Rejoinder to 'Comment' by S. J. Brams and M. D. Davis
| Autor: | Claude S. Colantoni, Terrence J. Levesque, Peter C. Ordeshook |
|---|---|
| Rok vydání: | 1975 |
| Předmět: |
Value (ethics)
education.field_of_study Sociology and Political Science media_common.quotation_subject Population Assertion Proposition State (functional analysis) Argument Voting Political Science and International Relations Empirical relationship education Mathematical economics Mathematics media_common |
| Zdroj: | American Political Science Review. 69:157-161 |
| ISSN: | 1537-5943 0003-0554 |
| DOI: | 10.2307/1957893 |
| Popis: | Brams and Davis begin their comment with the assertion that our "main criticism" of their research is that the 3/2's rule is an artifact of an empirical relationship rather than a theoretically derived proposition. This statement reverses our argument, however, which is that the apparent empirical support for their hypothesis is the artifact. Their remaining comments warrant more attention. Briefly, they assert that (1) their model, contrary to our statements, incorporates considerations of the relative competitiveness of states and that our empirical analysis "unwittingly" confirms this fact; (2) the parsimony of their model (as, presumably, against ours) is a virtue and not a vice, and; (3) the logic of our hypothesis as to why we observe greater than proportional allocations (even after controlling for competitiveness) is, at best, unintelligible to them while, at worst, the hypothesis is our initial assumption rather than a derived conclusion. First, Brams and Davis properly note that in their model, if nj is proportional to state j's size, the proportionate margin of victory (in absolute terms) should on the average be smaller in larger states. To see this, let Nj denote state j's voting population and x; denote the realized number of uncommitted voters voting for, say, the Republican candidate. Given their assumptions (including that, in each state, candidates match allocations and committed voters are evenly divided), a candidate's plurality in proportionate terms, (2xj-nj)/Nj, is normally distributed with zero mean and standard deviation a = V/ /Nj. Clearly, if nj= CNj, a = iC/N, which decreases as Nj increases and thus El (2xj-nj)/NjI = a-N2/-n decreases as well. Brams and Davis then state that the regression results we report in Table 4 confirm this consequence of their model and that they wished "all critics were so charitable with the ammunition they provide their adversaries." Indeed, a superficial examination of the data and of their model's implications supports their argument. In Table 1 we report, for the two competitive elections in our study, the average value of I P1jI and the standard deviation of Ptj. For both elections, I PljI and a are greater in smaller states (defining "small" to be those states with fewer than nine electoral votes, which approximately divides the sample). Furthermore, as we show in our essay, I P4jI does tend to decrease with the square root of electoral vote. Their model, however, not only predicts that a decreases with Nj but, given nj, it also renders a prediction about the magnitude of o. This consequence should also be tested lest we accept their model when the true cause of variations derive from a different stochastic process.' Using the data in Table 1 to estimate nj for small states, we obtain |
| Databáze: | OpenAIRE |
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