Tipsters: If you have not seen this yet, here is a snapshot of the Palm Beach "outlier" http://madison.hss.cmu.edu/ -- --------------------------------------------------------------- John W. Kulig [EMAIL PROTECTED] Department of Psychology http://oz.plymouth.edu/~kulig Plymouth State College tel: (603) 535-2468 Plymouth NH USA 03264 fax: (603) 535-2412 --------------------------------------------------------------- "What a man often sees he does not wonder at, although he knows not why it happens; if something occurs which he has not seen before, he thinks it is a marvel" - Cicero.Title: A Note on the Voting Irregularities in Palm Beach, Florida
A note on the voting irregularities in Palm Beach, Florida.
Related research
Prof. Craig Fox, Fuqua School of Business, Duke University, has a research note on the issue: http://faculty.fuqua.duke.edu/~cfox/Bio/election2000note.pdf
Prof. Burt Monroe, Dept. of Political Science, Indiana Univ, also has a research note on the issue: http://www.indiana.edu/~playpol/pbmodel.pdf
Chris Volinsky has a map of the Buchanan vote, by county. http://www.research.att.com/~volinsky/florida.html
Background
According to several news accounts, many voters in Palm Beach, Florida, have claimed that they were confused by the ballot structure and may have inadvertently voted for Buchanan when in fact they intended to vote for Gore. The event prompted a discussion among several academic friends and colleagues about whether the results could be statistically detected, since Palm Beach county alone had the unusual ballot structure. One of the participants in the discussion, Chris Fastnow, a political scientist and director of the Center for Women in Politics in Pennsylvania at Chatham College (and who is also my wife) found the Florida county-level returns for the election on the internet at the CBS News website and passed them on to me. We reasoned that if enough voters in Palm Beach county were confused and mistakenly voted for Buchanan, it should be statistically detectable by examining the vote for Buchanan relative to the votes for Gore and Bush for all of the counties in Florida.As a first cut, I did three simple plots: one of Buchanan's votes vs. Bush's votes, one of Buchanan's votes vs. Gore's votes, and one of Buchanan's votes vs. the total votes cast in a county (see graphs below). For all of the plots, all of the counties except one (Palm Beach) follow a pretty regular pattern. The more votes Bush got in a county, the more votes Buchanan got, and the number of votes that Buchanan got increases with Bush's vote by a fairly predictable amount -- except for Palm Beach, which has many, many more votes for Buchanan than would be reasonably expected, given all of the other Florida counties. Similar results hold for the plots for Buchanan's votes versus Gore's votes or versus the total votes cast. Again, Palm Beach sticks out as an outlier from all of the other Florida counties.
The results seem to suggest that indeed something unique happened in Palm Beach county. Just by visual inspection of the charts below, it appears that instead of the 3407 votes Buchanan received in Palm Beach county, he probably would have received under 1000 votes, if the other counties in Florida are any guide.
Within seconds of my seeing the results, a colleague of mine wandered into my office, saw the results himself, and urged me to make the results "public" as soon as possible. I hastily drafted an email to my dept., pointing them to a graph of the data, which I had put up on my internet server. The email spread across the university and onward, which prompted a string of phone calls, emails, and so forth. (The email also contained a typo -- at one point I referred to Bush when I meant Gore -- which caused some confusion and resulted in even more emails).
To direct traffic and answer questions, I've now set up this page on
my server.
Statistical Estimates
In order to get an estimate of the number of votes that Buchanan would have garnered in Palm Beach county, I ran three simple and straight-forward linear regressions: one predicting Buchanan's vote share based on Bush's votes in the other Florida counties, one predicting Buchanan's votes based on Gore's votes, and another using the total votes cast. The results are posted below, including estimates for Palm Beach county's Buchanan vote if the county were like the rest of Florida's counties. If you don't know what regression is, in this case I basically fit the "best" line to the scatterplots below (excluding Palm Beach county). Most of the vote shares for Buchanan fall pretty close to this line. If Palm Beach county were like the other counties, according to estimates (using Bush's votes) Buchanan would have gotten around 600 votes in that county instead of the 3407 votes he actually got. If we used Gore's votes to predict Buchanan's vote, we would have predicted Buchanan to get somewhere around 792 votes. The exact results, with confidence intervals (kind of like with polls, when they say +/- 3%) are listed below.If one accepts the statistical assumptions of the models, and if Buchanan's unusual performance can be attributed to voters who intended to vote for Gore (an assumption that some have contested), then it can be claimed with a high degree of statistical confidence that the mistakes cost Gore somewhere between 2000 and 3000 votes. If Bush wins Florida by an amount smaller than this, such as 1700 votes, a strong claim can be made that the confusion over the unique ballot structure in Palm Beach cost Gore the presidency.
Note: One does not does not have to accept my statistical analyses.
