The traveling group problem

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.

A discussion is presented regarding the single-stage election procedures Plurality, Negative Plurality, and Borda Rules; with an emphasis on their Condorcet Efficiency, which measures their propensity to elect the Condorcet Winner. A theoretical analysis shows how the Condorcet Efficiency of these voting rules change as the various measures of group mutual coherence change. Both Plurality and Negative Plurality Rules are found to perform very poorly over identifiable ranges of the defined measures of group mutual coherence. While Borda Rule is not always found to be the most Condorcet Efficient single-stage rule in all scenarios, it never performs poorly under any scenario. These theoretical results are then reinforced by empirically-based analysis to show very solid support for using Borda Rule, despite some concerns that have been expressed that Borda Rule requires voters to rank candidates, while Plurality and Negative Plurality Rules do not.

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.

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].

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.

In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer k, the difference of votes rule Mk outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. In addition, we state and prove Llamazares' theorem in voting models where either there is an infinite number of votes or each voter is allowed to express an intensity level for one alternative over the other. Finally, we will use a computer simulation to compare different voting methods to simple majority rule, in order to analyze the probability that the voting rules would output different results.

Which Voting Rule is Most Likely to Choose the 'Best' Candidate?

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.

When Do Conflicting Parties Share Political Power? An Experimental Study

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.

We have observed that some recent results cast serious doubts uponthe applicability of majority rule as a device for forming a group-willout of individual wills. On the other hand, majority rule has manyproperties to recommend it. Especially, the decisiveness propertyshould please anyone interested in efficiency considerations. How-ever, when it comes to the second major criterion, consistency, major-ity rule with pairwise comparison of alternatives often leads to diffi-culties. Indeed, we have seen that there is typically no core or Con-dorcet winner when the policy space is multidimensional real space.And when there is no core, the situation looks grim indeed for major-ity rule: literally any outcome may become the majority winner. Somerelief of this very strong result is provided by the fact that no majoritycycles can go through the outcomes that belong to the M2 bargainingset. This finding, of course, solves the problem facing majority rule onlyinsofar as a method can be devised by which the M2 bargaining set out-comes can be determined in a reliable way. Here, thus, we are con-fronted with the sincerity problem. The absence of the core can lead to chaotic trajectories of votingoutcomes in multidimensional space. However, there are ways of over-coming the difficulties if a sufficient amount of flexibility is allowedin institutional design. If we consider the various nonequilibrium solu-tion concepts, and the minimax set in particular, we can always designa decision rule which (under mild restrictions) makes the vote-maximiz-ing outcome trajectory enter the solution set. The flexibility needed isgreat, indeed: the decision rule, λ-majority, must be alterable for eachvoting situation. The determination of the winner in a pair-wise comparison of alter-natives is not the main source of the difficulties surrounding majorityrule. As a matter of fact, the method of building the agenda is the mostcrucial part of the problem of cyclical majorities. In multicandidatecontests the occurrence of cyclical majorities has motivated the studyof other.decision procedures in addition to the majority comparisonof alternatives. The most recent proposal, approval voting, is morestrategyproof than its competitors in the class of single-ballot, non-ranked voting systems. At the moment the relationships betweenapproval voting and majority rule are not clear. It seems that furtherstudy of the interrelationships of these procedures is called for. Thefeatures in which approval voting is superior to majority comparisonof pairs of alternatives, however, are not, strictly speaking, procedural,but are external to the method of making collective decisions.

Decentralized decision-making requires the interaction of various local decision-makers in order to arrive at a global decision. Limited sensing capabilities at each local site can create ambiguities in a decision-making process at each local site. We argue that such ambiguities are of differing gradations. We propose a framework for decentralized decision-making (applied to decentralized control in particular) that allows computation of such ambiguity gradations and utilizes their knowledge in arriving at a global decision. Each local decision is tagged with a certain grade or level of ambiguity, with zero being the minimum ambiguity level. A global decision is taken to be the same as a ldquowinningrdquo local decision, i.e., one having the minimum level of ambiguity. The computation of an ambiguity level for a local decision requires an assessment of the self-ambiguities as well as the ambiguities of the others, and an inference based upon such knowledge. For the existence of a decentralized supervisor, so that for each controllable event the ambiguity levels of all winning disablement or enablement decisions are bounded by some number N (such a supervisor is termed N-inferring), the notion of N-inference observability is introduced. We show that the conjunctive-and-permissive (C&P) V disjunctive-and-antipermissive (D&A) co-observability is the same as the zero-inference observability, whereas the conditional C&P V D&A co-observability is the same as the unity-inference observability. We also present examples of higher order inference-observable languages. Our framework does not require the existence of any a priori partition of the controllable events into permissive/antipermissive sets, nor does it require a global control computation based on conjunction/disjunction of local decisions, exhibiting that our ambiguity-based approach is more efficient.

Approval ballots provide an opportunity for agents to make a comment about every candidate, without incurring the overhead of determining a full ranking on the set of candidates; they are very natural for many practical settings. We study the computational complexity of the committee selection problem for several approval-based voting rules in the presence of outliers. Our first result shows that outliers render the committee selection problem intractable for approval, net approval, and minisum approval voting rules. We next study the parameterized complexity of this problem with five natural parameters, namely the target score, the size of the committee (and its dual parameter namely the number of candidates outside the committee); and the number of outliers (and its dual parameter namely the number of non-outliers). For approval, net approval, and minisum approval voting rules, we provide a dichotomous result, which resolves the parameterized complexity of this problem for all subsets of the above five natural parameters considered (by showing either fixed parameter tractability or W[1]-hardness for all subsets of parameters).

Utilitarian Collective Choice and Voting

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.