1

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Logical Inconsistency in King-based Ecological Regressions Herron, Michael C. Shotts, Kenneth W. Uploaded 07-03-2002 Keywords ecological inference EI-R consistency second stage regressions Abstract The statistical procedure EI-R, in which point estimates produced by the King (1997) ecological inference technique are used as dependent variables in a linear regression, can be logically inconsistent insofar as the assumptions necessary to support EI-R's first stage (ecological inference via King's method) can be incompatible with the assumptions supporting its second stage (linear regression). In light of this problem, we derive a specification test for logical consistency of EI-R and describe options available to a researcher who confronts test rejection. We then apply our test to the implementation of EI-R in Burden and Kimball's (1998) study of ticket splitting and find that this implementation is logically inconsistent. In correcting for this problem we show that Burden and Kimball's alleged substantive results are not results at all and instead are artifacts of a self-contradictory statistical technique.

2

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Aggregate Voting Data and Implied Spatial Voting Herron, Michael C. Uploaded 07-15-1998 Keywords spatial voting aggregate data ecological inference micro-foundations Abstract The paper draws attention to the micro--foundations of aggregate voting data by introducing the concept of an implied spatial voting model. The adjective ``implied'' refers to the fact that this paper's spatial theory primitives, which describe how individual--level preferences are distributed across and within voting districts, are implied by or derived from aggregate voting data. The key idea proposed here is that, given an observed distribution of aggregate voting data, it is possible to derive features of an individual--level, spatial voting model capable of generating the observed data. Thus, an implied spatial voting model is an inverse image of an observed, aggregate vote share distribution. We provide numerical examples of how spatial voting models can be implied by aggregate voting data and we then analyze aggregate data and National Election Study survey data from the 1980, 1984, and 1988 presidential elections. And, to demonstrate that implied spatial voting models can be calculated from aggregate data alone, we consider presidential elections 1928--1960 and the Chicago mayoral elections of 1983 and 1987. This paper's focus on the micro--foundations of aggregate data highlights the limitations inherent in aggregate data analyses. In particular, the paper discusses identification problems, in part a consequence of the lack of scale and location invariance in preference orderings and in part a consequence of the lack of individual--level information in aggregate data, that affect movement between individual--level theories like spatial voting theory and aggregate voting data.

3

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Did Illegally Counted Overseas Absentee Ballots Decide the 2000 U.S. Presidential Election? Imai, Kosuke King, Gary Uploaded 02-13-2002 Keywords 2000 U.S. Presidential Election Ecological Inference Bayesian Model Averaging Abstract Although not widely known until much later, Al Gore received 202 more votes than George W. Bush on election day in Florida. George W. Bush is president because he overcame his election day deficit with overseas absentee ballots that arrived and were counted after election day. In the final official tally, Bush received 537 more votes than Gore. These numbers are taken from the official results released by the Florida Secretary of State's office and so do not reflect overvotes, undervotes, unsuccessful litigation, butterfly ballot problems, recounts that might have been allowed but were not, or any other hypothetical divergence between voter preferences and counted votes. After the election, the New York Times conducted a six month long investigation and found that 680 of the overseas absentee ballots were illegally counted, and no partisan, pundit, or academic has publicly disagreed with their assessment. In this paper, we describe the statistical procedures we developed and implemented for the Times to ascertain whether disqualifying these 680 ballots would have changed the outcome of the election. The methods involve adding formal Bayesian model averaging procedures to King's (1997) ecological inference model. Formal Bayesian model averaging has not been used in political science but is especially useful when substantive conclusions depend heavily on apparently minor but indefensible model choices, when model generalization is not feasible, and when potential critics are more partisan than academic. We show how we derived the results for the Times so that other scholars can use these methods to make ecological inferences for other purposes. We also present a variety of new empirical results that delineate the precise conditions under which Al Gore would have been elected president, and offer new evidence of the striking effectiveness of the Republican effort to convince local election officials to count invalid ballots in Bush counties and not count them in Gore counties.

