Single-Stage Election Procedures

We compare the Condorcet Efficiencies of the plurality rule, the negative plurality rule, and the Borda rule to examine what might be gained by using a voting rule that requires candidate rankings. Previous analyses have considered (1) voting situations for which the three rules determine different candidates as winners (and the Condorcet Efficiencies might actually differ across the three rules) as well as (2) refined measures of Group Mutual Coherence that assess the presence of underlying models of rational behavior that governs voter preferences. In this paper, we present the final step of this particular line of analysis by analyzing (1) and (2) simultaneously. We conclude that there is a considerable benefit on the basis of Condorcet Efficiency from asking voters to submit candidate rankings in three-candidate elections.

The standard two-stage voting rules Plurality Elimination and Negative Plurality Elimination are evaluated relative to Borda Rule on the basis of Condorcet Efficiency. Theoretical analysis shows that the Condorcet Efficiency of these two-stage voting rules consistently marginally dominate Borda Rule as the various measures of group mutual coherence change. However, it is also found that the probability that either of the two-stage rules will elect a different candidate than the winner by Borda Rule is quite small. Empirically-based analysis reinforces this observation to lead to the general conclusion that the additional effort that is required to use a two-stage voting rule, rather than simply using Borda Rule, is not likely to be worthwhile. Other benefits are considered that result from using Borda Rule rather than a two-stage voting rule.

Previous research has developed a representation for the Condorcet efficiency of plurality and negative plurality rules on three candidates for large electorates under the impartial culture condition. This study considers the two stage voting rules on three candidates, plurality elimination and negative plurality elimination. A representation is obtained for the Condorcet efficiency of each for large electorates under impartial culture. The Condorcet efficiencies of both rules are equal and are shown to be substantially greater than the Condorcet efficiency of plurality and negative plurality.

We use preference data from the 2015 parliament election in the Austrian federal state of Styria to analyze different voting rules. An exit poll right after the election collected data on ordinal and cardinal preferences from approximately 1000 actual voters. Our analysis is threefold. First, we determine the hypothetical social outcomes under different voting rules; second, we investigate the stability of the outcomes under those rules. Finally, we provide a categorization of different types of parties and analyze the impact of certain voting rules (Plurality Rule, Plurality Run Off, Hare System, Condorcet Method, Approval Voting, Borda Rule, Evaluative Voting, and Majority Judgment) on the performances of parties in those scenarios.

In a large electorate it is natural to consider voters’ preference profiles as frequency distributions over the set of all possible preferences. We assume coherence in voters’ preferences resulting in accumulation of voters preferences. We show that such distributions can be studied via superpositions of simpler so called unimodal distributions. At these, it is shown that all well-known rules choose the mode as the outcome. We provide a set of sufficient conditions for a rule to have this trait of choosing the mode under unimodal distributions. Further we show that Condorcet consistent rules, Borda rule, plurality rule are robust under tail-perturbations of unimodal distributions.

Information retrieval on RDF data benefits greatly from additional provenance information attached to the individual pieces of information. Provenance information such as origin of data, certainty, and temporal information on RDF statements can be used to rank search results according to one of those dimensions. In this paper, we consider the problem of aggregating provenance information from different dimensions in order to obtain a joint ranking over all dimensions. We relate this to the problem of preference aggregation in social choice theory and translate different solutions for preference aggregation to the problem of aggregating provenance rankings. By exploiting the ranking orderings on the provenance dimensions, we characterize three different approaches for aggregating preferences, namely the lexicographical rule, the Borda rule and the plurality rule, in our framework of provenance aggregation.

This paper combines social choice theory with mathematical optimization by applying various group decision concepts to a classical problem of combinatorial optimization, namely the famous traveling salesperson (sales- man) problem. The aim of the latter is to find a tour through all vertices of a given graph along edges of minimal total cost. In this contribution we replace the measure of additive edge costs by the social acceptance of different edges and the resulting tours. In particular, for four different voting rules, the Borda rule, Approval voting, Plurality rule and Simple Majority rule, we will investi- gate the social acceptance of tours derived from global and local decisions. It will be shown that these two decision approaches can lead to widely varying results.

