Submajority Rules: Forcing Accountability upon Majorities

The evaluation of majority rules in a legislative bargaining model

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.

This paper re‐evaluates conventional Institutional Analysis and Development (IAD) scholarship which has traditionally prioritized the study of specific rules configurations and their role in forming effective institutional arrangements. We suggest that effective institutional governance may actually be more reliant on the narrative foundations and personal cognitive interpretations of these rules than on the explicit rules themselves. By drawing insights from the Narrative Policy Framework (NPF), which delves into the internal cognitive processes of individuals, we seek to enrich the understanding of institutional‐actor‐rule dynamics. We contend that policy actors often rely on narrative heuristics to navigate complex institutional landscapes, underscoring the role of narratives in both understanding institutional structures and instigating collective action. Although institutional scholarship recognizes the centrality of communication, its impact on shaping institutional arrangements and rule formation remains insufficiently explored. This paper advocates for the integration of the NPF and the Institutional Grammar Tools' (IGT) ADICO, identifying potential parallels between the two frameworks. Our preliminary theorization suggests a cyclical relationship between narratives and institutions, with narratives shaping and being shaped by institutional rules and norms. Building upon Narrative Attention Theory, we aim to understand the broader implications of institutional narratives in driving or reinforcing policy stasis. Our paper represents a foundational step toward a comprehensive theoretical framework on the role of narratives in institutions, spotlighting institutional rules and pointing to future research directions. Through the proposed integration of NPF and IGT's ADICO, we hope to provide a more nuanced understanding of narrative dynamics in institutional arrangements and pave the way for empirical exploration of this relationship.

Short-Term Deviations from Simple Majority Voting

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements but only up to a global phase ambiguity. This work proposes a novel approach to achieve ambiguity-free signal reconstruction using the magnitude of affine measurements, where an additional bias term is used as reference for phase recovery. The proposed scheme consists of two stages, i.e., a support identification stage followed by a signal recovery stage in which the nonzero signal entries are resolved. In the noise-free case, perfect support identification is guaranteed using a simple counting rule subject to a mild condition on the signal sparsity, and the exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed scheme is then extended to the sparse noise (or outliers) scenario. Perfect support identification is still ensured in this case under mild conditions on the support size of the sparse outliers. With perfect support estimation, exact signal recovery from noisy measurements can be achieved using a simple majority rule. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme.

Legislative Process With Open Rules

This is an essay about the legal theory of Thomas Hobbes and about the things that are revealed when one compares Hobbes's ideas with the main line of legal positivism. Hobbes occupies a paradoxical position in traditional jurisprudence-revered but frequently overlooked, hailed as a precursor but not as a founder, and used alternately as a bogeyman and an illustration of the difference between political and legal theory. If one actually looks at Hobbes's works, rather than footnoting them, cite unseen, one finds a rich stewpot of ideas; great dollops of wisdom about language, interpretation, power, legitimacy, epistemology, definition, scholasticism, human nature, and law. Of course, Hobbes has never been ignored. He still plays Mutt to Locke's Jeff in college courses in political theory. But at a time when legal theorists are rediscovering the fact that there is no bright line separating legal from political theory, that questions of legitimacy may resolve themselves into questions of epistemology, and that language and power *are inextricably connected, Hobbes's work deserves rereading, if only to see how legal positivism defines its own margins. The title of this essay is taken from a book' that describes some of the most remarkable examples of the manufacturing of tradition-the creation of myths that are then projected back into history. I want to suggest that something of the sort has happened with positivist legal philosophy. Of course, it would be ridiculous to suggest that positivism is as much an invented tradition as, for example, the Indian ceremonies that actually came from the British preconceptions about what a native ceremony should look like. We can all go back to the great texts and find what seem to be undeveloped and unsophisticated precursors

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Politics. Please check back later for the full article.Narrowly understood, social choice theory is a specialized branch of applied logic and mathematics that analyzes abstract objects called preference aggregation functions, social welfare functions, and social choice functions. But more broadly, social choice theory identifies, analyzes, and evaluates rules that may be used to make collective decisions. So understood, social choice is a subfield of the social sciences that examines what may be called “voting rules” of various sorts. While social choice theory typically assumes a finite set of alternatives over which voter preferences are unrestricted, the spatial model of social choice assumes that policy alternatives can be represented by points in a space of one or more dimensions, and that voters have preferences that are plausibly shaped by this spatial structure.Social choice theory has considerable relevance for the study of legislative (as well as electoral) institutions. The concepts and tools of social choice theory make possible formal descriptions of legislative institutions such as bicameralism, parliamentary voting procedures, effects of decision rules (e.g., supramajority vs. simple majority rule and executive veto rules), sincere vs. strategic voting by legislators, agenda control, and other parliamentary maneuvers. Spatial models of social choice further enrich this analysis and raise additional questions regarding policy stability and change. Spatial models are used increasingly to guide empirical research on legislative institutions and processes.

