Related papers: A comparative study of scoring systems by simulati…
Scoring rules are widely used to rank athletes in sports and candidates in elections. Each position in each individual ranking is worth a certain number of points; the total sum of points determines the aggregate ranking. The question is…
In this paper, a new continuous scoring system for soccer is proposed, based on the proportion of time that a team is winning, losing or tied. Several simulations are made applying this technique to complete seasons of different leagues. As…
Nowadays, several crowdsourcing projects exploit social choice methods for computing an aggregate ranking of alternatives given individual rankings provided by workers. Motivated by such systems, we consider a setting where each worker is…
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…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
We characterize the optimal reward functions (scoring rules) that incentivize an agent to acquire information and report it truthfully to the principal. The optimal scoring rules let the agent make a simple binary bet in single-dimensional…
This document focuses on modeling a complex situations to achieve an advantage within a competitive context. Our goal is to devise the characteristics of games to teach and exercise non-easily quantifiable tasks crucial to the math-modeling…
Conflict of interest is the permanent companion of any population of agents (computational or biological). For that reason, the ability to compromise is of paramount importance, making voting a key element of societal mechanisms. One of the…
If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and…
Stochastic optimization algorithms have been successfully applied in several domains to find optimal solutions. Because of the ever-growing complexity of the integrated systems, novel stochastic algorithms are being proposed, which makes…
The outcome of some football matches has benefited both teams at the expense of a third team because head-to-head results were used for breaking ties. Inspired by these examples, our mathematical analysis identifies all possible collusion…
The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another taking into account all the instances of the assumed preference model…
This paper presents two complementary frameworks to optimize Formula 1 race strategies, jointly accounting for energy allocation, tire wear and pit stop timing. First, the race scenario is modeled using lap time maps and a dynamic tire wear…
Formula One race weekends are structured around multiple sessions: practices, qualifying, and the Grand Prix itself, each contributing to final race performance. This study analyzes nearly two decades of races, encompassing 7,800…
To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, ranking by repeatedly choosing a winner that we delete and rank at the…
We examine a controlled school choice model where students are categorized into different types, and the distribution of these types within a school influences its priority structure. This study provides a general framework that integrates…
Scoring rules are used to evaluate the quality of predictions that take the form of probability distributions. A scoring rule is strictly proper if its expected value is uniquely minimized by the true probability distribution. One of the…
The organisers of major sports competitions use different policies with respect to constraints in the group draw. Our paper aims to rationalise these choices by analysing the trade-off between attractiveness (the number of games played by…
Scoring rules are an established way of comparing predictive performances across model classes. In the context of survival analysis, they require adaptation in order to accommodate censoring. This work investigates using scoring rules for…
We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might…