The proliferation of elections in even those states that are arguably anything but democratic has given rise to a focused interest on developing methods for detecting fraud in the official statistics of a state's election returns. Among these efforts are those that employ Benford's Law, with the most common application being an attempt to proclaim some election or another fraud free or replete with fraud. This essay, however, argues that, despite its apparent utility in looking at other phenomena, Benford's Law is problematical at best as a forensic tool when applied to elections. Looking at simulations designed to model both fair and fraudulent contests as well as data drawn from elections we know, on the basis of other investigations, were either permeated by fraud or unlikely to have experienced any measurable malfeasance, we find that conformity with and deviations from Benford's Law follow no pattern. It is not simply that the Law occasionally judges a fraudulent election fair or a fair election fraudulent. Its “success rate” either way is essentially equivalent to a toss of a coin, thereby rendering it problematical at best as a forensic tool and wholly misleading at worst.

“Benford's Law and the Detection of Election Fraud” raises doubts about whether a test based on the mean of the second significant digit of vote counts equals 4.187 is useful as a test for the occurrence of election fraud. The paper mistakenly associates such a test with Benford's Law, considers a simulation exercise that has no apparent relevance for any actual election, applies the test to inappropriate levels of aggregation, and ignores existing analysis of recent elections in Russia. If tests based on the second significant digit of precinct-level vote counts are diagnostic of election fraud, the tests need to use expectations that take into account the features of ordinary elections, such as strategic actions. Whether the tests are useful for detecting fraud remains an open question, but approaching this question requires an approach more nuanced and tied to careful analysis of real election data than one sees in the discussed paper.

Our goal in this paper is to provide a formal explanation for how within-unit causal process information (i.e., data on posttreatment variables and partial information on posttreatment counterfactuals) can help to inform causal inferences relating to total effects—the overall effect of an explanatory variable on an outcome variable. The basic idea is that, in many applications, researchers may be able to make more plausible causal assumptions conditional on the value of a posttreatment variable than they would be able to do unconditionally. As data become available on a posttreatment variable, these conditional causal assumptions become active and information about the effect of interest is gained. This approach is most beneficial in situations where it is implausible to assume that treatment assignment is conditionally ignorable. We illustrate the approach with an example of estimating the effect of election day registration on turnout.

The similarity of states' foreign policy positions is a standard variable in the dyadic analysis of international relations. Recent studies routinely rely on Signorino and Ritter's (1999, Tau-b or not tau-b: Measuring the similarity of foreign policy positions. International Studies Quarterly 43:115–44) S to assess the similarity of foreign policy ties. However, S neglects two fundamental characteristics of the international state system: foreign policy ties are relatively rare and individual states differ in their innate propensity to form such ties. I propose two chance-corrected agreement indices, Scott's (1955, Reliability of content analysis: The case of nominal scale coding. The Public Opinion Quarterly 19:321–5) π and Cohen's (1960, A coefficient of agreement for nominal scales. Educational and Psychological Measurement 20:37–46) κ, as viable alternatives. Both indices adjust the dyadic similarity score for a large number of common absent ties. Cohen's κ also takes into account differences in individual dyad members' total number of ties. The resulting similarity scores have stronger face validity than S. A comparison of their empirical distributions and a replication of Gartzke's (2007, The capitalist peace. American Journal of Political Science 51:166–91) study of the ‘Capitalist Peace’ indicate that the different types of measures are not substitutable.

The Shapley-Owen value (SOV, Owen and Shapley 1989, Optimal location of candidates in ideological space. International Journal of Game Theory 125–42), a generalization of the Shapley-Shubik value applicable to spatial voting games, is an important concept in that it takes us away from a priori concepts of power to notions of power that are directly tied to the ideological proximity of actors. SOVs can also be used to locate the spatial analogue to the Copeland winner, the strong point, the point with smallest win-set, which is a plausible solution concept for games without cores. However, for spatial voting games with many voters, until recently, it was too computationally difficult to calculate SOVs, and thus, it was impossible to find the strong point analytically. After reviewing the properties of the SOV, such as the result proven by Shapley and Owen that size of win sets increases with the square of distance as we move away from the strong point along any ray, we offer a computer algorithm for computing SOVs that can readily find such values even for legislatures the size of the U.S. House of Representatives or the Russian Duma. We use these values to identify the strong point and show its location with respect to the uncovered set, for several of the U.S. congresses analyzed in Bianco, Jeliazkov, and Sened (2004, The limits of legislative actions: Determining the set of enactable outcomes given legislators preferences. Political Analysis 12:256–76) and for several sessions of the Russian Duma. We then look at many of the experimental committee voting games previously analyzed by Bianco et al. (2006, A theory waiting to be discovered and used: A reanalysis of canonical experiments on majority-rule decision making. Journal of Politics 68:838–51) and show how outcomes in these games tend to be points with small win sets located near to the strong point. We also consider how SOVs can be applied to a lobbying game in a committee of the U.S. Senate.

Efforts to find empirical evidence that campaign money impacts policymaking choices have offered scant support for interest group influence. A possible explanation is that the hypothesis that those receiving campaign monies should adjust their policy choices to favor their donor requires the untenable assumption that interest groups and legislators can implement contracts. We develop a new, alternative, model in which legislators and interest groups cannot engage in any form of contracting, and legislators care about both the policy and fundraising implications of their policy choices. In our model, an interest group gives only to those it believes shares its policy preferences. Nonetheless, we show that the group's giving impacts incumbent policy choices. Importantly, when groups ideologically match, the relationship between actual contributions and bias is not straightforward. As long as a group is uncertain about a member's primitive policy preference, it can influence her policymaking even when it contributes to her challenger or abstains from giving altogether.

The empirical study of spatial issue voting has experienced a resurgence in recent years due to advances in data collection and research design. Grynaviski and Corrigan make several important contributions to this literature. In this note, we comment on one of Grynaviski and Corrigan's recommendations—to not include a main effect for issue importance when estimating models assessing the interactive relationship between importance and policy proximity. According to the authors, including the main importance term is incorrect because it is not necessary in representing a scale-invariant functional form under some assumptions and is insufficient under others. In deriving their reduced-form expression, the authors produce a model that is unintuitive and inappropriate for most data. Moreover, the restrictions Grynaviski and Corrigan impose on their model can produce perverse empirical predictions. We show that a model including main effect terms for importance is indeed scale invariant and that inclusion of the main importance term is necessary for scale invariance with respect to partial utility functions.

Lewis and Schultz (2003) develop a statistical signaling model to deal with international conflicts or bargaining situations in which states have private information about their payoffs. They claim that they can confirm that there always exists a unique equilibrium in their model. In this paper, I show that Lewis and Schultz's claim is not true and their model admits multiple equilibria under some parameter settings. Monte Carlo analysis shows that when there are multiple equilibria, the parameter estimates may not converge to their true values even if the number of observations increases.