Who Would Have Won Florida If the Recount Had Finished? 1

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1 Who Would Have Won Florida If the Recount Had Finished? 1 Christopher D. Carroll ccarroll@jhu.edu H. Peyton Young pyoung@jhu.edu Department of Economics Johns Hopkins University v. 4.0, December 22, Summary This study uses precinct-level data to estimate howvote totals might have changed in five Florida counties that contain most of Florida s uncounted undervoted ballots if the U.S. Supreme Court had allowed the hand count of undervotes ordered by the Florida Supreme court to conclude. 2 We find that simple statistical models similar to the ones we used in previous studies suggest that if a moderate or broad standard were applied to determine which ballots were readable, Al Gore might well have gained enough votes to surpass George W. Bush. But those simple statistical models also overpredict the number of votes Gore should have gained in the places where hand counts were actually completed. Unfortunately, it has proven difficult to construct a more sophisticated statistical model that is consistent with the actual outcomes in all three of the counties where some hand counting was done. Our clearest conclusion is that the only way to know what would have happened had a full hand count occurred is to examine all of the disputed ballots by hand. 1 This paper reflects several important insights gleaned from the discussions on the statselection ing list, particularly (but not exclusively) contributions by Henry Brady, Jonah Gelbach, Bruce Hansen, Robert Jackson, Walter Mebane, Dave Rusin, and Jasjeet Sekhon. I am grateful to Doug McManus and Joel Havemann of the LA Times for some of the data. 2 The counties for which we have the necessary data to conduct our analysis are Hillsborough, Marion, Duvall, Sarasota, and the portion of Dade county that remained uncounted by the county canvassing board when it called a halt to the hand recount. When we refer to five counties henceforth we mean the four full counties and the remaining part of Dade. 1

2 2 Some Simple Calculations The simplest statistical model one might imagine applying to our precinct-level data assumes that every voter who cast a ballot actually intended vote for President. If this were the case, it seems plausible to suppose that the intended votes on the undervoted ballots in a given precinct would have split in the same proportions as the tallied votes in that precinct. That is, if a precinct had ten undervotes, and among the successfully machine-tallied votes in that precinct Gore got 60 percent, then the assumption would be that the undervotes reflected six intended votes for Gore and four for Bush. Applying this procedure to the five counties for which we have data implies that all of the undervoted ballots toegther in those counties represent about 660 more intended votes for Gore than for Bush - even though Bush won the popular vote in these counties by 53 percent to 47 percent. 3 The reason Gore has more undervotes despite Bush s lead is that within counties (even Republican ones) the undervotes are concentrated in strongly pro-gore precincts. 4 This conclusion about the undervotes does not imply that a hand count in these counties could have netted Gore 660 votes, because even the most talented human ballot readers would not be able to determine the voter s intent for most of the undervoted ballots. In order for the hand counts to recover a vote, the intention of the voter must have been expressed sufficiently clearly (by a partially detached chad, an indentation, or another indication) for the people examining the ballots to be able to determine the clear intent of the voter. In practice, among the three counties that conducted substantial hand counts, the recovery rate of votes from undervoted ballots varied from about 9 percent in Palm Beach to 21 percent in Dade to about 30 percent in 3 These statistics reflect the total machine-tallied votes in the four counties mentioned above plus the remaining uncounted portion of Dade county. We omit undervoted absentee ballots from our analysis, because news reports indicate that procedures for processing undervoted absentee ballots vary widely across counties so that we have little basis to construct a model for the results of counting these ballots. Furthermore, the number of undervoted absentee ballots is fairly small compared to the regular undervotes, and in the one county (Palm Beach) for which we have the data necessary to calculate it, the recovery rate among undervoted absentee ballots was extremely low. (In Palm Beach, Gore gained a net of 6 votes from the hand count of the 1200 undervoted absentee ballots). 4 Our assumption that every voter intended to cast a vote for President is clearly counterfactual: As the Bush campaign has pointed out, some proportion of voters intentionally choose not to vote for President. However, in counties that used the optical voting system, which is generally agreed to be much more reliable than the punch-card system, only about 0.3 percent of ballots failed to register a vote for President. In contrast, the machine tallies found an undervoting rate of 1.5 and 2 percent of the ballots in the punch-card counties. It therefore seems reasonable to suppose that only 0.3 percent of the ballots in punch-card counties were cast by voters who truly desired not to vote for President. Note that since Bush dominated the small-undervote precincts, an attempt to correct for a presumed 0.3 percent of ballots in every precinct that were true undervotes would actually boost the statistical model s prediction for Gore s gains. In fact, making this assumption boosts Gore s net lead among undervotes to about 850. (Thanks to Henry Brady and Bruce Hansen for their discussions of this point.) 2

