process concurrent transactions asynchronously. However, most DAG distributed ledgers do not implement consistent sorting of transactions, making it difficult to deploy smart contracts. To overcome this problem, in this paper, an epoch-based transaction consistency sorting protocol for DAG distributed ledger is proposed, which not only provides the possibility for the deployment of smart contracts but also can be used to resolve conflicting transactions in the ledger. Transaction consistency sorting protocol provides a more reasonably ordered list of all transactions by taking scalars, such as the set of their own past and future, parent block, and timestamp. In addition, through theoretical analysis, the stability and rationality of the transaction consistency sorting protocol are proved, and there is no Condorcet cycle. Finally, the simulation results demonstrate the protocol is efficient and achieve a throughput of at least 2000 transactions per second.

Minimal voting paradoxes

Voting paradoxes date back to the origin of social choice theory in the 18th century, when the Chevalier de Borda pointed out that plurality—then and now the most common voting rule—may elect a candidate who loses pairwise majority comparisons against every other candidate. Since then, a large number of similar, seemingly paradoxical, phenomena have been observed in the literature. As it turns out, many paradoxes only materialize under some rather contrived circumstances and require a certain number of voters and candidates. In this paper, we leverage computational optimization techniques to identify the minimal numbers of voters and candidates that are required for the most common voting paradoxes to materialize. The resulting compilation of voting paradoxes may serve as a useful reference to social choice theorists as well as an argument for the deployment of certain rules when the numbers of voters or candidates are severely restricted.

Radial Symmetry Does Not Preclude Condorcet Cycles If Different Voters Weight the Issues Differently

Radial symmetry, by our definition, is a precise condition on continuous ideal-point distributions, rarely if ever found exactly in practice, that is similar to the classical 1967 symmetry condition of Plott but pertains to an infinite electorate; the bivariate normal distribution provides an example. A Condorcet cycle exists if the electorate prefers alternative X to Y, Y to Z, and Z to X. An alternative K is a Condorcet winner if there is no alternative that the electorate prefers to K. Lack of a Condorcet winner may engender turmoil. The nonexistence of a Condorcet winner implies that a Condorcet cycle exists. Radial symmetry precludes the existence of Condorcet cycles and thus guarantees a Condorcet winner; but this result assumes that all voters weight the dimensions alike. Our counterexamples show that a Condorcet cycle can arise, even under radial symmetry, if the weighting of issues varies across voters. This finding may be of more than theoretical value: It may suggest that in an empirical setting (without radial symmetry), a Condorcet cycle may be more frequent if voters differ as to how they weight the dimensions. We examine, for illustration based on two dimensions (left–right, linguistic), a Condorcet preference cycle in Finland’s 1931 presidential election.

From deliberation to participation: Democratic commitments and the paradox of voting

In this paper, I examine the view that, surprisingly, the more citizens deliberate about politics, the less likely they are to participate in the realm of the political, and vice versa. In the first part of the paper, I approach the problem from the perspective of the paradox of voting, the claim that voting itself is instrumentally irrational because of the very low probability that a single vote will make any difference at the elections. In the second part of the paper, I argue that rather than analyzing voting instrumentally, it is better to view it as part of the civic commitments that constitute what it means to be a citizen in a democratic society. The act of voting is not primarily an individual?s attempt to decisively influence any particular outcome, but an affirmation of the key practice that upholds the democratic society in which citizens play a part. This reveals a meta-paradox of voting. Namely, to not vote is to exhibit a type of behavior that implies acceptance of democracy simultaneously with rejecting its defining component. Because of that, I will claim, not voting is itself irrational. In light of that conclusion, in the third part of the paper, I explore the extant divide between deliberation and participation by referring back to the analysis of civic commitments. Whereas participation without deliberating reveals ideological bias, deliberation without participation expresses a lack of understanding of what it means to be a citizen. The way to connect them is to engage in a process of attaining reflective equilibrium between the two, starting from the practice of deliberation that would be fully informed by the awareness of our democratic commitments and disconnected from ideologically motivated participation.

The Trembling Chairman Paradox

The Chairman Paradox (Farquharson, 1969) is a classical observation in voting games showing that a Chairman endowed with tie-breaking power might end up with her worst outcome. The analysis posits three players whose preferences build a Condorcet cycle and invokes Iterated Elimination of Weakly Dominated Strategies (IEWDS) to select a unique equilibrium. However, IEWDS is a controversial procedure which exhibits well-known weaknesses. This work relies on non-controversial equilibrium refinements instead. For any cardinal payoffs representing the preferences, two pure-strategy equilibria are trembling-hand perfect, the paradoxical one and another one where the Chairman attains her best outcome. The original paradox is restored (and shown not to actually depend on IEWDS) if one considers the stronger concept of proper equilibrium. The analysis casts new light on a classical paradox and illustrates the difference between properness and trembling-hand perfection in a relevant example.

Degrees of commensurability and the repugnant conclusion

AbstractTwo objects of valuation are said to be incommensurable if neither is better than the other, nor are they equally good. This negative, coarse‐grained characterization fails to capture the nuanced structure of incommensurability. We argue that our evaluative resources are far richer than orthodoxy recognizes. We model value comparisons with the corresponding class of permissible preference orderings. Then, making use of our model, we introduce a potentially infinite set of degrees of approximation to better, worse, and equally good, which we interpret as degrees of commensurability.One payoff is the solution our approach provides to a paradox in population ethics, generated by Parfit's “Continuum Argument”. Parfit imagines a sequence of populations, starting with one consisting of excellent lives and, by a sequence of apparent improvements, reaching a much larger population of lives barely worth living. What he dubs “the Repugnant Conclusion” is that the final population is better than the first. Developing Parfit's response, we argue that some of the populations in the sequence are merely almost better than their immediate predecessors. Almost better is not transitive (unlike better). We offer analogies to other ‘spectrum arguments’, Condorcet's paradox, and to developments in formal epistemology.