4

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If the Assumption Fits...: A Comment on the King Ecological Inference Solution Cho, Wendy K. T. Uploaded 08-20-1998 Keywords ecological inference Abstract I examine a recently proposed solution to the ecological inference problem (King 1997). It is asserted that the proposed model is able to reconstruct individual-level behavior from aggregate data. I discuss in detail both the benefits and limitations of this model. The assumptions of the basic model are often inappropriate for instances of aggregate data. The extended version of the model is able to correct for some of these limitations. However, it is difficult in most cases to apply the extended model properly.

5

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Entropy optimization: computer implementation of the MaxEnt and MinxEnt principles Veiga, Alvaro Mattos, Rogerio Uploaded 09-01-2004 Keywords entropy optimization Shannon's measure Kullback's measure ecological inference MaxEnt MinxEnt Abstract The entropy optimization principles MaxEnt of Jaynes (1957a,b) and MinxEnt of Kullback (1959) can be used in a variety of scientific fields. Among many possible applications, the principles are suitable to tackle the ecological inference problem that often shows up in social science research. Formally, both principles involve the constrained optimization of entropy measures that are intrinsically nonlinear functions of probabilities. Since each is a nonlinear programming problem, the solutions to both depend on iterative search algorithms. In addition, the constraints that probabilities are non–negative and sum up to one restrict in a particular way the solution space. The paper presents in detail a computer efficient implementation of those two principles in the linearly constrained case that makes a prior check for the existence of solution to the optimization problems. A description, made with the aid of two flowcharts, of an algorithm allows interested researchers to develop computer codes in practically any language. The authors also make available their own, easy–to–use codes written in MatLab.

6

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Elections and the National Election Studies King, Gary Uploaded 00-00-0000 Keywords surveys aggregate data ecological inference Abstract This paper, which was written for the National Election Studies, Congressional Elections Conference, argues that the National Election Studies can best contribute knowledge about American politics, and best ensure that the organization prospers, by a data collection strategy that includes a creative combination of detailed aggregate election data with traditional survey research. A sampling design similar to, but considerably less expensive than, the voter validation studies could produce a bounty of information about real precinct-level electoral returns from numerous electoral offices, along with valuable demographic and economic data.

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Inferring Transition Probabilities from Repeated Cross Sections: A Cross-level Inference Approach to US Presidential Voting Pelzer, Ben Eisniga, Rob Franses, Philip Hans Uploaded 07-04-2001 Keywords Markov model repeated cross sections cross-level inference ecological inference Abstract This paper outlines a nonstationary, heterogeneous Markov model designed to estimate entry and exit transition probabilities at the micro-level from a time series of independent cross-sectional samples with a binary outcome variable. The model has its origins in the work of Moffitt (1993) and shares features with standard statistical methods for ecological inference. We show how ML estimates of the parameters can be obtained by the method-of- scoring, how to estimate time-varying covariate effects, and how to include non-backcastable variables in the model. The latter extension of the basic model is an important one as it strongly increases its potential application in a wide array of research contexts. The example illustration uses survey data on American presidential vote intentions from a five-wave panel study conducted by Patterson (1980) in 1976. We treat the panel data as independent cross sections and compare the estimates of the Markov model with the observations in the panel. Directions for future work are discussed.

8

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Racial Polarization and Turnout in Louisiana: New Insights from Aggregate Data Analysis Palmquist, Bradley Voss, D. Stephen Uploaded 00-00-0000 Keywords ecological inference aggregate data turnout South racial polarization redistricting Abstract This paper applies recent developments in aggregate data analysis to newly assembled precinct-level datasets for Louisiana. We validate the usefulness of these methods for answering common voting behavior questions, such as estimating racial polarization/cohesion and predicting racial turnout rates, by applying them to known crosstabulations of turnout by race and party in Louisiana. Then we take the analysis a step further to show how the methods can be used to estimate unknown statistics relevant to redistricting litigation (and their uncertainty) using as much information as possible. In addition to the methodological insights, we draw some substantive conclusions about racial voting behavior and racial mobilization in the South.

