The Swiss-system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess tournaments caused by the odd number of rounds played. To analyse this issue, our paper compares the number of points scored in the tournament between players who played one game more with the white pieces and players who played one game less with the white pieces. Using data from 28 highly prestigious competitions, we find that players with an extra white game score significantly more points. In particular, the advantage exceeds the value of a draw in the four Grand Swiss tournaments. A potential solution to this unfairness could be organising Swiss-system chess tournaments with an even number of rounds, and guaranteeing a balanced colour assignment for all players using a recently proposed pairing mechanism.

The group stage of a sports tournament is often made more appealing by introducing additional constraints in the group draw that promote an attractive and balanced group composition. For example, the number of intra-regional group matches is minimised in several World Cups. However, under such constraints, the traditional draw procedure may become non-uniform, meaning that the feasible allocations of the teams into groups are not equally likely to occur. Our paper quantifies this non-uniformity of the 2026 FIFA World Cup draw for the official draw procedure, as well as for 47 reasonable alternatives implied by all permutations of the four pots and two group labelling policies. We show why simulating with a recursive backtracking algorithm is intractable, and propose a workable implementation using integer programming. The official draw mechanism is found to be optimal based on four measures of non-uniformity. Nonetheless, non-uniformity can be more than halved if the organiser aims to treat the best teams drawn from the first pot equally.

Existing match classification models in the tournament design literature have two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not distinguished with respect to the incentives of the contestants. We propose a probabilistic framework to address both issues. For each match, our approach relies on simulating all other matches played simultaneously or later to compute the qualifying probabilities under the three main outcomes (win, draw, loss), which allows the classification of each match into six different categories. The suggested model is applied to the previous group stage and the new incomplete round-robin league, introduced in the 2024/25 season of UEFA club competitions. An incomplete round-robin tournament is found to contain fewer stakeless matches where both contestants are indifferent, and substantially more matches where both contestants should play offensively. However, the robustly higher proportion of potentially collusive matches can threaten with serious scandals.

Penalty shootouts play an important role in the knockout stage of major football tournaments, especially since the 2021/22 season, when the Union of European Football Associations (UEFA) scrapped the away goals rule in its club competitions. Inspired by this rule change, 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, we find no evidence for the effect of the kicking order, the field of the match, or psychological momentum. In contrast to previous results, stronger teams, defined first by Elo ratings, do not perform better than their weaker opponents. Consequently, penalty shootouts seem to be close to a coin toss in top European club football.

We study lobbying as a seller's ploy to affect the buyer's learning process about the value of a singular good that he wishes to procure. In particular, we argue that a lobbying seller strategically distorts "soft" rather than private information. Our innovation is to model this as the seller "jamming" the buyer's signal -- not just by shifting its mean, but -- by skewing (increasing the third moment of) its distribution. An unobserved marginal increase in lobbying effort expands demand, thus, unless too expensive, the seller always lobbies, no matter how suspicious the buyer is. Crucially, even when correctly anticipated (in equilibrium), lobbying increases the price elasticity of the buyer's demand. This leads to a lower equilibrium price and increased efficiency. In the (skew-)normal learning model, in equilibrium the seller gains, the buyer loses as a result of lobbying. Nonetheless, the information gleaned during the process keeps the buyer from refusing to engage in it.

We model populism as the dissemination of a false “alternative reality”, according to which the intellectual elite conspires against the populist for purely ideological reasons. If enough voters are receptive to it, this alternative reality—by discrediting the elite’s truthful message— reduces political accountability. Elite criticism, because it is more consistent with the alternative reality, strengthens receptive voters’ support for the populist. Alternative realities are endogenously conspiratorial to resist evidence better. Populists, to leverage or strengthen beliefs in the alternative reality, enact harmful policies that may disproportionately harm the non-elite. These results explain previously unexplained facts about populism.