The broken Borda rule and other refinements of approval ranking

2021 ◽  
Author(s):  
Guy Barokas ◽  
Yves Sprumont
Keyword(s):  
Borda Rule

scholarly journals Characterising scoring rules by their solution in iteratively undominated strategies

2021 ◽  
Author(s):  
Christian Basteck
Keyword(s):  
Monotonicity Property ◽  
Scoring Rules ◽  
The Other ◽  
Approval Voting ◽  
Property A ◽  
Borda Rule ◽  
Scoring Rule ◽  
Direct Mechanism ◽  
Social Choice Correspondence ◽  
Choice Correspondence

AbstractWe characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.

scholarly journals A Social Choice Analysis of the Borda Rule in a General Linguistic Framework

2010 ◽  
Vol 3 (4) ◽  
pp. 501 ◽  
Author(s):  
Jose Luis Garcia-Lapresta ◽  
Bonifacio Llamazares ◽  
Miguel Martinez-Panero
Keyword(s):  
Social Choice ◽  
Borda Rule ◽  
Choice Analysis ◽  
General Linguistic ◽  
Linguistic Framework

scholarly journals Ordinal Theories and the Social Choice Analogy

2020 ◽  
pp. 57-76
Author(s):  
William MacAskill ◽  
Krister Bykvist ◽  
Toby Ord
Keyword(s):  
Decision Making ◽  
Social Choice ◽  
Borda Rule ◽  
Moral Uncertainty ◽  
The Social ◽  
The Right

We introduce and discuss the problems of intertheoretic incomparability and merely ordinal theories. We then introduce the analogy between decision-making under moral uncertainty and social choice, and explain how this analogy can help us to overcome these problems. The rest of the chapter is spent fleshing out how this idea can help us to develop a theory of decision-making under moral uncertainty that is applicable even when all theories under consideration are merely ordinal, and even when there is neither level-nor unit- comparability between those theories. We consider whether My Favourite Theory or My Favourite Option might be the right theory of decision-making under moral uncertainty in conditions of merely ordinal theories and incomparability, but reject both of these accounts. We defend the idea that, when maximizing choice worthiness is not possible, one should use the Borda Rule instead.

An Iterative Transient Rank Aggregation Technique for Mitigation of Rank Reversal

2018 ◽  
Vol 9 (1) ◽  
pp. 40-50
Author(s):  
Bikash Bepari ◽  
Shubham Kumar ◽  
Awanish Tiwari ◽  
Divyam ◽  
Sharjil Ahmar
Keyword(s):  
Terminal Condition ◽  
Rank Aggregation ◽  
Borda Rule ◽  
Average Rank ◽  
Rank Reversal ◽  
Linear Programming Methods ◽  
Copeland Method ◽  
Aggregation Technique ◽  
Weighted Aggregate ◽  
Separation Measure

With the advent of decision science, significant elucidation has been sought in the literature of multi criteria decision making. Often, it is observed that for the same MCDM problem, different methods fetch way-apart ranks and the phenomenon leads to rank reversal. To alleviate this problem, different methodologies like the Borda rule, the Copeland method, the Condorcet method, the statistical Thurstone scaling, and linear programming methods are readily available in the literature. In connection with the same, the authors proposed a novel technique to aggregate the ranks laid by different methods. The algorithm initially assigns equal weights to the methods involved to avoid biasness to a particular method and a simple average rank was obtained. Then, after the separation measures of individual methods with respect to average rank were calculated. Considering the separation measure the higher the weightage, the dynamic weights are ascertained to declare the weighted aggregate rank subjected to the terminal condition which include whether the previous rank equals to the current rank or not. To substantiate the proposed algorithm, a materials selection problem was taken into consideration and solved with the proposed technique. Moreover, the same problem was solved by existing voting techniques like the Borda and the Copeland-Condoract methods. The authors found a correlation of more than 85% between the proposed and existing methodologies.

Probabilistic Borda rule voting

2003 ◽  
Vol 21 (3) ◽  
pp. 455-468 ◽  
Author(s):  
Jac C. Heckelman
Keyword(s):  
Borda Rule
Sign in / Sign up

Export Citation Format

Share Document