scholarly journals An Analysis Framework for Metric Voting based on LP Duality

2020 ◽  
Vol 34 (02) ◽  
pp. 2079-2086
Author(s):  
David Kempe
Keyword(s):  
Social Choice ◽  
Social Choice Rule ◽  
Worst Case ◽  
Weak Preference ◽  
Worst Case Ratio ◽  
Strong Candidate ◽  
The Cost ◽  
Lp Duality ◽  
Social Choice Rules ◽  
Optimal Candidate

Distortion-based analysis has established itself as a fruitful framework for comparing voting mechanisms. m voters and n candidates are jointly embedded in an (unknown) metric space, and the voters submit rankings of candidates by non-decreasing distance from themselves. Based on the submitted rankings, the social choice rule chooses a winning candidate; the quality of the winner is the sum of the (unknown) distances to the voters. The rule's choice will in general be suboptimal, and the worst-case ratio between the cost of its chosen candidate and the optimal candidate is called the rule's distortion. It was shown in prior work that every deterministic rule has distortion at least 3, while the Copeland rule and related rules guarantee distortion at most 5; a very recent result gave a rule with distortion 2 + √5 ≈ 4.236.We provide a framework based on LP-duality and flow interpretations of the dual which provides a simpler and more unified way for proving upper bounds on the distortion of social choice rules. We illustrate the utility of this approach with three examples. First, we show that the Ranked Pairs and Schulze rules have distortion Θ(√n). Second, we give a fairly simple proof of a strong generalization of the upper bound of 5 on the distortion of Copeland, to social choice rules with short paths from the winning candidate to the optimal candidate in generalized weak preference graphs. A special case of this result recovers the recent 2 + √5 guarantee. Finally, our framework naturally suggests a combinatorial rule that is a strong candidate for achieving distortion 3, which had also been proposed in recent work. We prove that the distortion bound of 3 would follow from any of three combinatorial conjectures we formulate.

Three Social Choice Rules

2017 ◽  
pp. 54-71
Author(s):  
Andrei Marius Vlăducu
Keyword(s):  
Social Choice ◽  
Status Quo ◽  
Choice Rule ◽  
Borda Count ◽  
Social Choice Rule ◽  
Status Quo Bias ◽  
Approval Voting ◽  
The People ◽  
Viable Solution ◽  
Social Choice Rules

The authors analyze three social choice rules (plurality voting, approval voting and Borda count) from a behavioral economics perspective aiming three objectives: 1) if it is a viable solution to use these procedures during mass elections; 2) why individuals prefer a specific social choice rule and not another; 3) how status quo bias and framing effect influence the preference of individuals for a certain social choice rule. The research is conducted with 87 participants to a lab experiment and data suggest that for using approval voting and Borda count during mass elections is necessary to increase the people level of information about their benefits. When making a decision in a political or economic context seem that people tend to prefer simple plurality rule do to its availability and maybe because of its strong reliance with status quo bias.

scholarly journals Optimal Computer Crash Performance Precaution

2012 ◽  
Vol Vol. 14 no. 1 (Distributed Computing and...) ◽  
Author(s):  
Efraim Laksman ◽  
Hakan Lennerstad ◽  
Lars Lundberg
Keyword(s):  
Completion Time ◽  
Optimal Allocation ◽  
Parallel Program ◽  
Parallel Computer ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Worst Case Ratio ◽  
International Audience ◽  
Computer Crash ◽  
The Cost

Distributed Computing and Networking International audience For a parallel computer system with m identical computers, we study optimal performance precaution for one possible computer crash. We want to calculate the cost of crash precaution in the case of no crash. We thus define a tolerance level r meaning that we only tolerate that the completion time of a parallel program after a crash is at most a factor r + 1 larger than if we use optimal allocation on m - 1 computers. This is an r-dependent restriction of the set of allocations of a program. Then, what is the worst-case ratio of the optimal r-dependent completion time in the case of no crash and the unrestricted optimal completion time of the same parallel program? We denote the maximal ratio of completion times f(r, m) - i.e., the ratio for worst-case programs. In the paper we establish upper and lower bounds of the worst-case cost function f (r, m) and characterize worst-case programs.

scholarly journals Communication, Distortion, and Randomness in Metric Voting

2020 ◽  
Vol 34 (02) ◽  
pp. 2087-2094
Author(s):  
David Kempe
Keyword(s):  
Lower Bound ◽  
Social Choice ◽  
Metric Spaces ◽  
Social Choice Rule ◽  
Voting Rules ◽  
Ordinal Comparison ◽  
First Choice ◽  
Voting Mechanisms ◽  
Sum Of Distances ◽  
Social Choice Rules

In distortion-based analysis of social choice rules over metric spaces, voters and candidates are jointly embedded in a metric space. Voters rank candidates by non-decreasing distance. The mechanism, receiving only this ordinal (comparison) information, must select a candidate approximately minimizing the sum of distances from all voters to the chosen candidate. It is known that while the Copeland rule and related rules guarantee distortion at most 5, the distortion of many other standard voting rules, such as Plurality, Veto, or k-approval, grows unboundedly in the number n of candidates.An advantage of Plurality, Veto, or k-approval with small k is that they require less communication from the voters; all deterministic social choice rules known to achieve constant distortion require voters to transmit their complete rankings of all candidates. This motivates our study of the tradeoff between the distortion and the amount of communication in deterministic social choice rules.We show that any one-round deterministic voting mechanism in which each voter communicates only the candidates she ranks in a given set of k positions must have distortion at least 2n-k/k; we give a mechanism achieving an upper bound of O(n/k), which matches the lower bound up to a constant. For more general communication-bounded voting mechanisms, in which each voter communicates b bits of information about her ranking, we show a slightly weaker lower bound of Ω(n/b) on the distortion.For randomized mechanisms, Random Dictatorship achieves expected distortion strictly smaller than 3, almost matching a lower bound of 3 − 2/n for any randomized mechanism that only receives each voter's top choice. We close this gap, by giving a simple randomized social choice rule which only uses each voter's first choice, and achieves expected distortion 3 − 2/n.