3 Broward County. 5 Table 1: Predicted Gore Gains (or Losses) in 5 Counties Standard Net Range Applied Gore Gain Min Max Broward (30.3 Percent) Dade (20.5 Percent) Palm (8.9 Percent) At a recovery rate of 30 percent, our model implies that a hand count of all of the counties for which we have data should have netted Gore about 210 votes, which compares with a Bush lead of 193 votes in the final tally consistent with the last Florida Supreme Court ruling. 6 However, the statistical assumptions underlying our model imply a substantial degree of uncertainty about the exact figure that would have resulted: The range of uncertainty associated with our estimate of the Gore gain is between a loss of about 60 votes to a gain of about 500 votes. Note also that the counties included in this study account for only about 75 percent of the total ballots cast in Florida using the punch-card system. Either candidate might gain or lose a few more votes in the remaining counties. 7 All of the foregoing calculations were based on an assumption that the broad standard used in Broward county s hand count was applied to the other counties in our 5 We do not have precinct-level data for Broward county; the 30 percent figure is based on an assumption that the ratios of the recovery rates among absentee and nonabsentee ballots are the same in Palm Beach and Broward counties. 6 After the second Florida Supreme Court ruling, CNN reported a Bush lead of 154 votes. However, this tally was based on an assumption that Gore gained 215 votes in the hand count in Palm Beach county. According to the Palm Beach county website, the final audited tally shows a Gore gain of only 176 votes, leading to a Bush gain of 193 = 154+( ). 7 We have no hard data to indicate how many votes might be gained from the counties that used an optical system, but our data indicate only about 6500 undervotes in counties with optical systems who have reported their number of undervotes. Because optical systems are much more reliable than punch-card systems, we expect that the vast majority of these are true undervotes; that is, ballots where no marking at all was made to indicate a Presidential choice, and for which a hand count is therefore unlikely to change the outcome. However, a recent article in the Orlando Sentinel ( story.story?coll=orl%2dhome%2dheadlines) casts some doubt on this assumption; the Sentinel examined some undervotes and all overvotes in the heavily Republican Lake county, and among the 50 undervotes examined they were able to determine an intended vote on 12 ballots, for a recovery rate of 24 percent. The Sentinel was also able to determine intended votes on a large number of overvoted ballots, yielding a net gain to Gore of 130 votes. However, while very interesting, this finding has no bearing on the question addressed in this study, which is the likely effects of a hand count of undervotes. Undervotes have a special significance because Florida Supreme Court s last ruling directed that only the undervotes should be examined statewide (see pp. 2, 16, and 20 of the December 8 Florida Supreme Court ruling). 3

4 Table 2: Predicted Gore Gains Where Hand Counts Were Done Net Range Actual Standard Gore Gain Min Max Gain Model Predictions Broward Dade Palm sample. It is also possible that the somewhat stricter standard apparently used by the Dade county canvassing board might apply. In this case, as Table 1 shows, Gore would have been expected to gain about 140 votes, with a plausible range from a loss of 60 votes to a gain of about 340. Finally, if Palm Beach County s stringent standard were applied, Gore would be expected to gain only about 60 votes, with a plausible range from a loss of about 40 to a gain of about 170. Unfortunately, the statistical model applied here is subject to reasonable doubt, because it does not perform as well as might be hoped in explaining the actual votes identified in those counties where hand counts have actually been performed. As Table 2 shows, the model indicates that Gore should have gained between about 700 and about 900 votes from the hand count in Broward county, while he actually gained only 577. It implies that he should have gained about 320 in Palm Beach, and about 245 in the portion of Dade where counting was completed, compared to actual gains of 182 and Using the precinct-level data in Dade county, we find that there are two reasons that the Gore gains are smaller than our model predicts. The first is that Gore typically received somewhat fewer votes from the hand-counted ballots within a precinct than he had received of the machine-tallied ballots. The second problem is that the recovery rate in precincts with high numbers of undervotes was somewhat lower than the recovery rate in precincts with normal numbers of undervotes. Since the heavily undervoted precincts were heavily pro-gore, reducing the rate at which undervotes are turned into real votes in high-undervote precincts reduces Gore s gains. In principle, we could assume that Dade county s patterns of deviation between our model s predicted hand-count results and the actual hand-count results would be reproduced in the other counties. Such an assumption would allow us to calculate predicted Gore gains (or losses) in the remaining counties. However, we are reluctant to do this because in the one other county for which we have data, Palm Beach, 8 The spreadsheet we have for Palm Beach, which consists of precinct-level data downloaded from the Palm Beach county website, shows a Gore gain of 182 votes in the non-absentee precincts of Palm Beach and 6 in the absentee precincts, for a total gain of 188. This is in conflict with the Palm Beach county website which reports a net Gore gain of 176 from the hand count. We cannot account for the discrepancy. 4

5 the patterns of deviation from our model are rather different than for Dade county (especially the relationship between recovery rates and undervotes). This means that we cannot have much confidence that the patterns for either of these counties will be similar in the remaining Florida counties, so we would have little confidence in the results we would obtain from such a procedure. 3 Conclusion Our simple statistical model of precinct-level voting patterns in Florida suggests that there is a good chance that Gore would have gained enough votes to win Florida if a full hand count had been conducted under a broad standard in Florida. However, the model overpredicts the number of votes Gore should have gained from hand counts where such counts have already been conducted. As a result, our conclusion is that the only way it will be possible to get a reasonably certain idea of who would have won if a full hand count had been conducted in Florida is for someone to actually examine the ballots. Fortunately, several press organizations and private groups have already announced plans to do precisely that. One important piece of advice for those organizations is that it will be important to keep track of different categories of ballots (three corners detached, two corners, heavy indentation, etc.), so that at the end of the process it will be possible to calculate who would have won under various assumptions about the standard used for evaluating which ballots contain a vote. It is our suspicion that a conclusion about who would have won Florida may well depend on the assumption made about the standard that would have been applied (or the distribution of standards across counties, if it is assumed that different counties would have had different standards). 5