9

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The Binomial-Beta Hierarchical Model for Ecological Inference Revisited and Implemented via the ECM Algorithm Mattos, Rogerio Veiga, Alvaro Uploaded 05-21-2001 Keywords ecological inference hierarchical models binomial-beta distribution ECM Algorithm Abstract The binomia-beta hierarchical model is a recent contribution to ecological inference. Developed for the 2x2 tables case and under a bayesian perspective, the model is based on compounding the binomial and the beta distributions into a hierarchical structure to describe the behavior of aggregate variables. From a sample of aggregate observations, inference with this model can be made with regard to the values of the unobservable disaggregate variables. The paper discusses some issues regarding the construction of this EI model: First, previous uses of compounded binomial and beta distributions in the EI literature are reviewed; second, a faster approach to use the model in practice, based on posterior maximization implemented via the ECM algorithm, is proposed and illustrated with an application to a real dataset; finally, limitations regarding the use of marginal posteriors for binomial probabilities as elements of inference (basically, the failure to respect the accounting identity) instead of the predictive densities for the binomial proportions are pointed, together with suggestions of principles for EI model building in general.

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Uncertainty and Ambivalence in the Ecology of Race Alvarez, R. Michael Brehm, John Uploaded 08-22-1996 Keywords racial policy affirmative action ecological inference heteroskedastic ordered logit value conflict uncertainty ambivalence equivocation Abstract Since Myrdal (1944), scholars have regarded American attitudes towards racial policy as a conflict between values, groups, and interests. Although Myrdal viewed the conflict as a state internal to individuals, it begins as aggregate conflict. This mix of ecologies---individual and aggregate---carries forth to the present. This paper takes the question of different ecologies for racial politics seriously, developing tools to compare conflict at individual and aggregate level. We demonstrate that individual racial policy choices stems principally from racial resentment, and that the variability of that choice indicates a state of uncertainty, not ambivalence or equivocation. We further demonstrate that racial resentment does not surface as a predictor of aggregate racial policy choice, even though individual choices about racial policies appear to be more strongly influenced by the level of political informedness.

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Issue Voting and Ecological Inference Thomsen, Soren R. Uploaded 09-14-2000 Keywords issue voting ecological inference electoral geography multinomial logit Abstract This article proposes a unifying framework for individual and aggregate voting behavior. The proposed individual level model is a version of the multinomial logit model that applies to both issue voting, ideological voting and normative voting providing a close fit to survey data. The aggregate model is derived by using the binary logit model as an approximation to the multinomial logit model. The aggregate model is useful for modeling electoral change and for identification of homogenous political regions. Further, the unifying framework derives a method for ecological inference that applies to large tables and gives estimates of voter transitions close to survery results.

12

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On estimates of split-ticket voting Johnston, Ron Gschwend, Thomas Pattie, Charles Uploaded 09-20-2004 Keywords split-ticket Ecological Inference Entropy-Maximizing Abstract Kimball on split-ticket voting in the USA, suggesting that their estimates of the volume of such voting (derived using King's EI method) across Congressional Districts and States are unreliable. Using part of the Burden-Kimball data set, we report on a parallel set of estimates generated by a different procedure (EMax), which employs three rather than two sets of bounds. The results are extremely similar to Burden and Kimball's, providing strong circumstantial evidence for their conclusions regarding the impact of campaign spending and other influences on the volume of split-ticket voting.

13

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Strategic voting in mixed-member electoral systems: The Italian case Benoit, Kenneth Laver, Michael Giannetti, Daniela Uploaded 08-26-2000 Keywords elections italy strategic voting ecological inference Abstract The new Italian electoral system has two elements, a plurality element in single member districts and a PR element in larger multimember constituencies. The plurality element provides strong incentives for groups of parties to form pre-electoral coalitions. The PR element offers incentives for parties to contest the elections individually. We can think of two types of voter. The first type, whom we characterize as "strategic," votes for his or her first choice party in the PR election since there is no strategy that can improve on this. In the plurality election, a strategic voter supports the candidate sponsored by the coalition with which his or her first choice party is affiliated, even if this is not from the first choice party. The second type of voter, whom we characterize as "non-strategic," also votes for his or her first choice party in the PR election. In the plurality election, the non-strategic voter will vote for a first choice party if a candidate of this party is on the ballot but, if not, votes unpredictably. In this paper, we model the "strategic" and "non- strategic" elements of the vote flowing to candidates in the plurality element of the election. Using data from the 1996 and 1994 elections on both PR and plurality voting patterns in each single member district, and confining ourselves to districts where there is a run-off between two coalitions, we are able to estimate the relative numbers of strategic and non- strategic voters in each district, and characterize this in terms of a range of strategic variables.