The Paradoxes of Democratic Voting and the Peircean Justification of Democracy

La defense peircienne de la democratie propose de fonder l’attrait du gouvernement democratique sur des interets epistemiques universels que nous partageons en tant qu’agents epistemiques individuels. Le probleme avec cette approche est qu’elle se heurte a la maniere caracteristique dont la deliberation et la prise de decision democratique socialisent notre savoir et nos croyances. L’approche peircienne meconnait que ce trait caracteristique distingue la democratie comme un jeu epistemique fondamentalement a part des jeux dans lesquelles nous nous situons, en tant qu’agents epistemiques, dans des contextes non-politiques et non-democratiques. Les defauts de la defense peircienne se manifestent quand celle-ci fait face aux paradoxes du vote democratique qui, pour etre surmontes, demandent une conceptualisation profondement collectivisee et socialisee des processus democratiques de la deliberation et de la formation des opinions. Pour cette raison, la meconnaissance de la maniere distinctive dont la deliberation et la prise de decision democratique socialisent le savoir pose probleme a deux titres : premierement, en basant la defense peircienne de la democratie sure une conception inadequate de l’epistemologie democratique ; deuxiemement, en privant l’approche peircienne de sa capacite de repondre aux defis des paradoxes du vote.

Towards a unified aggregation framework for preferences and judgments

In their foundational work, List and Pettit formalized the judgment aggregation framework and showed that the preference aggregation framework from social choice theory can be mapped into it, arguing that the reverse was not possible. We show that a natural extension of a graph-theoretic representation of the preference aggregation framework indeed allows us to embed also the judgment aggregation framework. Moreover, we show that many concepts from the two original frameworks match up under the new one, show that it is possible to detect “logical consistency” with graph-theoretical properties, and give a new nuanced comparison between the doctrinal paradox and the Condorcet paradox.

Transitivity measurements of fuzzy preference relations

We report approaches for measuring the transitivity properties of fuzzy preference relations. The concept of transitivity measurement is proposed to quantify the transitivity degree of fuzzy preference relations. We reveal the equivalence conditions of three typical transitivity properties: weak stochastic transitivity, moderate stochastic transitivity, and strong stochastic transitivity. The likelihoods of the Condorcet paradox and inverted-order voting paradox occurring in a voting profile are measured by our defining a possibility degree index. When a fuzzy preference relation is not transitive, an iteration algorithm is proposed to obtain a new matrix with transitivity. It is observed that different transitivity properties of fuzzy preference relations correspond to different measurement methods. The occurrence of the voting paradoxes could be characterized by the development of a transitivity measurement.

Simple collective equilibria in stopping games

At each moment in time, an alternative from a finite set is selected by a stochastic process. Players observe the selected alternative and sequentially cast a yes or a no vote. If the set of players casting a yes vote is decisive for the selected alternative, it is accepted and the game ends. Otherwise the next period begins. We refer to this class of problems as stopping games. Collective choice games, quitting games, and coalition formation games are particular examples. When the core of a stopping game is non-empty, a subgame perfect equilibrium in pure stationary strategies is shown to exist. But in general, even subgame perfect equilibria in mixed stationary strategies may not exist. We show that aggregate voting behavior can be summarized by a collective strategy. We insist on pure strategies, allow for simple forms of punishment, and provide a constructive proof to show that so-called two-step simple collective equilibria always exist. This implies the existence of a pure strategy subgame perfect equilibrium. We apply our approach to the case with three alternatives exhibiting a Condorcet cycle and to a model of redistributive politics.

ПРЕДЛОЖЕНИЕ ПО РЕФОРМИРОВАНИЮ ИЗБИРАТЕЛЬНОЙ СИСТЕМЫ РОССИЙСКОЙ ФЕДЕРАЦИИ

Introduction: the article analyzes the extent to which electoral systems meet different (mathematical and judicial) evaluation criteria. Purpose: to identify the fairest algorithm for mandate distribution when electing deputies and officials. Methods: apart from general scientific methods, we extensively used special scientific methods including comparative legal and systematic ones. Results: we have defined the range of mathematical criteria (the absolute majority rule, the Condorcet paradox, the principle of proportional representation of the parties, etc.) and legal criteria (the provisions of the principles of equal, free, and fair election). Preferential voting systems have been found to meet mathematical and judicial criteria most of all. A number of preferential voting systems meet the Condorcet paradox and ensure proportional representation of the parties. During such an election, free and equal participation of independent and party candidates is ensured. Many other systems of majoritarian, proportional, and mixed types do not meet the abovementioned criteria. Unfortunately, in particular cases the Condorcet paradox does not allow determining the candidate to be elected. Consequently, we suggest combining the algorithms developed by Tideman, Kemeny, Young, and Schulze in order to find the ‘strongest path’, or the most reliable way of determining the candidates’ positions in the election. Conclusions: the preferential voting system developed by us is universal and can be used while electing both officers (the president, the governor) and deputies. If it was implemented, electoral legislation would be standardized, as well as the operation of election committees. Such a unification would allow improving the level of citizens' electoral rights protection.