Individual rankings are often aggregated using scoring rules: each position in each ranking brings a certain score; the total sum of scores determines the aggregate ranking. We study whether scoring rules can be robust to adding or deleting particular candidates, as occurs with spoilers in political elections and with athletes in sports due to doping allegations. In general the result is negative, but weaker robustness criteria pin down a one-parameter family of geometric scoring rules with the scores 0, 1, 1 + p, 1 + p + p 2 , . . .. These weaker criteria are independence from deleting unanimous winner (e.g., doping allegations) and independence from deleting unanimous loser (e.g., spoiler candidates). This family generalises three central rules: the Borda rule, the plurality rule and the antiplurality rule. For illustration we use recent events in biathlon; our results give simple instruments to design scoring rules for a wide range of applications.

The frequency dependence of the transfer function of an electrochemical cell is studied experimentally and theoretically in the frequency region 0.005 to 1 Hz under conditions of controlled convective diffusion, at various boundary conditions on the anodes. It is shown that the results are independent of the conditions on the anodes at frequencies exceeding a diffusion frequency. On the other hand, the effect of the boundary conditions al low frequencies is substantial. In particular, it is shown that it is feasible to design a cell with a conversion efficiency indefinitely increasing in the direction of lower frequencies.

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Dozens of school districts and college admissions systems around the world have reformed their admissions rules in recent years. As the main motivation for these reforms, the policymakers cited the strategic flaws of the rules in place: students had incentives to game the system. However, after the reforms, almost none of the new rules became strategy‐proof. We explain this puzzle. We show that the rules used after the reforms are less prone to gaming according to a criterion called “strategic accessibility”: each reform expands the set of schools wherein each student can never get admission by manipulation. We also show that the existing explanation of the puzzle due to Pathak and Sönmez (2013) is incomplete.

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.