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Iff the Assumption Fits...: A Comment on the King Ecological Inference Solution Tam, Wendy Uploaded 12-08-1997 Keywords ecological inference Abstract I examine a recently proposed solution to the ecological inference problem (King 1997). It is asserted that the proposed model is able to reconstruct individual-level behavior from aggregate data. I discuss in detail both the benefits and limitations of this model. The assumptions of the basic model are often inappropriate for instances of aggregate data. The extended version of the model is able to correct for some of these limitations. However, it is difficult in most cases to apply the extended model properly.

15

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A Specification Test for Linear Regressions that use King-Based Ecological Inference Point Estimates as Dependent Variables Herron, Michael C. Shotts, Kenneth W. Uploaded 08-16-2000 Keywords ecological inference second stage regressions ordinary least squares logical consistency Abstract Many researchers use point estimates produced by the King (1997) ecological inference technique as dependent variables in second stage linear regressions. We show, however, that this two stage procedure is at risk of logical inconsistency. Namely, the assumptions necessary to support the procedure's first stage (ecological inference via King's method) can be incompatible with the assumptions supporting the second (linear regression). We derive a specification test for logical consistency of the two stage procedure and describe options available to a researcher whose ecological dataset fails the test.

16

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Overtime Inference from Cross-Sectional Surveys Schuessler, Alexander Penubarti, Mohan Uploaded 08-26-1997 Keywords opinion polls ecological inference EI Abstract To derive panel inferences at the micro level from cross-sectional surveys invites an ecological inference problem. Drawing on King's EI method we derive an application that allows us to estimate overtime change from cross-sectional opinion surveys. We validate our application in panel data where magnitudes of micro-level change are known. We subsequently apply the method to independent surveys on presidential approval. In doing so, we detect micro-level volatility that has been unavailable to previous researchers, leading them to derive imprecise conclusions.

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Bayesian and Frequentist Inference for Ecological Inference: The RxC Case Rosen, Ori King, Gary Jiang, Wenxin Tanner, Martin A. Uploaded 07-25-2000 Keywords EM MCMC least squares ecological inference Bayes Nazi Abstract In this paper we propose Bayesian and frequentist approaches to ecological inference, based on RxC contingency tables, including a covariate. The proposed Bayesian model extends the binomial-beta hierarchical model developed by King, Rosen and Tanner (1999) from the 2x2 case to the RxC case. As in the 2x2 case, the inferential procedure employs Markov chain Monte Carlo (MCMC) methods. As such, the resulting MCMC analysis is rich but computationally intensive. The frequentist approach, based on first moments rather than on the entire likelihood, provides quick inference via nonlinear least-squares, while retaining good frequentist properties. The two approaches are illustrated with simulated data, as well as with real data on voting patterns in Weimar Germany. In the final section of the paper we provide an overview of a range of alternative inferential approaches which trade-off computational intensity for statistical efficiency.

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Structural Shifts And Deterministic Regime Switching in Aggregate Data Analysis Tam, Wendy Uploaded 06-04-1997 Keywords ecological inference Abstract It is common for the only available data to be aggregated at a level above \r\nthe microeconomic unit in question. Analyzing aggregate data with ecological \r\nregression implicitly assumes constancy of parameters across aggregate units. \r\nThis assumption is rarely tenable in aggregate data analysis since the\r\naggregation process often generates new macro-level observations where the \r\nparameters vary across the aggregate units. Standard ecological regression \r\nestimates are not useful when they are employed on data with changing structural\r\nparameters. A switching regressions context is proposed where the state-defining \r\nvariable is deterministic and measures homogeneity between the macro-level \r\nunits.

