Sophisticated voting outcomes and agenda control

Banks, Jeffrey S.

doi:10.1007/bf00649265

Cited by 257 publications

(205 citation statements)

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“…We will also explore the characterization of extended stable sets in the case that X is infinite. Another research topic in our program is to investigate the relations between extended stable sets, Banks set (see Banks 1985;Penn 2006) and the variations of uncovered set in Duggan (2013). We may explore under which condition an extended stable set is included in the Banks set or the solution of uncovered set.…”

Section: Resultsmentioning

confidence: 99%

A note on extended stable sets

2016

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We study abstract decision problems by introducing an extended dominance relation with respect to a set of alternatives. This extension is in between the traditional dominance relation as formulated by Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944) and the transitive closure of it. Subsequently, stable sets are defined and studied for this extended relation. We formulate a characterization of stable sets for this relation and an existence theorem. Finally, we discuss its relation with Von Neumann-Morgenstern stable sets and generalized stable sets.

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Section: Resultsmentioning

confidence: 99%

A note on extended stable sets

2016

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“…At the other extreme, the Condorcet set contains the Condorcet winner when there exists one, and is empty otherwise; we recall that the Condorcet winner is a candidate who beats every other candidate in the majority graph. In particular, the Schwartz set contains the set of Copeland winners [22], 1 as well as the uncovered set, 2 the Banks set [1], and the Slater set [33]. 3 Finally, all these rules are Condorcet-consistent: when a Condorcet winner A exists, all these sets coincide with the singleton {A}.…”

Section: ) Given a Majority Graph G A Candidate A Is A Schwartz Winnmentioning

confidence: 99%

“…An agent with integer weight k can be viewed as k agents voting identically. Although human 1 Copeland winners are those candidates who maximize the number of outgoing edges in the majority graph [12]. 2 The uncovered set are those candidates that defeat every other alternative either directly or indirectly at one remove [25].…”

Section: Weighted Votesmentioning

confidence: 99%

“…Now, let G 3 be the tournament obtained from G 1 Now, because no candidate appears in more than one leaf of T , the sets of candidates appearing in T 1 and T 2 are disjoint. Therefore no pair of candidates can be concerned by more than one of the cases (a), (b), and (c), and the definition of G 3 is well-founded.…”

Section: If T Is a Tree With A Single Node Then H (T ) Holds Trivialmentioning

confidence: 99%

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Winner determination in voting trees with incomplete preferences and weighted votes

Lang¹,

Pini

Rossi

et al. 2011

Auton Agent Multi-Agent Syst

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In multiagent settings where agents have different preferences, preference aggregation can be an important issue. Voting is a general method to aggregate preferences. We consider the use of voting tree rules to aggregate agents' preferences. In a voting tree, decisions are taken by performing a sequence of pairwise comparisons in a binary tree where each comparison is a majority vote among the agents. Incompleteness in the agents' preferences is common in many real-life settings due to privacy issues or an ongoing elicitation process. We study how to determine the winners when preferences may be incomplete, not only for voting tree rules (where the tree is assumed to be fixed), but also for the Schwartz rule (in which the winners are the candidates winning for at least one voting tree). In addition, we study how to determine the winners when only balanced trees are allowed. In each setting, we address the complexity of computing necessary (respectively, possible) winners, which are those candidates winning for all completions (respectively, at least one completion) of the incomplete profile. We show that many such winner determination problems are computationally intractable when the votes are weighted. However, in some cases, the exact complexity remains unknown. Since it is generally computationally difficult to find the exact set of winners for voting trees and the Schwartz rule, we propose several heuristics that find in polynomial time a superset of the possible winners and a subset of the necessary winners which are based on the completions of the (incomplete) majority graph built from the incomplete profiles.This article is a revised and extended version of the conference papers [23,28].

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“…Assuming X is compact and P −1 (x) = {y ∈ X | x P y} is open for all x ∈ X, there exists a P -maximal element if and only if the following condition holds: for every finite set Y ⊆ X, there exists x ∈ X such that, for all y ∈ Y , x R y. 2 In some applications, however, acyclicity of P turns out to be restrictive: when P represents the preferences of a society through a given aggregation mechanism, for example, it is common for P to violate this regularity condition. The well-known Condorcet Paradox demonstrates this for social preferences derived from majority rule: if three voters have rankings, xyz, yzx, zxy, respectively, over three alternatives, and if P represents the strict majority preference relation, then we have x P y P z P x, a cycle, so that M (P ) = ∅.…”

Section: Frameworkmentioning

confidence: 99%

A systematic approach to the construction of non-empty choice sets

Duggan

2006

Soc Choice Welfare

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Suppose a strict preference relation fails to possess maximal elements, so that a choice is not clearly defined. I propose to delete particular instances of strict preferences until the resulting relation satisfies one of a number of known regularity properties (transitivity, acyclicity, or negative transitivity), and to unify the choices generated by different orders of deletion. Removal of strict preferences until the subrelation is transitive yields a new solution with close connections to the "uncovered set" from the political science literature and the literature on tournaments. Weakening transitivity to acyclicity yields a new solution nested between the strong and weak top cycle sets. When the original preference relation admits no indifferences, this solution coincides with the familiar top cycle set. The set of alternatives generated by the restriction of negative transitivity is equivalent to the weak top cycle set.

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Sophisticated voting outcomes and agenda control

Cited by 257 publications

References 10 publications

A note on extended stable sets

A note on extended stable sets

Winner determination in voting trees with incomplete preferences and weighted votes

A systematic approach to the construction of non-empty choice sets

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