V. The Role of CountyLevel Conditions as Explanations for Serious Capital ErrorThus far, we have studied the relationship to state capital reversal rates of conditions measured at the state level. There are two reasons to study conditions measured at the local level as well. First, the significant explanations for reversal rates that our state analyses identify may not actually be statelevel conditions but instead an aggregate reflection of local conditions. Directly studying local conditions can help resolve this ambiguity. Second, there may be local influences on capital reversal rates—e.g., from the array of capital decisions made by local prosecutors, trial judges and juries^{501}— that our state analyses miss entirely. For these reasons we conducted eight analyses of local capital reversal rates and of explanations for them that operate or can be measured at the local level. As is discussed above, we analyze local conditions at the county level because the county is the most frequent site of local capital decision making, and the local jurisdiction about which relevant information is most often available.^{502} Even so, county level analysis encounters three difficulties. First, as Figures 42A and 42B, pp. 24849 below, reveal, a large proportion—58%—of the 2300plus counties in the 34 states with active death penalties during the 23year study period imposed no death verdicts in the period. Even in wellknown capital states such as Texas and Virginia, most counties—respectively, 59% and 68% of the states' 394 counties— imposed no death verdicts in 23 years. These proportions are influenced in part by how many counties states have. For example, the state with the smallest number of counties—Delaware (3 counties)Cis the state with the largest proportion of capital counties (100%).^{503} But even states with similar numbers of counties have strikingly different proportions of capital counties. Like Delaware, Connecticut has only a small number of counties (8), but unlike Delaware's counties, a majority of Connecticut's counties (5, or 62%) imposed no death verdicts in the study period. Among the five states with 6367 counties, the proportion of capital counties ranged from 79% in Florida and 75% in Alabama to 55% in Pennsylvania, 42% in Louisiana and 10% in Colorado. The map in Figure 42B roughly indicates the average size of counties in states, revealing that all states in the midAtlantic region (west of the Chesapeake Bay), the Midwest, and the South have large numbers of relatively small counties. But the counties in those regions used the death penalty at quite different rates: The highest concentrations of deathsentencing counties are in states below the MasonDixon Line: the Carolinas, Georgia, Florida, Alabama, Mississippi, Louisiana, Arkansas and eastern Texas and Oklahoma. Even here, however, there are differences: Counties in the Carolinas, Florida and Alabama use the death penalty much more uniformly than, e.g., Georgia and Louisiana counties. Next highest in terms of the concentration of capital counties are industrial states of the North and Midwest: Pennsylvania (especially around Philadelphia), Ohio, Indiana and Illinois (especially around Chicago). Less predictably, perhaps, deathsentencing counties are noticeably less concentrated in the border states of Virginia, Kentucky, Tennessee and Missouri. Figure 42B provides less information about the West, but heavy use of the death penalty among counties in Arizona, California and to a lesser extent Nevada and Idaho can be contrasted to light use in, e.g., Nebraska, New Mexico and Colorado. For these reasons, our regressions have fewer counties to compare than one might expect— 1002.^{504} The inability to study counties with no death verdicts also decreases variability because counties that use the death penalty are probably more like each other than counties that do not use it. If so, there is less diversity among the counties studied than one might expect.^{505} By contrast, when states as a whole are studied, the data being examined are from an aggregate of both sets of counties— noncapital as well as capital.