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A Specification Test for Linear Regressions that use King-Based Ecological Inference Point Estimates as Dependent Variables Herron, Michael C. Shotts, Kenneth W. Uploaded 07-14-2000 Keywords ecological inference second stage regressions ordinary least squares logical consistency Abstract Many researchers use point estimates produced by the King (1997) ecological inference technique as dependent variables in second stage linear regressions. We show, however, that this two stage procedure is at risk of logical inconsistency. Namely, the assumptions necessary to support the procedure's first stage (ecological inference via King's method) can be incompatible with the assumptions supporting the second (linear regression). We derive a specification test for logical consistency of the two stage procedure and describe options available to a researcher whose ecological dataset fails the test.

20

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Breaking Up Isn't So Hard to Do: Ecological Inference and Split-Ticket Voting in the 1988 Presidential Election Burden, Barry C. Kimball, David Uploaded 04-01-1997 Keywords ecological inference split-ticket voting Abstract This method uses Gary King's (1997) solution to the ecological inference problem to examine split-ticket voting patterns in the 1988 elections. Earlier studies of split-ticket voting used either aggregate data, which suffer from the ecological fallacy, or survey data, which suffer from misreporting and small, unrepresentative sample sizes within states and districts. This paper produces accurate estimates of the proportions of voters splitting their ballots in each state and district for the first time. With these results we test several competing theories of split-ticket voting and divided government. We find, contrary to Fiorina's (1996) balancing argument, that voters are not intentionally splitting their tickets to produce moderate policies. In most cases split outcomes are the result of lopsided congressional campaigns that feature well-funded, high quality candidates versus unknown competitors.

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Using Ecological Inference Point Estimates in Second Stage Linear Regressions Herron, Michael C. Shotts, Kenneth W. Uploaded 07-14-2000 Keywords ecological inference second stage regressions ordinary least squares consistency Abstract The practice of using point estimates produced by the King (1997) ecological inference technique in second stage linear regressions leads to second stage results that, in general, are inconsistent. This conclusion holds, notably, even when all the assumptions behind King's ecological technique are satisfied. Second stage inconsistency is a consequence of the fact that King--based point estimates of disaggregated quantities are themselves inconsistent, and, moreover, these point estimates are contaminated by errors correlated with the true quantities the estimates measure. Our findings on second stage inconsistency follow from econometric theory in conjunction with an analysis of simulated and real ecological datasets, and based on the findings we propose a bootstrap that researchers can use to produce consistent second stage estimates and valid confidence intervals.

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Paper

Unemployment and Violence in Northern Ireland: a missing data model for ecological inference Honaker, James Uploaded 07-19-2005 Keywords Multiple Imputation Ecological Inference Count Data Political Violence Abstract Contrary to the body of literature in political violence, and the rhetoric of many parties of the conflict, time-series models of ``the troubles'' in Northern Ireland by White (1993) and Thompson (1989) have found no evidence that economic conditions effect the intensity, sources or direction of violence. I show that several methodological flaws exist in previous models. They fail to address the discrete, count nature of the data, the contagion present from aggregation over time, pooling issues from different types of violence, and the over dispersal of deaths. However, the key problem, acknowledged even by the authors themselves, is that all measures of unemployment aggregate Protestant and Catholic unemployment rates into one single measure. Using a model that combines methods of Multiple Imputation to recover missing data (King Honaker Joseph Scheve 2001) and the literature of models for Ecological Inference problems (especially King 1997) I estimate the disaggregated unemployment rates by religion from the available data. Unemployment is shown to be a leading cause of the violence by Republican factions in Northern Ireland.

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Estimating King's ecological inference normal model via the EM algorithm Mattos, Rogerio Veiga, Alvaro Uploaded 04-20-2000 Keywords ecological inference disaggregate data exponential families truncated normal EM Algorithm Abstract Recently, Gary King introduced a new model for ecological inference, based on a truncated bivariate normal, which he estimates by maximum probability and uses to simulate the predictive densities of the disaggregate data. This paper reviews King's model and its assumption of truncated normality, with the aim to implement maximum probability estimation of his model and disaggregate data prediction in an alternative fashion via the EM Algorithm. In addition, we highlight and discuss important modeling issues related to the chance of non-existence of maximum likelihood estimates, and to the degree that corrections for this non-existence by means of suitably chosen priors are effective. At the end, a Monte Carlo simulation study is run in order to compare the two approaches.

