The evaluation of majority rules in a legislative bargaining model

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.

Short-Term Deviations from Simple Majority Voting

This paper contributes to the understanding of how flexibility in the number of members in a decision-making committee in a multistage project can enhance the accuracy and efficiency of the decisions taken. While most projects typically employ a fixed number of decision makers, the paper demonstrates the advantages of adjusting the committee size according to the project’s varying complexity at different phases of the project. In particular, we show that allowing for flexibility in the size of a committee increases the likelihood of reaching a correct decision under the unanimity rule. We analyze this issue when the decision maker’s competence is independent of the state of nature and when it is not. The results are compared to those under the simple majority rule.

On the Generic Efficiency of Takeovers under Incomplete Information

We extend the Baron and Ferejohn (1989) model of multilateral bargaining by allowing the players to attempt commiting to a bargaining position prior to negotiating. If successful,commitment binds a player to reject any proposal which allocates to her a share below a self-imposed threshold. Any such attempted commitment fails and decays with an exogenously given probability. We characterize and compare symmetric stationary subgame perfect equilibria under unanimity rule and majority rules. Under unanimity rule, there are potentially many equilibria which can be ordered from the least to most inefficient, according to how how many commitment attempts must fail in order for an agreement to arise. The most inefficient equilibrium exists independently of the number of players, and the delay in this equilibrium is increasing in the number of players. In addition, more efficient commitment profiles cannot be sustained in equilibrium if the number of players is sufficiently large. The expected inefficiency due to delay at the least and at the most efficient equilibrium increases as the number of players increases. Under any (super)majority rule, however, there is no equilibrium with delay or inefficiency. The reason is that competition to be included in the winning coalition discourages attempts to commit to an aggressive bargaining position. We also show that inefficiencies related to unanimity decision making may be aggravated by longer lags between consecutive bargaining rounds. The predicted patterns are by and large consistent with observed inefficiencies in many international arenas including the European Union, WTO, and UNFCCC. The results suggest that the unanimity rule is particularly damaging if the number of legislators is large and the time lags between consecutive sessions are long.

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.

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.

We use a general cellular automata model to study the consumer decision-making process. Within this general model we use three different rules governing word-of-mouth communication (w-o-m), one majority rule and two unanimity rules, and ask the question if differences between these three w-o-m rules, introduced on the microscopic level, will manifest on the macroscopic level. We show that in the model with the majority rule the neighborhood plays a significant role in terms of the market shares whereas movement (interpreted as seeking for information in other sources) is almost negligible. Exactly the opposite phenomena are observed for models in which unanimity, instead of majority, is needed to convince agents. We also introduce a modification of the unanimity rule, based on the Latane theory of the social influence, and show that on the macroscopic level this modification is indistinguishable from the simple unanimity rule. We conclude the paper with a recommendation which rules are more appropriate to model particular marketing phenomena.

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.

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.

Dynamic Stability and Reform of Political Institutions

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.