Figure 42A: Percent of Counties in 34 Active Capital States That Imposed No Death Verdicts, 197395* Second, most of our analyses compare each county's reversal experience in each of the 23 study years in which they imposed death verdicts. In those analyses the number of counties available for study drops to 967, because 35 counties are omitted where the year their death verdicts were imposed is unknown. More importantly, in any given year, only a small minority of the 967 capital counties imposed even one death verdict. As a result, there are not 22,241 (23 x 967) countyyears to compare, but only 3054. In other words, each of the 967 deathsentencing counties imposed death sentences in an average of only 3 of the 23 study years.506 In 72% of those 3054 countyyears, moreover, a total of only 1 death verdict was imposed, with an additional 16% of the countyyears imposing only 2 death verdicts during the study period. Thus, 72% of the observed reversal rates being analyzed had only two possible outcomes (0% or 100% reversed), and 16% had only three possible outcomes (0%, 50% or 100% reversed). Given the small number of possible outcomes for a large proportion of the observed reversal rates, the amount of variation to be explained is diminished. Finally, because of how hard it is for government agencies and scholars to gather data from over 3000 counties nationally, as opposed to only 50 states, not as much data are available on countylevel, as opposed to statelevel, conditions that might affect capital error. B. Results of CountyOnly Analysis 7: Importance of CountyLevel Factors Similar to Those Identified by the State Analyses We begin with Analysis 7, which is designed to make it as easy as possible to identify countylevel factors that may be related to capital reversal rates. To do this, the analysis omits all states and statelevel explanatory factors from the analysis. This makes the analysis an incomplete basis for drawing conclusions about county effects—because it invites county conditions to receive credit for each county's share of what, in fact, are statelevel influences. But the approach is a useful starting point, since it identifies the broadest possible set of potentially important countylevel factors for consideration in later analyses. Analysis 7 uses Poisson regression analysis to explain differences among capital reversal rates in the 967 counties in the 34 study states that imposed at least one death verdict during the 19731995 study period and in which the year of the verdict is known.^{507} To maximize the range of reversal rates available for analysis, Analysis 7 (like Analyses 1, 2, 14 and 15 above) calculates reversal rates as the proportion of all death verdicts imposed in particular counties and years that were reversed at any of the three review stages during the study period. This produced 3054 observed reversal rates for the 967 counties in each of the 23 or fewer years in which the county imposed death verdicts. We also enhanced the amount of unexplained variance among counties in this initial analysis Cagain to help us identify the widest possible universe of potentially important county factors for examination in subsequent analyses—by treating only time trend, but not year or county, as a random effect in the baseline and in the more specific Analysis 7 inquiries. Under these circumstances, highly significant countytocounty and yeartoyear variance among the 967 counties' reversal rates remained after Analysis 7's baseline inquiry of the effect of time trend. The types of countylevel factors our county analyses tested are outlined in Table 2, pp. 13637 above.^{508} Those factors replicate at the county level most, but not all, significant statelevel factors that our state analyses identify, as well as analogues of various statelevel factors that were tested in our state regressions but were not found significant. Among the factors tested in the county analyses are countylevel analogues of the following statelevel factors:
One important statelevel factor—the statutory method of selecting judges—has no countylevel analogue, because it measures a single statelevel condition that is uniform throughout the state. In other cases, a countylevel analogue for an important statelevel factor could theoretically be calculated, but the factor in fact operates at the state level and none of the data needed to calculate a county analogue are centrally available. This is true for general court caseloads (which are collected only on a statewide basis by centrally organized state court systems with uniform policies across the state), and for imprisonment rates relative to rates of serious crimes (because states, not counties, operate prisons, and do not report the locality where prisoners committed their crimes and were convicted). The number of death verdicts awaiting review is also a statelevel factor, because court delays are the responsibility of state courts. We can calculate a county analogue for this factor, however, using the county of origin of backlogged verdicts, and we did so in Analysis 7 only as a control for the effect of delay.511 Unlike Analysis 7, the other county analyses test state as well as county factors, so those analyses instead use the more appropriate, statelevel backlog factor. Analysis 7A is a single best set of factors, which identifies five significant explanations for county reversal rates (including time trend, which was also included in the baseline analysis).512 Analysis 7A had less unexplained variance among counties and years than did the baseline analysis, although it did not fit the data better.^{513} Confidence in Analysis 7A is enhanced somewhat because all five (highly) significant factors it identifies are countylevel analogues of significant factors identified at the state level:
Two important statelevel factors with testable countylevel analogues had no statistically significant effect at the county level: (1) homicide rates among whites compared to blacks, and (2) the AfricanAmerican proportion of the population. Given the link Analyses 14 and 15 revealed between these racial factors and general homicide rates,^{516} the significance of homicide rates in Analysis 7 may explain the failure of these racial factors to register at that level. If, as we have suggested, white, relative to black, homicide rates and the black proportion of the population are measures of the perceived threat of serious crime to people with influence over deathsentencing practices, it is not surprising that a grosser measure of those fears—homicide rates generally— registers at the county level, where the small numbers of death verdicts and reversals being compared may make it harder to pick up more subtle effects. As later county analyses become more complete and sophisticated (see below), the explanatory power of the two racial factors (operating at the state level) becomes pronounced, while the explanatory power of simple homicide rates decreases.^{517} Overall, the important countylevel factors Analysis 7 provisionally identifies are similar to factors the statelevel analyses identify. But given that Analysis 7 entirely omits consideration of states and state factors, one would expect countylevel analogues of factors important at the state level to register some of the effect of those conditions. The result thus calls for simultaneous consideration of county and statelevel explanations in order to identify the level (state or county) or levels at which the important conditions operate or can best be measured. An equally important result of Analysis 7 is the absence of significant factors identified at the county level that have no analogue among the factors found important at the state level. This result is particularly revealing, given that Analysis 7 was designed to maximize the effect of countylevel factors.^{518} The result tends to validate the statelevel analyses as reliable and fairly complete indicators of important explanations for capital reversal rates. One method of gauging the effect of both state and county factors is to include both in the same analysis, treating factors operating at one level of the hierarchy of jurisdictions (here, the lower level: counties) as random effects and factors operating at the higher level (here, states) as fixed effects. Analyses 8, 9 and 10 use this approach. Analysis 8 is a binomial regression analysis of county reversal rates calculated as proportions of imposed death verdicts that were reversed at any of the three review stages. Each of the 967 counties with at least one death verdict in a known year is treated as a subject variable and is nested in the state among the 34 studied in which the county is located. Nesting programs the analysis to assume that counties in the same state are more like each other than counties in other states. Reversal rates are calculated for death verdicts imposed in each of the 967 counties in each of the 23 years in which that county imposed at least one death verdict, producing 3054 observations. As in Analysis 7, variance is enhanced, as is the capacity of countylevel variables to explain reversal rates, by omitting county and year as random effects. The baseline analysis measures only the effect of time trend, treated as a fixed effect. Analysis 9 conducts the same analysis as Analysis 8, but using Poisson regression analysis. Analysis 10 conducts the same analysis as Analysis 8 (both are binomial analyses), but analyzes reversals as a proportion of death verdicts reviewed at the direct appeal stage. Because Analyses 8 and 9 calculate reversal rates as proportions of imposed verdicts, reversal rates are depressed over time as a result of declining rates of review for verdicts imposed too late in the study period to have been finally reviewed at some or all three review stages as of the study end date. By contrast, Analysis 10 calculates reversal rates as proportions of verdicts reviewed at the single, direct appeal stage, assuring that changes in reversal rates over time are not affected by changing rates of review and, instead, are sensitive only to changing amounts of reversible error found on state direct appeal of verdicts imposed in later, as opposed to earlier, years.^{519} Analysis 10 compares county reversal rates for death verdicts in each of 851 counties in each of the 23 years in which at least one fully reviewed death verdict was imposed, producing 2472 observations. Analyses 8, 9 and 10 have similar results. In all three, a highly significant amount of unexplained variance remained after the baseline analysis of time trend. In each case, the best analyses revealed nearly identical sets of significant state and countylevel explanations for county differences in capital reversal rates. Those explanations all matched ones identified in stateonly Analyses 16, 14 and 15 and countyonly Analysis 7. And the three best analyses left no unexplained variance among county reversal rates beyond the differences expected as a result of random variation. Cautioning against too much reliance on these analyses, however, the reversal rates that they predict do not fit the actual data as well as those predicted by their baseline analyses.^{520}