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Paper

Voter transition estimation in multiparty systems Andreadis, Ioannis Uploaded 07-07-2008 Keywords Elections Voter transition rates Ecological inference Multiparty systems Abstract Recent advances in the field of ecological inference have provided researchers with new tools to estimate voter transition in two-party systems. Although some researchers have dealt with the R x C ecological inference problem, voter transition estimation remains a difficult and tedious goal. As a result scholars of multi-party systems still struggle with their electoral data. In this paper we present a new approach and we propose a new method that deals with this issue.

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Paper

Analysis of Crossover Voting Alvarez, R. Michael Uploaded 02-26-1999 Keywords crossover voting strategic voting ecological inference exit poll analysis Abstract We undertake the analysis of primary elections from 1980 through 1996 using both academic individual level survey data, media exit-polls, and aggregate election returns on a county by county basis. We come to the following conclusions: 1. there is very little crossover voting in general in United States primaries; 2. the difference in the amount of crossover voting between states with open primaries and closed primaries is not substantively large; 3. thee amount of strategic behavior on the part of voters is extremely small.

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Ecological Inference with Covariates Park, Won-ho Uploaded 07-08-2008 Keywords ecological inference Thomsen voter transition South Korean democratization Abstract The building block of ecological inference strategies is to construct a two-by-two table that describes the individual-level relationship from aggregate information. Extensions to this baseline model, whichever particular technique is employed, have been developed in the context of constructing bivariate R-by-C tables. However, another important and substantively interesting extension is a model that would let the researcher include additional covariates into the model and is yet to be fully discussed and developed. In the paper, I propose a method of moment estimator that incorporates covariates into the ecological inference process by extending Thomsen (1987)'s voter transition model. I apply the developed model to estimate the impact of demographic variables on turnout in South Korean voters over time, especially around democratization, using precinct-level electoral returns and census records.

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Paper

Federal Elections Project: A Grant Proposal Lublin, David Uploaded 07-09-1999 Keywords grant proposals data data collection election data EI ecological inference Abstract The central goal of the Federal Elections Project is to collect the 2000 federal election results at the precinct level and match them with demographic data from the 2000 U.S. Census. D. Stephen Voss of the University of Kentucky and I plan to gather data for all federal elections, specifically for president and vice president, senator, and representative. Although the focus is on federal offices, the data set will also include results from the eleven states holding gubernatorial elections in 2000. The matching of election and demographic data are especially critical now that new techniques of ecological inference allow the study of numerous political questions utilizing aggregate data. Gary King's (1997) EI makes it possible to estimate with standard errors the voting behavior of units like precincts and counties utilizing election and census data.

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Paper

An Ecological Item-Response Model for Multiple Subsets of Respondents with Application to the European Court of Justice Malecki, Michael Uploaded 07-30-2009 Keywords ideal point estimation item response judicial politics ecological inference hierarchical model Abstract The European Court of Justice (ECJ) has fostered the development of a common European legal order, and in doing so, has asserted itself and its supremacy more, and more successfully, than any other international court. It has maintained features of international courts such as its composition of one judge per member state, while employing other tools of national high courts such as en banc decisions and organization into chambers, that together hide internal dissent and shield the ECJ from direct monitoring or curbing by the member states. The same shield has frustrated efforts to quantify the court's responsiveness to member states, with limited evidence that the ECJ yields to some member-state interest some of the time, but nonetheless has advanced integration beyond national governments' wishes. This equivocation arises at least in part from a failure to include relevant information about the court's composition and organization. In fact, the six-year renewable terms of judges, their previous qualifications and affiliations, and the internal organization into chambers all provide prior information that can and should be incorporated into a more complete model of judicial behavior. I develop an extension of the well-studied item-response model to infer judges' preferences, using the structured ecological data from the cases they heard and relevant prior information about judges and the national governments that appoint them as well as information about cases. I offer new, more rigorous tests for existing theoretical hypotheses about the ECJ's deference to certain actors and preference for integration. The model is applicable to other settings of structured ecological data. Many other national and international courts hear cases in subset chambers, and relevant prior information should be included rather than ignored in models of judicial behavior.

