arXiv subjects

Dóra Gréta Petróczy

Publications and source records attributed to Dóra Gréta Petróczy.

14 recordsLinked to original sources

arXiv2026

Ranking-based competitive balance measures in Formula One

Competitiveness in racing sports can be measured by comparing the start and finish rankings within races, as well as the start and finish rankings across races in a season. Since the importance of position changes is non-uniform and variance at the top of the ranking is more interesting than at the bottom of the ranking, we propose using weighted distances for this purpose. Therefore, two weighting schemes are applied and compared to the standard Kemeny distance to analyse the Formula One between 1950 and 2024. The evolution of competitive balance is unexpectedly robust to the weights, but competition is more intense if one focuses on the top positions. Competitive balance has been more unfavourable in the last two decades than ever before. Statistical tests uncover three structural breaks in competitive balance that are closely related to regulatory changes, highlighting the role of decision-makers in the evolution of competitiveness.

econ.GN↗

arXiv2026

Optimising the decision threshold in a weighted voting system: The case of the IMF's Board of Governors

In a weighted majority voting game, the players' weights are determined based on the constitutional planner's intentions. The weights are challenging to change in numerous cases, as they represent some desired disparity. However, the voting weights and the actual voting power do not necessarily coincide. Changing a decision threshold would offer some remedy. The International Monetary Fund (IMF) is one of the most important international organisations that uses a weighted voting system to make decisions. The voting weights in its Board of Governors depend on the quotas of the 191 member countries, which reflect their economic strengths to some extent. We analyse the connection between the decision threshold and the a priori voting power of the countries by calculating the Banzhaf indices for each threshold between 50% and 87%. The difference between quotas and voting powers is minimised if the decision threshold is 58% or 59%.

econ.GN↗

arXiv2026

Are penalty shootouts better than a coin toss? Evidence from international club football in Europe

Penalty shootouts play a crucial role in the knockout stage of major football tournaments. Their importance has substantially increased from the 2021/22 season, when the Union of European Football Associations (UEFA) scrapped the away goals rule. Our paper examines whether the outcome of a penalty shootout can be predicted in UEFA club competitions. Based on all shootouts between 2000 and 2025, no evidence is found for the effect of the kicking order, the field of the match, or psychological momentum. In contrast to previous results, we do not detect any relationship between shootout success and relative team strength, quantified by differences in Elo ratings and the implied winning probability. Thus, the hypothesis that penalty shootouts are close to a coin toss in international competitions for European football clubs cannot be rejected.

econ.GN↗

arXiv2026

Voting power in the Council of the European Union: A comprehensive sensitivity analysis

The Council of the European Union (EU) is one of the main decision-making bodies of the EU. A number of decisions require a qualified majority, the support of 55% of the member states (currently 15) that represent at least 65% of the total population. We investigate how the power distribution based on the Shapley--Shubik index and the proportion of winning coalitions change if these criteria are modified within reasonable bounds. The power of the two countries, with approximately 4% of the total population each, is found to be almost flat. The decisiveness index decreases if the population criterion is above 68\% or the states criterion is at least 17. Some quota combinations contradict the principles of double majority. The proportion of winning coalitions can be increased from 13.2% to 20.8% (30.1%) such that the maximal relative change in the Shapley--Shubik indices remains below 3.5% (5.5%). Our results are indispensable for evaluating any proposal to reform the qualified majority voting system.

physics.soc-ph↗

arXiv2025

The impact of the European Union's enlargement with the Western Balkans and the Association Trio on the power of member states in the Council

As of 2022, the European Union has taken several steps regarding enlargement. We focus on the accession of countries with which the Union is actively negotiating membership. This is examined under two enlargement scenarios: first, the enlargement along the lines of the Western Balkan countries, and second, the accession of a trio (Ukraine, Moldova, and Georgia) to the already enlarged Union. We determine the a priori power of the member states based on the Banzhaf and Shapley--Shubik indices. Various coalitions are also assumed to assess the power and influence of member states, considering both pre- and post-enlargement scenarios. We found a rare case when the two indices give different rankings. In the case of the Western Balkan countries' accession, the smaller population member states gain power, presenting an example of the new member paradox. While in a Union of 36 members, every member state loses some of their current power. However, some coalitions are better off with the EU36 enlargement than a EU33 one.

econ.GN↗

arXiv2025

Competitive balance in the UEFA Champions League group stage: Novel measures show no evidence of decline

Competitive balance, which refers to the level of control teams have over a sports competition, is a crucial indicator for tournament organisers. According to previous studies, competitive balance has significantly declined in the UEFA Champions League group stage over the recent decades. Our paper introduces alternative indices to investigate this issue. Two ex ante measures are based on Elo ratings, and four dynamic concentration indicators compare the final group ranking to reasonable benchmarks. Using these indices, we find no evidence of any long-run trend in the competitive balance of the UEFA Champions League group stage between the 2003/04 and 2023/24 seasons.