scholarly journals Randomized Social Choice Functions Under Metric Preferences

2017 ◽  
Vol 58 ◽  
pp. 797-827 ◽  
Author(s):  
Elliot Anshelevich ◽  
John Postl
Keyword(s):  
Social Choice ◽  
Choice Functions ◽  
Worst Case ◽  
Ordinal Information ◽  
Deterministic Algorithms ◽  
Distortion Bounds ◽  
Special Cases ◽  
Agent Cost ◽  
Social Choice Functions ◽  
The Cost

We determine the quality of randomized social choice algorithms in a setting in which the agents have metric preferences: every agent has a cost for each alternative, and these costs form a metric. We assume that these costs are unknown to the algorithms (and possibly even to the agents themselves), which means we cannot simply select the optimal alternative, i.e. the alternative that minimizes the total agent cost (or median agent cost). However, we do assume that the agents know their ordinal preferences that are induced by the metric space. We examine randomized social choice functions that require only this ordinal information and select an alternative that is good in expectation with respect to the costs from the metric. To quantify how good a randomized social choice function is, we bound the distortion, which is the worst-case ratio between the expected cost of the alternative selected and the cost of the optimal alternative. We provide new distortion bounds for a variety of randomized algorithms, for both general metrics and for important special cases. Our results show a sizable improvement in distortion over deterministic algorithms.

scholarly journals Partially-honest Nash implementation: a full characterization

2019 ◽  
Vol 70 (3) ◽  
pp. 871-904 ◽  
Author(s):  
Michele Lombardi ◽  
Naoki Yoshihara
Keyword(s):  
Social Choice ◽  
Complete Characterization ◽  
Choice Rule ◽  
Social Choice Rule ◽  
Nash Implementation ◽  
Full Characterization ◽  
Material Interest ◽  
Welfare Implications ◽  
Social Choice Rules

Abstract A partially-honest individual is a person who follows the maxim, “Do not lie if you do not have to”, to serve your material interest. By assuming that the mechanism designer knows that there is at least one partially-honest individual in a society of $$ n\ge 3$$ n ≥ 3 individuals, a social choice rule that can be Nash implemented is termed partially-honestly Nash implementable. The paper offers a complete characterization of the (unanimous) social choice rules that are partially-honestly Nash implementable. When all individuals are partially-honest, then any (unanimous) rule is partially-honestly Nash implementable. An account of the welfare implications of partially-honest Nash implementation is provided in a variety of environments.

Implementation by Vote-Buying Mechanisms

2021 ◽  
Vol 111 (9) ◽  
pp. 2811-2828
Author(s):  
Jon X. Eguia ◽  
Dimitrios Xefteris
Keyword(s):  
Willingness To Pay ◽  
Cost Function ◽  
Social Choice ◽  
Wealth Inequality ◽  
Single Parameter ◽  
Vote Buying ◽  
The Family ◽  
The Cost ◽  
Social Choice Rules

Vote-buying mechanisms allow agents to express any level of support for their preferred alternative at an increasing cost. Focusing on large societies with wealth inequality, we prove that the family of binary social choice rules implemented by well-behaved vote-buying mechanisms is indexed by a single parameter, which determines the importance assigned to the agents’ willingness to pay to affect outcomes and to the number of supporters for each alternative. This parameter depends solely on the elasticity of the cost function near its origin: as this elasticity decreases, the intensities of support matter relatively more for outcomes than the supporters’ count. (JEL D63, D71, D72)

scholarly journals Exploration of Faulty Hamiltonian Graphs

2016 ◽  
Vol 27 (07) ◽  
pp. 809-827
Author(s):  
David Caissy ◽  
Andrzej Pelc
Keyword(s):  
Mobile Agent ◽  
Optimal Algorithm ◽  
Worst Case ◽  
Hamiltonian Graphs ◽  
Competitive Algorithm ◽  
Worst Case Ratio ◽  
The Cost ◽  
Location Of Faults

We consider the problem of exploration of networks, some of whose edges are faulty. A mobile agent, situated at a starting node and unaware of which edges are faulty, has to explore the connected fault-free component of this node by visiting all of its nodes. The cost of the exploration is the number of edge traversals. For a given network and given starting node, the overhead of an exploration algorithm is the worst-case ratio (taken over all fault configurations) of its cost to the cost of an optimal algorithm which knows where faults are situated. An exploration algorithm, for a given network and given starting node, is called perfectly competitive if its overhead is the smallest among all exploration algorithms not knowing the location of faults. We design a perfectly competitive exploration algorithm for any ring, and show that, for networks modeled by hamiltonian graphs, the overhead of any DFS exploration is at most 10/9 times larger than that of a perfectly competitive algorithm. Moreover, for hamiltonian graphs of size at least 24, this overhead is less than 6% larger than that of a perfectly competitive algorithm.

scholarly journals Social choice rules driven by propositional logic

2013 ◽  
Vol 70 (3) ◽  
pp. 279-312
Author(s):  
Rosa Camps ◽  
Xavier Mora ◽  
Laia Saumell
Keyword(s):  
Social Choice ◽  
Propositional Logic ◽  
Social Choice Rules
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