There exists a large literature on two-person bargaining games and distribution games (or divide-the-dollar games) under simple majority rule, where in equilibrium a minimal winning coalition takes full advantage over everyone else. Here we extend the study to an n-person veto game where players take turns proposing policies in an n-dimensional policy space and everybody has a veto over changes in the status quo. Briefly, we find a Nash equilibrium where the initial proposer offers a policy in the intersection of the Pareto optimal set and the Pareto superior set that gives everyone their continuation values, and punishments are never implemented. Comparing the equilibrium outcomes under two different agendas – sequential recognition and random recognition – we find that there are advantages generated by the order of proposal under the sequential recognition rule. We also provide some conditions under which the players will prefer to rotate proposals rather than allow any specific policy to prevail indefinitely.

Dynamic Stability and Reform of Political Institutions

Understanding the dynamics of social networks is the objective of interdisciplinary research ranging from animal collective behaviour to epidemiology, political science and marketing. Social influence is key to comprehending emergent group behaviour, but we know little about how inter-individual relationships emerge in the first place. We conducted an experiment where participants repeatedly performed a cognitive test in a small group. In each round, they were allowed to change their answers upon seeing the current answers of other members and their past performance in selecting correct answers. Rather than following a simple majority rule, participants granularly processed the performance of others in deciding how to change their answers. Toward a network model of the experiment, we associated a directed link of a time-varying network with every change in a participant's answer that mirrored the answer of another group member. The rate of growth of the network was not constant in time, whereby links were found to emerge faster as time progressed. Further, repeated interactions reinforced relationships between individuals' performance and their network centrality. Our results provide empirical evidence that inter-individual relationships spontaneously emerge in an adaptive way, where good performers rise as group leaders over time.

Unmanned aerial vehicle (UAV) can be used as an aerial base station to provide rapid wireless connectivity to ground users. Given UAV's agility and mobility, a key problem is how to adapt UAV deployment to best cater to the instantaneous wireless traffic in a territory. In this paper, we propose a traffic-aware adaptive UAV deployment scheme in a UAV-aided communication network, where the UAV initiated at the cell center adapts its displacement direction and distance to the spatial randomness of the Poisson distributed mobile users within its target cell. In each realization, the UAV chooses its displacement direction based on a simple majority rule, i.e., to fly to the sector that has the greatest number of users. To balance the service for the users in different sectors, we further optimize the UAV's displacement distance in the chosen sector to maximize the average throughput. We show that the optimal displacement distance under the proposed scheme decreases with the user density. Extensive simulations illustrate that the proposed adaptive deployment scheme outperforms the traditional non-adaptive scheme, where the performance gain is especially significant for small user density.

So far we have been concerned with various problems that were due mainly to the heterogeneity in individual preferences. However, various problems associated with the aggregation of individual decisions also arise when individuals share identical preferences, but have to make decisions given their different decisional capabilities. The problem of aggregating individual decisions under an uncertain dichotomous choice setting had already been studied in the eighteenth century and in recent years it has attracted continuous renewed interest. The last two chapters are devoted to various aspects of this problem.

In this paper an expression for determining the frequency of the “voting paradox” as a function of the number of voters, the number of alternatives to be voted upon, and cultural characteristics of the voters, is derived. In the analysis a voter's ranking of the given alternatives is represented by a skewsymmetric matrix whose elements also satisfy a certain transitivity condition. The collective ranking of the alternatives is obtained under simple majority rule by summation of the actual individual rankings and consequently can likewise be represented by a skewsymmetric matrix. It is then shown that the existence of the paradox corresponds to the nonexistence of a row in the matrix denoting the collective ranking whose entries are all nonnegative. Cultural effects are incorporated by assigning to each possible individual ranking of alternatives a probability. It is then shown that when all possible rankings of three alternatives are equally likely and the number of voters becomes very large, the probability of the paradox approaches a definite limit, vig .087. Exact values for the probability of the paradox for several cases in which the number of alternatives exceeds three are also presented.

On the Generic Efficiency of Takeovers under Incomplete Information