econ.GN↗

arXiv2025

Attractiveness and equal treatment in a group draw

National teams from different continents can play against each other only in afew sports competitions. Therefore, a reasonable aim is maximising the number of intercontinental games in world cups, as done in basketball and football, in contrast to handball and volleyball. However, this objective requires additional draw constraints that imply the violation of equal treatment. In addition, the standard draw mechanism is non-uniformly distributed on the set of valid assignments, which may lead to further distortions. Our paper analyses this novel trade-off between attractiveness and fairness through the example of the 2025 World Men's Handball Championship. We introduce a measure of inequality, which enables considering 32 sets of reasonable geographical restrictions to determine the Pareto frontier. The proposed methodology can be used by policy-makers to select the optimal set of draw constraints.

math.OC↗

arXiv2023

Bibliometric indices as a measure of performance and competitive balance in the knockout stage of the UEFA Champions League

We argue for the application of bibliometric indices to quantify the long-term uncertainty of outcome in sports. The Euclidean index is proposed to reward quality over quantity, while the rectangle index can be an appropriate measure of core performance. Their differences are highlighted through an axiomatic analysis and several examples. Our approach also requires a weighting scheme to compare different achievements. The methodology is illustrated by studying the knockout stage of the UEFA Champions League in the 20 seasons played between 2003 and 2023: club and country performances as well as three types of competitive balance are considered. Measuring competition at the level of national associations is a novelty. All results are remarkably robust concerning the bibliometric index and the assigned weights. Since the performances of national associations are more stable than the results of individual clubs, it would be better to build the seeding in the UEFA Champions League group stage upon association coefficients adjusted for league finishing positions rather than club coefficients.

stat.AP↗

arXiv2022

Fairness in penalty shootouts: Is it worth using dynamic sequences?

The sequence of moves in a dynamic team tournament may distort the ex-ante winning probabilities and harm efficiency. This paper compares seven soccer penalty shootout rules that determine the kicking order, from a theoretical perspective. Their fairness is evaluated in a reasonable model of First Mover Advantage. We also discuss the probability of reaching the sudden death stage. In the case of stationary scoring probabilities, dynamic mechanisms are not better than static rules. However, it is worth compensating the second-mover by making it the first-mover in the sudden death stage. Our work has the potential to impact decision-makers who can guarantee fairer outcomes in dynamic tournaments by a carefully chosen sequence of actions.

cs.GT↗

arXiv2021

The Fundamental Theorem of Barzilai does not hold

The extensively cited work of Barzilai, J. (1997): Deriving weights from pairwise comparison matrices, published in Journal of the Operational Research Society, 48(12), 1226-1232., derives the geometric mean method from two simple axioms. This note reveals that the central result of the paper called the Fundamental Theorem by the author does not hold as there exists at least one further method satisfying both requirements.

math.OC↗

arXiv2021

An alternative quality of life ranking on the basis of remittances

Remittances provide an essential connection between people working abroad and their home countries. This paper considers these transfers as a measure of preferences revealed by the workers, underlying a ranking of countries around the world. In particular, we use the World Bank bilateral remittances data of international salaries and interpersonal transfers between 2010 and 2015 to compare European countries. The suggested least squares method has favourable axiomatic properties. Our ranking reveals a crucial aspect of quality of life and may become an alternative to various composite indices.

econ.GN↗

arXiv2020

Revenue allocation in Formula One: a pairwise comparison approach

A model is proposed to allocate Formula One World Championship prize money among the constructors. The methodology is based on pairwise comparison matrices, allows for the use of any weighting method, and makes possible to tune the level of inequality. We introduce an axiom called scale invariance, which requires the ranking of the teams to be independent of the parameter controlling inequality. The eigenvector method is revealed to violate this condition in our dataset, while the row geometric mean method always satisfies it. The revenue allocation is not influenced by the arbitrary valuation given to the race prizes in the official points scoring system of Formula One and takes the intensity of pairwise preferences into account, contrary to the standard Condorcet method. Our approach can be used to share revenues among groups when group members are ranked several times.

econ.GN↗

arXiv2020

On the monotonicity of the eigenvector method

Pairwise comparisons are used in a wide variety of decision situations where the importance of alternatives should be measured on a numerical scale. One popular method to derive the priorities is based on the right eigenvector of a multiplicative pairwise comparison matrix. We consider two monotonicity axioms in this setting. First, increasing an arbitrary entry of a pairwise comparison matrix is not allowed to result in a counter-intuitive rank reversal, that is, the favoured alternative in the corresponding row cannot be ranked lower than any other alternative if this was not the case before the change (rank monotonicity). Second, the same modification should not decrease the normalised weight of the favoured alternative (weight monotonicity). Both properties are satisfied by the geometric mean method but violated by the eigenvector method. The axioms do not uniquely determine the geometric mean. The relationship between the two monotonicity properties and the Saaty inconsistency index are investigated for the eigenvector method via simulations. Even though their violation turns out not to be a usual problem even for heavily inconsistent matrices, all decision-makers should be informed about the possible occurrence of such unexpected consequences of increasing a matrix entry.

math.OC↗

arXiv2018

Brexit: The Belated Threat

Debates on an EU-leaving referendum arose in several member states after Brexit. We want to highlight how the exit of an additional country affects the power distribution in the Council of the European Union. We inspect the power indices of the member states both with and without the country which might leave the union. Our results show a pattern connected to a change in the threshold of the number of member states required for a decision. An exit that modifies this threshold benefits the countries with high population, while an exit that does not cause such a change benefits the small member states. According to our calculations, the threat of Brexit would have worked differently before the entry of Croatia.

econ.GN↗