In all three analyses, seven statelevel factors were significantly related to county reversal rates. In each case, and as a group, these statelevel factors associated with county differences in capital error rates parallel the finding of Analyses 15, 14 and 15 that the same factors explain state differences in those rates. After controlling for the other factors in Analyses 810:
The best Analysis 8 group of factors was different from the best Analysis 9 and 10 group in two other respects: In Analysis 8, but not the others, counties in states with higher per capita caseloads for all types of court cases, and lower homicide rates, had higher capital reversal rates. Effect size is small for both factors. See Figures 43N and 43(O), p. 263 below.^{527}
In Analyses 8, 9 and 10, we included a linear trend for time but excluded the random effects for individual years. For reasons noted above, Analyses 8 and 9 of all three review stages combined had to calculate reversal rates as proportions of imposed, not reviewed, death verdicts and thus cannot reliably assess whether verdicts imposed later in the study period are more or less prone to reversible error than earlier verdicts. Given the time final review takes, later verdicts (no matter how errorprone) are less likely than earlier ones to have been finally reviewed, and thus to have been reversed (or affirmed), by the study end date. In other words, in studies of reversal rates as proportions of imposed verdicts, time trend controls for the effect of unfinished appeals, rather than gauging changes in error rates over time.^{528} In contrast, directappealonly Analysis 10 calculates reversal rates as a proportion of only reviewed verdicts. This avoids the confounding effect of delay and enables the analysis to measure the effect of the passage of time on the probability, not of review, but of reversal due to serious error. Under these circumstances, Analyses 810 provide substantial evidence that, after controlling for other factors, countylevel rates of reversible error have increased over time:
Figures 43 PQ: Effect Size; Year of Death Verdict (Influence of Unfinished Verdicts) CountyState
The results reported above reveal that, neither (1) the switch from explaining state differences in reversal rates to explaining county differences, nor (2) the inclusion of countylevel explanatory factors undermines the importance of the interlocking set of statelevel explanations for high capital reversal rates identified by stateonly Analyses 16, 14 and 15Ci.e., aggressive use of the death penalty in conjunction with and possibly in response to specific political, racial and crimerelated conditions creating pressure to use the death penalty more frequently. To this extent, the three countystate analyses tend to confirm the results and reliability of the stateonly analyses. Another question is whether including statelevel explanatory factors affects the results of Analysis 7, which identified a number of countylevel factors that were significantly associated with county reversal rates, when no state factors were considered. The answer is that countystate Analyses 810 clarify the role of one of the four countylevel factors identified by Analysis 7 (time),^{530} support two other factors (county deathsentencing rates and population structure) and reveal that statelevel factors better capture the effect that a fourth factor appeared to have when only county factors are tested (county homicide rates):
Although not decisive by themselves, Analyses 810 indicate that neither a focus on county as opposed to state capital reversal rates, nor the inclusion of county as well as state explanatory factors, changes the results or challenges the reliability of main Analysis 1 and supporting Analyses 24. The same set of forces appears to be at work: Fears about crime among citizens with influence over public officials impel officials to use the death penalty in weak cases where the temptation to cut corners and the risk of mistake is great. For the most part, conditions measured at the state level capture these effects, although two parallel countylevel factors also have explanatory power—high deathsentencing rates and population density. These results do not necessarily mean that only or mainly statelevel conditions are related to capital error rates. It also could mean that the relevant conditions—despite operating at multiple levels—are more effectively detected by the often superior data available at the state level.^{535} Five other analyses—1113, 16 and 17—also assess the power of the statelevel explanations identified by main Analysis 1 and supporting statelevel Analyses 26 to explain differences in county reversal rates and compare state and countylevel explanations for reversal rates.
