Approval Gap of Weighted k-Majority Tournaments Coste, Jeremy; Flesch, Breeann; Laison, Joshua ...
Theory and applications of graphs (Statesboro, Ga.),
2024, Letnik:
11, Številka:
1
Journal Article
Recenzirano
Odprti dostop
A $k$-majority tournament $T$ on a finite set of vertices $V$ is defined by a set of $2k-1$ linear orders on $V$, with an edge $u \to v$ in $T$ if $u>v$ in a majority of the linear orders. We think ...of the linear orders as voter preferences and the vertices of $T$ as candidates, with an edge $u \to v$ in $T$ if a majority of voters prefer candidate $u$ to candidate $v$. In this paper we introduce weighted $k$-majority tournaments, with each edge $u \to v$ weighted by the number of voters preferring $u$. We define the maximum approval gap $\gamma_w(T)$, a measure by which any dominating set of $T$ beats the next most popular candidate. This parameter is analogous to previous work on the size of minimum dominating sets of (unweighted) $k$-majority tournaments. We prove that $k/2 \leq \gamma_w(T) \leq 2k-1$ for any weighted $k$-majority tournament $T$, and construct tournaments with $\gamma_w(T)=q$ for any rational number $k/2 \leq q \leq 2k-1$. We also consider the minimum number of vertices $m(q,k)$ in a $k$-majority tournament with $\gamma_w(T)=q$.
We study elimination tournaments with n stages and 2n symmetric players. The players have effort budgets that decrease within the stages proportionally to the efforts allocated in the previous stages ...such that for each effort unit that a player allocates, he loses α (the fatigue parameter) units of effort from his budget. We show that if the fatigue parameter α is larger than 1n−t+1, the players allocate their efforts equally over all the first t stages, t≤n−1. In particular, if the fatigue parameter α is larger than 12, the players allocate their efforts equally over all the first n−1 stages, and only in the final stage, they exert a lower effort.
•We study elimination tournaments with n stages and 2n symmetric players.•For each effort unit that a player allocates, he loses α units of effort from his budget.•It is shown that if α>0.5 the players allocate their efforts equally over the stages.
Social impacts are increasingly used as one of the main justifications for staging and funding events, and yet there is very little empirical evidence on the extent to which these impacts are ...realised by different kinds of events or in different settings.
This timely volume fills this gap by being the first to explore the different social aspects of events, looking in particular at the role of events in developing social capital, social cohesion and participation in local communities. Based on cutting edge empirical research, it evaluatesthe contribution of both cultural and sports events to social capital, social cohesion, community spirit and local pride in range of different types of events and settings, with case studies drawn from Europe, Australia and South Africa. It therefore furthers knowledge about the social benefits and impacts of events and significantly contributes to the development of Events as a discipline.
Written by leading academics in this area, this volume is essential reading for all those interested in Events Management and Studies.
The localization game on oriented graphs Bonato, Anthony; Cushman, Ryan; Marbach, Trent G. ...
Discrete Applied Mathematics,
10/2023, Letnik:
338
Journal Article
Recenzirano
In the Localization game played on graphs, a set of cops uses distance probes to identify the location of an invisible robber. We present an extension of the game and its main parameter, the ...localization number, to oriented graphs. We present several bounds on the localization number of an oriented graph, including a tight bound via strong components, a bound using a linear programming problem on hypergraphs, and bounds in terms of DAG-width. A family of oriented graphs of order n is given with localization number (1−o(1))n/2. We investigate the localization number of random and quasi-random tournaments, including Paley tournaments.
How does a small provincial city in southern Japan become the site of a world-famous wheelchair marathon that has been attracting the best international athletes since 1981? In More Than Medals, ...Dennis J. Frost answers this question and addresses the histories of individuals, institutions, and events—the 1964 Paralympics, the FESPIC Games, the Ōita International Wheelchair Marathon, the Nagano Winter Paralympics, and the 2021 Tokyo Summer Games that played important roles in the development of disability sports in Japan. Sporting events in the postwar era, Frost shows, have repeatedly served as forums for addressing the concerns of individuals with disabilities. More Than Medals provides new insights on the cultural and historical nature of disability and demonstrates how sporting events have challenged some stigmas associated with disability, while reinforcing or generating others. Frost analyzes institutional materials and uses close readings of media, biographical sources, and interviews with Japanese athletes to highlight the profound—though often ambiguous—ways in which sports have shaped how postwar Japan has perceived and addressed disability. His novel approach highlights the importance of the Paralympics and the impact that disability sports have had on Japanese society. Open access edition funded by the National Endowment for the Humanities.
The aim of this study was to analyze key kinematic, spatiotemporal, and global mechanical characteristics in world‐class middle‐distance racing. Eight men were recorded halfway along the home ...straight on the second, third, and final laps in the 2017 IAAF World Championship 1500 m final. Video data (150 Hz) from three high‐definition camcorders were digitized to calculate relevant variables, subsequently analyzed in relation to running speed and finishing position. Better‐placed finishers had greater hip extension at initial contact and through late stance, greater knee excursion throughout stance, and longer overstriding distances. Step length did not change with faster speeds as runners relied on increasing step frequency, but the highest‐finishing athletes had longer contact phases and greater fluctuations in speed through the step cycle, which were related to higher normalized peak horizontal forces. The best athletes also had lower leg stiffnesses and vertical stiffnesses. The extended contact phase and greater compression could allow for more sustained force production, enabling better acceleration and maintenance of sprinting speed, indicating a trade‐off between aerobic energetic efficiency and anaerobic power capacity. Coaches should note that these factors, as well as the best athletes' greater overstriding distances, show that elite 1500 m runners might prioritize a technique that favors running speed over economy.
We investigate the effects of tangible versus cash rewards in a repeated tournament setting. Firms frequently use tangible rewards to motivate employees, but minimal research has examined their ...effects relative to cash rewards. We conducted a field experiment at a rug wholesaler that held two consecutive sales tournaments for its retailers. The top three retailers in each tournament received either cash rewards or tangible rewards (gift cards) to be distributed to sales staff. We do not find significant effects of reward type in the first tournament. However, in the second tournament, retailers eligible for tangible rewards significantly outperformed those eligible for cash rewards, and this effect is driven by Tournament One losers. Our results are consistent with the theory that Tournament One losers competing for tangible rewards increased sales effort in the second tournament significantly more than their counterparts competing for cash rewards. Our results have practical and theoretical implications.
This paper studies a multi-task tournament in which each agent undertakes two tasks. Agents’ efforts on one of the tasks create externalities on the performances of other competing agents. We discuss ...the design of an optimal tournament to achieve a social optimum in the presence of such externalities. In particular, we show that the traditional single-prized tournament is unable to elicit a social optimum, while a task-specific, multi-prized tournament proposed in this paper can achieve a socially optimal outcome.
