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Pairwise Cluster Randomization: An Exposition
In: Evaluation review: a journal of applied social research, Band 38, Heft 3, S. 217-250
ISSN: 1552-3926
Background: Cluster randomization (CR) is often used for program evaluation when simple random assignment is inappropriate or infeasible. Pairwise cluster random (PCR) assignment is a more efficient alternative, but evaluators seemed to be deterred from PCR because of bias and identification problems. This article explains the problems, argues that they can be mitigated through design choices, and demonstrates that the suitability of PCR can be tested using Monte Carlo procedures. Research Design: The article presents simple formulas showing how the PCR estimator is biased and explains why its standard error is not identified. Formal derivations appear in a longer companion article. Using those formulas, this article discusses how good design can mitigate the problems with bias and identification. Using Monte Carol simulation, this article also shows how to choose between CR and PCR at the design stage. Conclusions: This article advocates for wider use of the PCR design. PCR loses its appeal when the investigator lacks baseline data for matching the clusters. Its use is less compelling when there are a large number of clusters. But when the evaluator is working with a fairly small number of clusters—26 in the running example used in this article—PCR is an attractive alternative to CR.
SSRN
Working paper
Pairwise Dichotomous Cohesiveness Measures
In: Group decision and negotiation, Band 24, Heft 5, S. 833-854
ISSN: 1572-9907
SSRN
Working paper
Nonignorable Attrition in Pairwise Randomized Experiments
In: Political analysis: PA ; the official journal of the Society for Political Methodology and the Political Methodology Section of the American Political Science Association, Band 30, Heft 1, S. 132-141
ISSN: 1476-4989
AbstractIn pairwise randomized experiments, what if the outcomes of some units are missing? One solution is to delete missing units (the unitwise deletion estimator, UDE). If attrition is nonignorable, however, the UDE is biased. Instead, scholars might employ the pairwise deletion estimator (PDE), which deletes the pairmates of missing units as well. This study proves that the PDE can be biased but more efficient than the UDE and, surprisingly, the conventional variance estimator of the PDE is unbiased in a super-population. I also propose a new variance estimator for the UDE and argue that it is easier to interpret the PDE as a causal effect than the UDE. To conclude, I recommend the PDE rather than the UDE.
Pairwise Equilibria in Probabilistic Voting Models
In: European journal of political economy, Band 6, Heft 1, S. 99-106
ISSN: 0176-2680
Pairwise equilibria (in which voters are paired off so that they cancel each other out) are studied in the context of voting models where candidates may be uncertain about voters' choices -- & therefore, may have expectations (about those choices) that are not deterministic. A model is presented where candidates' expectations are based on the ratios of scale values assigned to their strategies, & a necessary & sufficient condition for the candidates' strategies to be a pairwise equilibrium for each of the feasible mappings to their expectations is derived. Implications for a corresponding model in which candidates' expectations are (alternatively) based on scale differences are identified. 7 References. Adapted from the source document.
A Pairwise Local Correlation Model
In: Journal of Computational Finance, Forthcoming
SSRN
Pairwise consensus and Borda rule
We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the distance of the profile to the former is not greater than its distance to the latter. We say that a social choice rule satisfies the pairwise consensus property if it selects the top ranked alternative in the preference relation around which there is such a consensus. We show that the Borda rule is the unique scoring rule that satisfies this property.
BASE
Pairwise consensus and Borda rule
We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the distance of the profile to the former is not greater than its distance to the latter. We say that a social choice rule satisfies the pairwise consensus property if it selects the top ranked alternative in the preference relation around which there is such a consensus. We show that the Borda rule is the unique scoring rule that satisfies this property.
BASE
Pairwise consensus and Borda rule
We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the distance of the profile to the former is not greater than its distance to the latter. We say that a social choice rule satisfies the pairwise consensus property if it selects the top ranked alternative in the preference relation around which there is such a consensus. We show that the Borda rule is the unique scoring rule that satisfies this property.
BASE
Pairwise consensus and Borda rule
We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the distance of the profile to the former is not greater than its distance to the latter. We say that a social choice rule satisfies the pairwise consensus property if it selects the top ranked alternative in the preference relation around which there is such a consensus. We show that the Borda rule is the unique scoring rule that satisfies this property.
BASE
Pairwise consensus and Borda rule
We say that a preference profile exhibits pairwise consensus around some fixed preference relation, if whenever a preference relation is closer to it than another one, the distance of the profile to the former is not greater than its distance to the latter. We say that a social choice rule satisfies the pairwise consensus property if it selects the top ranked alternative in the preference relation around which there is such a consensus. We show that the Borda rule is the unique scoring rule that satisfies this property.
BASE
SSRN
Pairwise equilibria in probabilistic voting models
In: European Journal of Political Economy, Band 6, Heft 1, S. 99-106