Analyses 11 and 12 use a "predicted value" technique to compare state and county effects. Each analysis uses a set of explanatory factors identified by Analyses 1 and 2 to generate predicted values— i.e., capital error rates the state analyses predict—for each county in the 34 capital states. The predicted values then are treated as a countylevel explanatory factor in an analysis designed to determine (1) if the amounts of capital error the state analyses predict for each county are, indeed, significantly related to actual county reversal rates, and (2) whether, after accounting for the values predicted by the state analyses, other local factors are significantly related to county reversal rates. Analysis 11, a binomial regression analysis, uses the set of significant factors identified by Analysis 1B (also a binomial analysis) to generate predicted county reversal rates. Analysis 12, a Poisson regression analysis, uses the set of factors identified by Analysis 2A (a Poisson analysis) for the same purpose. Both analyses test the power of county reversal rates predicted by 519 observed state reversal rates (34 states x each of the 23 study years in which the state imposed at least one death verdict) and various other county factors to explain 3054 observed county reversal rates (967 deathsentencing counties x each of the 23 years in which the county imposed at least one death verdict). In both analyses, reversal rates are the proportion of all death verdicts imposed in the relevant county that were reversed at one of the three review stages. In two ways, Analyses 11 and 12 make it more difficult than Analyses 710 for specific local factors—including the county reversal rates the state analyses predict—to achieve significance. First, Analyses 11 and 12 use a baseline analysis to test the power of county reversal rates predicted by three general factors— state, year and time trend—to explain actual county reversal rates. Second, they treat each of the 967 capital counties as a random effect. These methods keep specific county factors, including the county reversal rates predicted by specific statelevel factors, from achieving significance unless they surpass four general factors as explanations for county reversal rates: state, county, year and time trend. And they keep county factors other than the predicted reversal rates from achieving significance unless they surpass the predicted rates as explanations for actual county reversal rates. The Analysis 11 and 12 baseline inquiries show that at the state level, consideration of the effect of state, year and time trend leaves ample variance in state reversal rates to be explained by specific statelevel factors,^{536} but the same is not as true at the county level. Thus, the county reversal rates predicted by a baseline analysis of only the state, the year, and the relevant points in the 19731995 time trend when the county imposed its capital verdicts do such a good job of explaining nonrandom variance among county reversal rates that there is little or no variance left to be explained by specific countylevel factors.^{537} This suggests that, although capital reversal rates vary greatly from state to state, variance among county reversal rates is harder to detect or to model. This could mean either that reversal rates do not differ much from county to county within states,^{538} or that the number of homicides and resulting death verdicts in many counties and years is too small to reliably reveal variance that exists.^{539} In Analyses 11 and 12, the state reversal rates predicted by specific statelevel explanatory factors fit the actual state reversal rates significantly better than the baseline analyses of only state, year and time trend, and greatly diminish the unexplained variance remaining after the baseline analyses. The same is not true for the county level, however. There, the baseline analyses fit the actual data slightly better than analyses of specific countylevel factors. The analyses of specific factors do, however, modestly decrease the small amount of unexplained variance left by the baseline analysis.^{540} This provides more evidence that factors associated with the state in which a county sits, or that influence along with the years in which the county imposed its death verdicts, are about as good at predicting county capital reversal rates as any other factors that can be identified—at least given how difficult it is to compare the minute bits of information contained in each countyandyear's worth of reversal rates.^{541} This reveals the value of our statelevel analyses: Assuming policy responses to chronically high capital error rates cannot wait for decades until a larger body of countylevel outcomes builds up—especially given that additional data might simply confirm that counties within the same state do not vary enough to make further inquiry possible^{542}—the best way to understand county differences in capital reversal rates is to understand state differences. Because Analyses 11 and 12's study of specific county level factors decrease unexplained variance somewhat, they provide clues about the relationship between specific countylevel factors and county reversal rates. Those clues lead to the same conclusion, however: Conditions operating or best measured at the state level provide the best explanations for countylevel capital reversal rates:
