This paper analyzes the computational complexity involved in solving fairness issues on graphs, e... more This paper analyzes the computational complexity involved in solving fairness issues on graphs, eg, in the installation of networks such as water networks or oil pipelines. Based on individual rankings of the edges of a graph, we will show under which conditions solutions, ie, ...
While distance functions are a natural way to derive prefer-ences over outcomes for the aggregati... more While distance functions are a natural way to derive prefer-ences over outcomes for the aggregation of arbitrary characteristics, they also open the door to impossibility results familiar from the literature on proximity preservation in the framework of classical Arrovian social choice theory. We establish an impossibility result involving intuitively plausible properties of abstract aggregation rules all formulated in terms of distances.
We show how ultrafilters can be used to prove a central impossibility result in judgement aggrega... more We show how ultrafilters can be used to prove a central impossibility result in judgement aggregation introduced by Nehring and Puppe (2005), namely that for a logically strongly interconnected agenda, an independent and monotonic judgement aggregation rule which satisfies universal domain, collective rationality and sovereignty is necessarily dictatorial.
The Condorcet efficiency of three widely used scoring rules is investigated with the help of comp... more The Condorcet efficiency of three widely used scoring rules is investigated with the help of computer simulations for larger numbers of candidates than are usually considered in the literature and it is shown that for this case the superiority of the Borda rule does not hold. A new distance-based measure of Condorcet efficiency is introduced which extends the superiority of the Borda rule to larger numbers of candidates.
The fact that rank aggregation rules are susceptible to manipulation by varying degrees has long ... more The fact that rank aggregation rules are susceptible to manipulation by varying degrees has long been known. In this work we study the effect of noise on manipulation i.e. we assume that individuals are not able to perceive the preferences of others without distortion. To study the frequency of various outcomes we simulate a large number of rank aggre-gations and manipulations on random profiles with the help of a software package developed by the authors in the Python language and discuss some preliminary results.
In this paper we compare a minisum and a minimax procedure as suggested by Brams et al. for selec... more In this paper we compare a minisum and a minimax procedure as suggested by Brams et al. for selecting committees from a set of candidates. Using a general geometric framework as developed by Don Saari for preference aggregation, we show that antipodality of a unique maximin and a unique minisum winner can occur for any number of candidates larger than
Don Saari has developed a geometric approach to the analysis of paradoxes of pref- erence aggrega... more Don Saari has developed a geometric approach to the analysis of paradoxes of pref- erence aggregation such as the Condorcet paradox or Arrow's general possibility theorem. In this paper we extend this approach to judgment aggregation. In par- ticular we use Saari's representation cubes to provide a geometric representation of profiles and majority rule outcomes. We then show how profile
This paper analyzes the computational complexity involved in solving fairness issues on graphs, e... more This paper analyzes the computational complexity involved in solving fairness issues on graphs, eg, in the installation of networks such as water networks or oil pipelines. Based on individual rankings of the edges of a graph, we will show under which conditions solutions, ie, ...
While distance functions are a natural way to derive prefer-ences over outcomes for the aggregati... more While distance functions are a natural way to derive prefer-ences over outcomes for the aggregation of arbitrary characteristics, they also open the door to impossibility results familiar from the literature on proximity preservation in the framework of classical Arrovian social choice theory. We establish an impossibility result involving intuitively plausible properties of abstract aggregation rules all formulated in terms of distances.
We show how ultrafilters can be used to prove a central impossibility result in judgement aggrega... more We show how ultrafilters can be used to prove a central impossibility result in judgement aggregation introduced by Nehring and Puppe (2005), namely that for a logically strongly interconnected agenda, an independent and monotonic judgement aggregation rule which satisfies universal domain, collective rationality and sovereignty is necessarily dictatorial.
The Condorcet efficiency of three widely used scoring rules is investigated with the help of comp... more The Condorcet efficiency of three widely used scoring rules is investigated with the help of computer simulations for larger numbers of candidates than are usually considered in the literature and it is shown that for this case the superiority of the Borda rule does not hold. A new distance-based measure of Condorcet efficiency is introduced which extends the superiority of the Borda rule to larger numbers of candidates.
The fact that rank aggregation rules are susceptible to manipulation by varying degrees has long ... more The fact that rank aggregation rules are susceptible to manipulation by varying degrees has long been known. In this work we study the effect of noise on manipulation i.e. we assume that individuals are not able to perceive the preferences of others without distortion. To study the frequency of various outcomes we simulate a large number of rank aggre-gations and manipulations on random profiles with the help of a software package developed by the authors in the Python language and discuss some preliminary results.
In this paper we compare a minisum and a minimax procedure as suggested by Brams et al. for selec... more In this paper we compare a minisum and a minimax procedure as suggested by Brams et al. for selecting committees from a set of candidates. Using a general geometric framework as developed by Don Saari for preference aggregation, we show that antipodality of a unique maximin and a unique minisum winner can occur for any number of candidates larger than
Don Saari has developed a geometric approach to the analysis of paradoxes of pref- erence aggrega... more Don Saari has developed a geometric approach to the analysis of paradoxes of pref- erence aggregation such as the Condorcet paradox or Arrow's general possibility theorem. In this paper we extend this approach to judgment aggregation. In par- ticular we use Saari's representation cubes to provide a geometric representation of profiles and majority rule outcomes. We then show how profile
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