Frequency Based Analysis of Voting Rules

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.

This paper focuses on two properties of points voting schemes: their vulnerability to preference misrepresentation and their potential for preference expression. In the spirit of the seminal work of Buchanan and Tullock [2], this dual criterion might be used for the choice of an optimal points voting scheme when the above two aspects only are considered. Unlike recent treatment of the manipulability phenomenon, Gardenfors [3], Gibbard [4], Satterthwaite [8], we do suggest measures for the immunity to mispresentation of a given method. The first measure I[X, f)] is interpreted as a lower bound for δ-manipulation. In other words, I[(X, f)] = c implies that there exists at least one preference profile [xij] ∈ X, such that δ-manipulation is possible for δ > c. The second measure K ranges from 0 to 1, and it is interpreted as the relative frequency of preference profiles in X under which the scheme is immune. Another measure D is proposed for the potential of preference expression under each variation. This measure counts the number of possible preference configurations under the scheme (X, f). The use of this measure for the comparison of two voting schemes (T, f), (Z, f) is especially meaningful whenever T ⊂ Z. This approach is illustrated by five variations of the points voting scheme: the well-known points voting method, the Borda scores method, the plurality rule, the federative plurality rule and a dictatorial type voting scheme. It is shown that, as these variations become more restrictive in terms of preference expression (D decreases), they tend to be more immune to individual preference misrepresentation (I increases). We conjecture, first, that a similar relationship will be generally obtained for variations of the points voting method, and, second, that such a relationship also exists between K and D.

Voting rules producing a single absolute winner include unanimity, majority, and plurality rules. Multiple winners are created, in contrast, by electoral systems of proportional representation and further multi‐party coalition formation. Different electoral rules are evaluated for the frequency with which they produce winners, corresponding to the median voter's preference.

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.

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.

A voting rule maps voter preferences into outcomes, and is called sophisticated if there exists a voting tree whose sophisticated outcomes coincide with the voting rule for every voter preference. As yet, no complete characterization of such rules is available. In this paper, we provide an important step toward this characterization by completely solving the problem when there are two possible sets of voter preferences.

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].

Manipulation in elections with uncertain preferences

PP144—Assessing In Vivo Enzyme Genetic Variation in the Presence of Transporter Effect

Voting systems have a great impact on the results of contests or elections. Simple methods are actually used, whereas they do not provide most accurate results. For example, in the Eurovision Song Contest, the winner may not be the most preferred candidate. Condorcet criterion, which consists in preserving most of the individual votes in the final ranking, seems intuitively the most relevant. In this paper, we propose a new ranking method founded on Condorcet voting count principle which minimizes the number of pairwise inversions of the individual preferences. We propose a two-step method: computing the cycles among vote preferences and removing a minimal set of pairwise preferences to erase all the cycles and turn the votes into a partial order as close as possible to a total order. Finally, we evaluate the impact of our ranking procedure on the last 30 Eurovision Song Contests.

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 backtest in pigs revisited – An analysis of intra-situational behaviour

The concept of distance rationalizability of voting rules has been explored in recent years by several authors. Roughly speaking, we first choose a consensus set of elections (defined via preferences of voters over candidates) for which the result is specified a priori (intuitively, these are elections on which all voters can easily agree on the result). We also choose a measure of distance between elections. The result of an election outside the consensus set is defined to be the result of the closest consensual election under the distance measure. Most previous work has dealt with a definition in terms of preference profiles. However, most voting rules in common use are anonymous and homogeneous. In this case there is a much more succinct representation (using the voting simplex) of the inputs to the rule. This representation has been widely used in the voting literature, but rarely in the context of distance rationalizability. We show exactly how to connect distance rationalizability on profiles for anonymous and homogeneous rules to geometry in the simplex. We develop the connection for the important special case of votewise distances, recently introduced and studied by Elkind, Faliszewski and Slinko in several papers. This yields a direct interpretation in terms of well-developed mathematical concepts not seen before in the voting literature, namely Kantorovich (also called Wasserstein) distances and the geometry of Minkowski spaces. As an application of this approach, we prove some positive and some negative results about the decisiveness of distance rationalizable anonymous and homogeneous rules. The positive results connect with the recent theory of hyperplane rules, while the negative ones deal with distances that are not metrics, controversial notions of consensus, and the fact that the $\ell^1$-norm is not strictly convex.

We consider two-sided many-to-one matching markets where hospitals have responsive preferences. In this context, we study the preference revelation game induced by the student-proposing deferred acceptance mechanism. We show that acyclicity of the hospitals’ preference profile (Romero-Medina and Triossi 2013a. “Acyclicity and Singleton Cores in Matching Markets.” Economics Letters 118 (1):237–9) is a necessary and sufficient condition to ensure that the outcome of every Nash equilibrium in which each hospital plays a dropping strategy is stable.