Short-Term Deviations from Simple Majority Voting

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.

Dynamic Stability and Reform of Political Institutions

Declaring a winner by adopting the Simple majority criterion is a fundamental mistake. The outcome could be in deep contrast with both Condorcet’s and Borda’s methods. A better result can be obtained with Run-off voting or with Instant run-off voting. Though the ranking could not comply with Condorcet’s method, yet the outcome is not as flawed as that provided by the Simple majority criterion.

This chapter explores the debate about the debate and two procedures that US senators use to extend and close the debate: filibuster and cloture. I first outline the history of the filibuster and cloture. Within the debate about the debate are two controversies: the senate as an exclusive deliberative body, and the meaning of majority rule. I show how the exclusive deliberative body theory envisioned by James Madison, Alexander Hamilton, and George Washington has devolved to where the Senate has become more like the House. Majority rule, because of changes made to cloture, has become more like what the framers of the Constitution likely envisioned: simple majority rule.

In Ruling Majorities and Reasoning Pluralities, Professor Saul Levmore explores the “division of labor” between the various thresholds of agreement required for collective action—supermajority, simple majority, or plurality rule. His particular emphasis is on the choice between the last two options. To improve our understanding of this choice in various settings, Professor Levmore considers the relationship between two well-known contributions to the study of group decisionmaking, namely, the Condorcet Jury Theorem and the Condorcet Criterion, which have not generally been treated together. This essay explores the relationship between these two insights in the context of judicial decisionmaking. Counterintuitively, the essay demonstrates that while the Condorcet Criterion continues to hold great promise as a tool of decision in en banc appellate courts, the Condorcet Jury Theorem is most appealing in judicial contexts that appear less collegial and thus less like a jury. In contexts in which jurists engage in deliberation and in which they anticipate that their outputs will have precedential effect, the Jury Theorem has little if any role to play. In contrast, the Theorem might prove more useful in evaluating low-level judicial outputs or decisions that otherwise are not expected to be treated as precedent. Thus, common law trial court decisions and civil law court decisions are more likely to be useful benchmarks in a Condorcet Jury Theorem analysis. It is because such courts do not anticipate that their decisions will have the force of precedent that they are more likely to be derived from governing legal texts, and thus more prone to characterizations of accuracy, than are judicial outputs that are driven by policy concerns and are generated with the understanding that they will be treated as precedent.

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

Instant runoff voting (IRV) is an electoral system that produces better elections and more representative outcomes in races with three or more candidates. Used by over 50 American jurisdictions, IRV addresses the challenges of plurality voting in crowded candidate fields. It upholds majority rule, promotes voter engagement, discourages personal attacks, and minimizes strategic voting. IRV is preferable to runoff systems and other proposed single-winner methods. In comparison to runoffs, IRV produces higher, more equitable turnout and reduces costs and demands on voters. In contrast to methods based on rating candidates, voters in IRV elections have incentives to indicate their honest preferences. IRV demonstrates greater political viability and more intuitively fair outcomes than Condorcet methods. For legislative elections, IRV complements the single transferable vote, which is the best way to address the U.S.’s governance and polarization crises, end gerrymandering, and secure fairer representation for all.

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.

Submajority Rules: Forcing Accountability upon Majorities

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.