arXiv subjects

Alexander S. Nesterov

Publications and source records attributed to Alexander S. Nesterov.

5 recordsLinked to original sources

arXiv2022

How should we score athletes and candidates: geometric scoring rules

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 how to choose a scoring rule for a specific application. First, we derive a one-parameter family with geometric scores which satisfies two principles of independence: once an extremely strong or weak candidate is removed, the aggregate ranking ought to remain intact. This family includes Borda count, generalised plurality (medal count), and generalised antiplurality (threshold rule) as edge cases, and we find which additional axioms characterise these rules. Second, we introduce a one-parameter family with optimal scores: the athletes should be ranked according to their expected overall quality. Finally, using historical data from biathlon, golf, and athletics we demonstrate how the geometric and optimal scores can simplify the selection of suitable scoring rules, show that these scores closely resemble the actual scores used by the organisers, and provide an explanation for empirical phenomena observed in biathlon and golf tournaments. We see that geometric scores approximate the optimal scores well in events where the distribution of athletes' performances is roughly uniform.

cs.GT↗

arXiv2020

Stealed-bid Auctions: Detecting Bid Leakage via Semi-Supervised Learning

Bid leakage is a corrupt scheme in a first-price sealed-bid auction in which the procurer leaks the opponents' bids to a favoured participant. The rational behaviour of such participant is to bid close to the deadline in order to receive all bids, which allows him to ensure his win at the best price possible. While such behaviour does leave detectable traces in the data, the absence of bid leakage labels makes supervised classification impossible. Instead, we reduce the problem of the bid leakage detection to a positive-unlabeled classification. The key idea is to regard the losing participants as fair and the winners as possibly corrupted. This allows us to estimate the prior probability of bid leakage in the sample, as well as the posterior probability of bid leakage for each specific auction. We extract and analyze the data on 600,000 Russian procurement auctions between 2014 and 2018. We find that around 9% of the auctions are exposed to bid leakage, which results in an overall 1.5% price increase. The predicted probability of bid leakage is higher for auctions with a higher reserve price, with too low or too high number of participants, and if the winner has met the auctioneer in earlier auctions.

econ.GN↗

arXiv2020

Comparing School Choice and College Admission Mechanisms By Their Immunity to Strategic Admissions

Recently dozens of school districts and college admissions systems around the world have reformed their admission rules. As a main motivation for these reforms the policymakers cited strategic flaws of the rules: students had strong incentives to game the system, which caused dramatic consequences for non-strategic students. However, almost none of the new rules were strategy-proof. We explain this puzzle. We show that after the reforms the rules became more immune to strategic admissions: each student received a smaller set of schools that he can get in using a strategy, weakening incentives to manipulate. Simultaneously, the admission to each school became strategy-proof to a larger set of students, making the schools more available for non-strategic students. We also show that the existing explanation of the puzzle due to Pathak and Sönmez (2013) is incomplete.

econ.TH↗

arXiv2019

Measuring Majority Power and Veto Power of Voting Rules

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful, and whether minorities can veto the candidates they do not prefer. For a given voting rule, the minimal share of voters that guarantees a victory to one of their most preferred candidates is the measure of majority power, and the minimal share of voters that allows them to veto each of their least preferred candidates is the measure of veto power. We find tight bounds on these minimal shares for voting rules that are popular in the literature and in real elections. We order these rules according to majority power and veto power. The instant-runoff voting has both the highest majority power and the highest veto power and the plurality rule has the lowest. In general, the higher the majority power of a voting rule is, the higher its veto power. The three exceptions are: voting with proportional veto power, Black's rule, and Borda rule, which have a relatively low level of majority power and a high level of veto power and thus provide minority protection. Our results can shed light on how voting rules provide different incentives for voter participation and candidate nomination.

cs.GT↗

arXiv2019

Minimal Envy and Popular Matchings

We study ex-post fairness in the object allocation problem where objects are valuable and commonly owned. A matching is fair from individual perspective if it has only inevitable envy towards agents who received most preferred objects -- minimal envy matching. A matching is fair from social perspective if it is supported by majority against any other matching -- popular matching. Surprisingly, the two perspectives give the same outcome: when a popular matching exists it is equivalent to a minimal envy matching. We show the equivalence between global and local popularity: a matching is popular if and only if there does not exist a group of size up to 3 agents that decides to exchange their objects by majority, keeping the remaining matching fixed. We algorithmically show that an arbitrary matching is path-connected to a popular matching where along the path groups of up to 3 agents exchange their objects by majority. A market where random groups exchange objects by majority converges to a popular matching given such matching exists. When popular matching might not exist we define most popular matching as a matching that is popular among the largest subset of agents. We show that each minimal envy matching is a most popular matching and propose a polynomial-time algorithm to find them.

cs.GT↗