Consider a three-alternative election with n voters and assume that preferences are single-peaked. LetC(λ,n) be the Condorcet efficiency of the rule that assigns 1,λ and 0 points (respectively) to each first, second and third place vote. An exact representation is obtained forC(λ,∞). This relation shows that Borda rule (λ=1/2) is not the most efficient rule. In addition to this result, exact closed form relations are provided forC(0,n),C(1/2,n) andC(1,n). All these relations are obtained by assuming that every admissible configuration of preferences is equally likely to occur.

Perhaps the most influential result in social choice theory is Arrow’s impossibility theorem, which states that a seemingly modest set of desiderata cannot be satisfied when aggregating preferences [1]. While Arrow’s theorem might appear rather negative, it can also be interpreted in a positive way by identifying what can be achieved in preference aggregation.In this talk, I present a number of variations of Arrow’s theorem–such as those due to Mas-Colell and Sonnenschein [8] and Blau and Deb [2]–in their choice-theoretic version. The critical condition in all these theorems is the assumption of a rationalizing binary relation or equivalent notions of choice-consistency. The bulk of my presentation contains three escape routes from these results. The first one is to ignore consistency with respect to a variable set of alternatives altogether and require consistency with respect to a variable electorate instead. As Smith [12] and Young [14] have famously shown, this essentially characterizes the class of scoring rules, which contains plurality and Borda’s rule. For the second escape route, we factorize choice-consistency into two parts, contraction-consistency and expansions-consistency [11]. While even the mildest dose of the former has severe consequences on the possibility of choice, varying degrees of the latter characterize a number of appealing social choice functions, namely the top cycle, the uncovered set, and the Banks set [3,9,4]. Finally, I suggest to redefine choice-consistency by making reference to the set of chosen alternatives rather than individual chosen alternatives [6]. It turns out that the resulting condition is a weakening of transitive rationalizability and can be used to characterize the minimal covering set and the bipartisan set. Based on a two decades-old conjecture due to Schwartz [10], the tournament equilibrium set can be characterized by the same condition or, alternatively, by a weak expansion-consistency condition from the second escape route. Whether Schwartz’s conjecture actually holds remains a challenging combinatorial problem as well as one of the enigmatic open problems of social choice theory.Throughout the presentation I will discuss the algorithmic aspects of all considered social choice functions. While some of the mentioned functions can be easily computed, other ones do not admit an efficient algorithm unless P equals NP [13,5,7].

Inferring programming rules from source code based on data mining techniques has been proven to be effective to detect software bugs. Existing studies focus on discovering positive rules in the form of A ⇒ B, indicating that when operation A appears, operation B should also be here. Unfortunately, the negative rules (A ⇒ ¬ B), indicating the mutual suppression or conflict relationships among program elements, have not gotten the attention they deserve. In fact, violating such negative rules can also result in serious bugs.

Robust Political Equilibria Under Plurality and Runoff Rule

In this paper, we take a new perspective to describe the model uncertainty, and thus propose two new classes of risk measures under model uncertainty. To be precise, we use an auxiliary random variable to describe model uncertainty. By proposing new sets of axioms under model uncertainty, we axiomatically introduce and characterize conditional coherent and convex risk measures under a random environment, respectively. As examples, we also discuss the connections of the introduced conditional coherent risk measures under random environments with two existing risk measures. This paper mainly gives some theoretical results, and it is expected to make meaningful complement to the study of coherent and convex risk measures under model uncertainty.

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.

The Condorcet efficiency of Borda Rule with anonymous voters

We report the results of duopoly market experiments where firms first commit to capacities and then compete in prices. The theoretical literature pertaining to these duopoly models suggests that the way residual demand is rationed is fundamental to the character of equilibrium outcomes when capacity costs are sufficiently low. The experiments test this prediction by varying capacity cost and demand‐rationing schemes. We find that residual demand rationing does not significantly impact the capacity choices of experimental subjects, although it does affect pricing. Regardless of rationing scheme, the Cournot outcome is common with high capacity costs and rare with low capacity costs.