Open Access
League competitions and fairness
(Springer, 2023) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Economía; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE
We formulate two fairness principles and characterize the league competition systems that satisfy them. The first principle requires that all players should have the same chance of being the final winner if all players are equally strong, while the second states that the league competition should not favor weaker players. We apply these requirements to a class of systems which includes round-robin tournaments as a particular case.
Open Access
Fair elimination-type competitions
(Elsevier, 2020) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE; Economía
We study the impact of two basic principles of fairness on the structure of elimination-type competitions and perform our analysis by focusing on sports competitions. The first principle states that stronger players should have a larger chance of winning than weaker players, while the second principle provides equally strong players the same chances of being the final winner. We apply these requirements to different kinds of knockout competitions, and characterise the structures satisfying them. In our results, a new competition structure that we call an antler is found to play a referential role.
Open Access
Fair competition design
(2018) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE; Economía
We study the impact of two basic principles of fairness on the structure of competition systems and perform our analysis by focusing on sports competitions. The first principle states that equally strong players should have the same chances of being the final winner, while the second principle requires that the competition system should not favor weaker players. We apply these requirements to a class of competitions which includes, but is not limited to, the sport tournament systems that are most commonly used in practice, such as round-robin tournaments and different kinds of knockout competitions, and we characterize the structures satisfying these requirements. In our results, a new competition structure that we call an antler is found to play a referential role. Finally, we show that the class of fair competition systems becomes rather small when both fairness principles are jointly applied.
Open Access
Power set extensions of dichotomous preferences
(Elsevier, 2016) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Economía; Ekonomia
This paper is devoted to the study of how to extend a dichotomous partition of a universal set X into good and bad objects to an ordering on the power set of X. We introduce a family of rules that naturally take into account the number of good objects and the number of bad objects, and provide axiomatic characterizations of two rules that are particularly appealing when it comes to compating sets in which the good
Open Access
On freedom of choice, ambiguity, and the preference for easy choices
(2006) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Economía; Ekonomia
This paper is devoted to the study of opportunity set comparisons when the characteristics of the options within the sets in question may be ambiguous. We assume that agents display a preference for freedom of choice, but also aversion to the presence of ambiguous options. We propose a suitable environment for approaching this problem, and provide axiomatic characterizations of several rules for ranking sets in such a context.
Open Access
Manipulative agendas in four-candidate elections
(Elsevier, 2020) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE; Economía
We consider a setting where it is known for an electorate what probability a given candidate has of beating another in a pairwise ballot. An agenda assigns candidates to the leaves of a binary tree and is called manipulative if it inverts the final winning probabilities for two candidates. We compare standard and symmetric agendas in four-candidate elections and show that in monotone environments the former are more manipulative.
Open Access
On procedural freedom of choice
(2004) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Economía; Ekonomia
Numerous works in the last decade have analyzed the question of how to compare opportunity sets as a way to measure and evaluate individual freedom of choice. This paper defends that, in many contexts, external procedural aspects that are associated to an opportunity set should be taken into account when making judgements about the freedom of choice an agent enjoys. We propose criteria for comparing procedure-based opportunity sets that are consistent with both the procedural aspect of freedom and most of the standard theories of ranking opportunity sets.