Analysis 13 confirms the power of statelevel factors and the weakness of most measurable countylevel factors as explanations for county reversal rates. This is a Poisson regression analysis of 3054 observed county reversal rates for each of 967 capital counties in the 34 study states in each of the 23 study years in which the county is known to have imposed a death verdict. Unlike Analyses 810, this analysis does not include any random effects,544 but like those three analyses, it treats each county with at least one death verdict in a known year as a subject variable and nests the county in the state where it is located—programming the analysis to assume that counties in the same state are more like each other than counties in other states. By removing general factors such as county and year, and omitting continuous countylevel factors as random effects, this technique considers whether any aspect of our statistical methodology is keeping countylevel factors from outcompeting statelevel factors as explanations of county reversal rates. Reversal rates are calculated as proportions of imposed capital verdicts that were reversed at one of the three review stages during the 23year study period. Its baseline analysis includes only time trend as a fixed effect. The reversal rates predicted by two "best" analyses of specific factors do not fit actual reversal rates as well as the baseline analysis, but leave substantially less unexplained variance.^{545} Analyses 13A and 13B provide additional support for three overlapping propositions:
There are nine results common to Analyses 13A and 13B. The first shows the nonsignificance of time trend. The rest identify significant factors that track results of main Analysis 1. Taking account of all other factors:
Other Analysis 13 findings of interest are:
One hypothesis about the weakness of countylevel explanations for reversal rates is that dividing counties into each of 23 years of reversal experience leaves too few death verdicts in most counties and years to study reliably.^{561} Analysis 16 (a binomial analysis) and Analysis 17 (a Possion analysis) test this hypothesis by treating each county, not as up to 23 separate observations—one for each study year in which the county imposed at least one death verdict—but instead as a single observation made up of the county's aggregate reversal rate during the entire 23year period. Aggregating many years of experience into a single reversal rate increases the number of death verdicts and reversals in each observation, and thus the observation's reliability as a reflection of the county's relative proclivities during the period. Whereas countyyears with only one or two death verdicts account for 88% of the reversal rates analyzed by Analyses 713, they account for only 59% of the 23year reversal rates analyzed by Analyses 16 and 17. In addition, Analyses 16 and 17Clike Analyses 14 and 15, in this respect—directly compare each of the 34 states' overall experiences with capital reversals during the 23year study period. Analyses 16 and 17 do this by treating state as a subject variable, which programs the regression analysis to assume that the capital reversal experience of counties within states is likely to be more similar than the experience of counties from different states. These analyses thus treat each state as a composite of the 23year capital experiences of all of the state's capitalsentencing counties. Aggregating each county's various years of capital experience into a single reversal rate, and treating each state's 23year experience as the composite of its capital counties' aggregate reversal rates, removes time as a consideration. This, in turn, enables us to include in the analysis 35 counties in which death verdicts were imposed during the study period but in unknown years—increasing from 967 to 1002 the number of counties whose reversal rates are being compared. As does Analysis 13, Analyses 16 and 17 treat state and county explanatory factors as fixed effects, testing their comparative strength by forcing state and county factors to compete directly with each other. In Analyses 16 and 17, highly significant amounts of variance remain to be explained after conducting the baseline inquiries. The best set of specific factors—Analyses 16A and 17AC substantially reduce the unexplained variance left by the baseline analyses, although the improvement in fit is not quite significant.^{562} Controlling for other factors:
All of the significant factors listed above are statelevel factors. Although comparable countylevel factors were tested, none was significantly related to counties' 23year aggregate reversal rates or to state composites of those rates. Thus, in an analysis designed to test the hypotheses that larger aggregates of county data would enhance the explanatory power of countylevel explanations for capital reversal rates, the opposite occurred: The modest countylevel effects identified in the other countystate analyses disappeared. This indicates that the weak power of countylevel explanations for capital reversal rates is not a function of too little information about particular counties in particular years, and instead is a function of the strong explanatory power of the statelevel predictors of reversal rates identified by our main Analysis 1, and supporting Analyses 26, 14 and 15. 4. Summary: additional support for results of state analyses. The main message of countystate Analyses 1113, 16 and 17 is the same as that of countystate Analyses 810. The explanations for differences in rates of serious capital error among states identified by Analysis 1 and the other state analyses also are the best explanations for differences in rates of reversible capital error among counties. The only countylevel conditions that sometimes appear significant in the countystate analyses are county analogues of two significant state factors: deathsentencing rates, and population size and density. Overall, therefore, understanding the factors related to state capital error rates goes a long way towards predicting county reversal rates in capital cases. To seek additional clues about the relative roles of state and county factors in explaining capital reversal rates, we next study differences in capital error rates among counties in each of the three states with the largest pools of capital verdicts and capitalsentencing counties.