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Paper

The Binomial-Beta Hierarchical Model for Ecological Inference: Methodological Issues and Fast Implementation via the ECM Algorithm de Mattos, Rogerio S. Veiga, Alvaro Uploaded 10-17-2002 Keywords ecological inference hierarchical models binomial-beta distribution ECM Algorithm Abstract The binomial-beta hierarchical model from King, Rosen, and Tanner (1999) is a recent contribution to ecological inference. Developed for the 2x2 tables case and from a bayesian perspective, the model is featured by the compounding of binomial and beta distributions into a hierarchical structure. From a sample of aggregate observations, inference with this model can be made regarding values of unobservable disaggregate variables. The paper reviews this EI model with two purposes: First, a faster approach to use it in practice, based on explicit modeling of the disaggregate data generation process along with posterior maximization implemented via the ECM algorithm, is proposed and illustrated with an application to a real dataset; second, limitations concerning the use of marginal posteriors for binomial probabilities as the vehicle of inference (basically, the failure to respect the accounting identity) instead of the predictive distributions for the disaggregate proportions are pointed. In the concluding section, principles for EI model building in general and directions for further research are suggested.

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Iterative Approaches to R x C Ecological Inference Problems: Where They Can Go Wrong Ferree, Karen E. Uploaded 07-10-1999 Keywords Ecological Inference South Africa. R x C Tables Coloured Voting Abstract King's iterative approach to R x C ecological inference problems involves aggregating groups into broad conglomerate categories like "non-whites" or "non-Christians." Under certain general conditions, this can introduce aggregation bias and multimodality to the data, even when these problems are not present in the original data. The paper develops this argument abstractly and illustrates it with the example of coloured voting during the 1994 South African elections. It then explores methods for averting the problem, both "quick fixes" within the context of King's program, as well ones that move in new directions.

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The Ordinary Election of Adolf Hitler: A Modern Voting Behavior Approach King, Gary Rosen, Ori Wagner, Alexander F. Uploaded 08-23-2002 Keywords Voting Behavior Ecological Inference Elections Abstract How did free and fair democratic elections lead to the extrordinarily anti-democratic Nazi Party winning control of the Weimar Republic? The profound implications of this question have led scholars to make the Weimar elections the most studied elections in history and ``who voted for Hitler'' the single most asked question in elections research. Yet, despite this overwhelming attention, mostly from historians, the Nazi voting literature has treated these elections as largely unique events and thus comparison with other democratic elections as mostly irrelevant. The literature has also ignored most voting behavior theory and research in political science, and it has only rarely used modern statistical methods. In this paper, we adapt existing political science theories and new methods and find that many of the explanations offered in the Nazi voting literature, while probably correct, do not distinguish this election from almost any other, occuring in any country. For example, the prevailing explanation in the literature, that the Nazis were a ``catch all party'' because most social groups shifted in their favor by roughly the same amount, is a characteristic of the vast majority of election swings in every democracy, and so does not provide a useful explanation. We also show that a standard ``retrospective voting'' account of Nazi voting fits the distinctive aspects of this election well, once we recognize that the voters who were most hurt by the economic depression and hence most likely to oppose the government fall into two separate groups that have divergent interests. Those who were unemployed or at high risk of becomming unemployed shifted to the Communists, whose platform was designed to appeal mainly to this group, whereas the working poor, those at low risk of unemployment but still poor because of the economy (such as self-employed shop keepers and professionals, domestic workers, and helping family members), shifted disproportionately towards the Nazis, and accounted for most of the unusual dynamics of this election. The consequences of the election of Hitler were extraordinary, but the voting behavior that led to it was not.

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Binomial-Beta Hierarchical Models for Ecological Inference King, Gary Rosen, Ori Tanner, Martin A. Uploaded 05-28-1998 Keywords ecological inference aggregation MCMC hierarchical models iterative simulation Abstract We develop a binomial-beta hierarchical model for ecological inference, using insights from King's (1997) ecological inference model and from the literature on hierarchical models based on Markov chain Monte Carlo algorithms (Tanner, 1996). Models in the framework we provide appear to scale up well, to have few numerical difficulties, and to recognize and avoid automatically problems with multiple modes and some other statistical issues.