6 For precinct i define Appendix u i = number of undervotes g i = number of machine tallied Gore votes b i = number of machine tallied Bush votes g + i = number of votes gained by Gore in the hand count b + i = number of votes gained by Gore in the hand count γ i = g i /(g i + b i ) = Gore proportion of two-party vote in the precinct γ + i = g + i /(g+ i + b + i ) = Gore proportion of the newly readable votes f i = fraction of undercounted votes in precinct i that are hand-readable. and define a capital letter as the countywide sum of the corresponding small-letter variable, e.g. the countywide number of undervotes is U = i u i. The number of readable ballots in precinct i will be f i u i. 9 We describe first our procedure in Dade, then howwe adapt this procedure for the other counties. In an earlier analysis, we assumed that each precinct would experience the same yield rate, f i = f for all i. However, a Chi-Squared test performed on the data generated by the Dade county s Canvassing Board s partial count was able to reject the hypothesis of identical yield rates with a high degree of statistical confidence. This implies that our initial standard errors were too tight. To address this problem, we use the actual distribution of yield rates across the successfully hand-counted precincts in Dade as a sample from which we draw random yield rates to apply to the remaining precincts in the county A simple statistical analysis of the actual yield rate among actually-counted precincts did not find any predictable differences in yield rates across precinct by demographic characteristics, political makeup, or size. 10 This procedure is slightly problematic because the lumpiness of votes restricts the possible recovery rates in precincts with very small numbers of undervotes. For example, in a precinct with only one undervote, the recovery rate in principle will be either 0 or 100 percent. With an average recovery rate of 20 percent across many one-undedrvote precincts, we would expect a recovery rate of 100 percent for roughly one out of five of the one-undervote precincts, and of zero percent for the other four. When the yield rate of 100 percent is sampled in our Monte Carlo procedure and potentially applied to a precinct with a large number of undervotes, it will generate a large number of recovered votes (though if the same recovery rate applies to the large-undervote precinct the mean recovery rate will remain unaffected. Thus, this problem tends to boost the standard error of our Monte Carlo estimates. However, since there are many sources of uncertainty which our model does not capture, we are not too uncomfortable with such an upward bias. 6

7 For precinct i, we draw a recovery rate f i from the empirical distribution of recovery rates across the hand-counted precincts of the county. 11 Once f i has been drawn the number of votes Gore could be expected to gain is E[g + i ] = ˆγ+ i f i u i If we assume that the actual number of votes Gore receives is a binomial with mean f i γ i u i and variance f i u i γ i (1 γ i ), we can approximate the distribution of g + i with a normal distribution with mean f i u i γ i and variance f i u i γ i (1 γ i ). Thus, after drawing a f i for each precinct, we then draw a random actual number of votes for Gore and allocate the remainder of the newly-readable votes to Bush, i.e. g + i = γ i fui + ɛ i where ɛ i N(0,γ i (1 γ i ) f i u i ) is generated using a normal random number generator. The county-wide gain for Gore is thus G + = i g + i We conduct this simulation exercise forty thousand times, and the confidence intervals reported in the text are drawn from the resulting simulated distribution of the G + variable. Adapting this procedure to the non-dade precincts is simple. Suppose there are N precincts for which we have data on the two-party candidate shares and number of undervotes, and we wish to assume an average recovery rate of r new will apply among these precincts. Defining r dade as the recovery rate in Dade county, our procedure is as follows. For each Monte Carlo simulation, we expand the pool of values of f by drawing a random sample of size N from the Dade county f s. Indexing the precincts in our target dataset by j, we then create an adjusted precinct-level recovery rate by multiplying the randomly drawn f j s by r new /r dade. We then proceed as outlined above to calculate the predicted Gore gains (or losses) for this Monte Carlo draw. We repeat this procedure forty thousand times to generate our distribution of draws. 11 One puzzle is that there are a few precincts for which the recovery rate, or the number of Bush or Gore votes gained, is negative. This is possible because the hand counts were conducted for all of the ballots in a precinct, not just of the machine-produced undervotes. It is not clear what the most plausible explanation is for a reduction in the number of votes in a precinct in the hand count compared to the machine count. One possibility is that there were some ballots with a fully detached chad for one Presidential ticket and a partially detached chad for another ticket. A machine count could register such a vote as a valid vote, while a hand count might identify it as an overvote. At any rate, the presence of these negative yield rate precincts is one reason we view our procedure of applying the actual empirical distribution of f i s as superior to our previous assumption of a constant (positive) value of f that applied to all precincts: Our Monte Carlo procedure produces (on average) as many negative yield precincts among the uncounted precincts as cropped up among the counted ones. 7