The data
are freely available to anyone, and certainly different models and
assumptions can be applied, although it is hard to come up with any model
that suggests Buchanan's vote would be greater than 1400 in Palm Beach
county, even with generous assumptions. That said, the results here support the contention that the ballot structure in Palm Beach cost Gore between 2000 and 3000 votes, but they do not prove it. Such a proof is impossible, because it requires eliminating all possible rival explanations, no matter how plausible or implausible they may be. We cannot rule out alternative factors, from any personal ties Buchanan has in Palm Beach, to equally confused Bush voters, to alien conspiracies. We can, however, comment on the statistical likelihood of such events, given various assumptions and our empirical observations.
Previous Elections (NEW)
Since posting my original results, I've received several hundred emails requesting the 1996 election results. I have now acquired the county-by-county data for the 2000 primaries, the 1996 general elections, and the 1996 primaries. These updated data are now included in the spreadsheet file, so that anyone can analyze them. Palm Beach is not an outlier in any other election. As the bottom figure on this page shows, Buchanan's vote in the 1996 primaries can be easily predicted using Dole's vote in the primaries. I will soon post the statistical analyses suggesting as much as well (I have a class to teach, but will then take care of it as soon as possible).Visual Displays of Florida Data
Statistical Analyses of Votes for President in Florida, by County
Regression Analysis: BUCHANAN votes versus BUSH votes
The regression equation isBUCHANAN = 65.6 + 0.00348 BUSH
Predictor Coef
SE Coef T
P
Constant 65.57
17.33 3.78 0.000
BUSH 0.0034819
0.0002501 13.92 0.000
S = 112.5 R-Sq = 75.2% R-Sq(adj) = 74.8%
Analysis of Variance
Source
DF SS
MS F
P
Regression 1
2451209 2451209 193.84
0.000
Residual Error 64
809323 12646
Total
65 3260532
Predicted Values for New Observations
New Obs Fit SE Fit
95.0% CI
95.0% PI
1 597.8
31.1 ( 535.7, 659.8) (
364.7, 830.8)
New Obs Fit SE Fit
99.0% CI
99.0 % PI
1 597.8
31.1 ( 515.3, 680.2) (
288.0, 907.5)
New Obs Fit SE Fit
99.9% CI
99.9% PI
1 597.8
31.1 ( 490.7, 704.9) (
195.4, 1000.2)
Values of Predictors for New Observations
New Obs BUSH
1 152846
Regression Analysis: BUCHANAN votes versus GORE votes
The regression equation isBUCHANAN = 109 + 0.00254 GORE
Predictor Coef
SE Coef T
P
Constant 109.35
19.52 5.60 0.000
GORE 0.0025401
0.0002438 10.42 0.000
S = 137.5 R-Sq = 62.9% R-Sq(adj) = 62.3%
Analysis of Variance
Source
DF SS
MS F
P
Regression 1
2051260 2051260 108.56
0.000
Residual Error 64 1209273
18895
Total
65 3260532
Predicted Values for New Observations
New Obs Fit SE Fit
95.0% CI
95.0% PI
1 792.5
58.3 ( 675.9, 909.0) (
494.2, 1090.8)
New Obs Fit SE Fit
99.0% CI
99.0% PI
1 792.5
58.3 ( 637.6, 947.4) (
396.0, 1188.9)
New Obs Fit SE Fit
99.9% CI
99.9% PI
1 792.5
58.3 ( 591.3, 993.7) (
277.4, 1307.5)
Values of Predictors for New Observations
New Obs GORE
1 268945
Regression Analysis: BUCHANAN votes versus TOTAL votes
The regression equation isBUCHANAN = 84.1 + 0.00151 TOTAL
Predictor Coef
SE Coef T
P
Constant 84.09
17.76 4.73 0.000
TOTAL 0.0015120
0.00011838 12.78 0.000
S = 119.7 R-Sq = 71.9% R-Sq(adj) = 71.4
Analysis of Variance
Source
DF SS
MS F
P
Regression 1
2342846 2342846 163.39
0.000
Residual Error 64 917686
14339
Total
65 3260532
Predicted Values for New Observations
New Obs Fit SE Fit
95.0% CI
95.0% PI
1 737.7
43.8 ( 650.2, 825.2) (
483.0, 992.4)
New Obs Fit SE Fit
99.0% CI
99.0% PI
1 737.7
43.8 ( 621.5, 853.9) (
399.2, 1076.2)
New Obs Fit SE Fit
99.9% CI
99.9% PI
1 737.7
43.8 ( 586.7, 888.7) (
298.0, 1177.5)
Values of Predictors for New Observations
New Obs TOTAL
1 432286
Contact:
Greg D. Adams, Asst. ProfessorDept. of Social & Decision Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
[EMAIL PROTECTED]
