S-PLUS Graphlets™ Gallery

In the 2000 USA Presidential election, claims were made by Palm Beach, Florida voters that the polling card was confusing, leading them to mistakenly vote for Buchanan instead of Gore. The S-PLUS Graphlet below provides evidence supporting their claims.

The graphic compares total votes in Florida for Buchanan and Bush.  Each dot on the scatter plot represents a county, and shows the number of votes allocated to the two candidates.  Votes to Buchanan are shown in the vertical direction, and votes to Bush in the horizontal direction. In most counties, Bush garnered more votes than Buchanan by a factor of about 200 to one, and so most of the counties fall roughly on a straight line.   But in Palm Beach, the ratio was closer to 45 to one.  Palm Beach stands out obviously in the scatter plot  as a county where voting trends were significantly different from other Florida counties.  That some Palm Beach voters mistakenly voted for Buchanan when intending to vote for Gore is a plausible explanation for this aberration.

Instructions: Click on any point in the scatter plot to see the votes for each candidate in that county.  To return to the scatter plot, click on the text "Click here to return" in the lower portion of the bar chart. Printable versions of this graphic are available in JPG, TIFF and Adobe PDF formats. Data as of 12:30PM Eastern, Nov 10 2000 supplied by ABCNEWS.com.

Similar results also appear if the Gore votes are plotted against the Buchanan votes, as shown below.

Data as of 12:30PM Eastern, Nov 10 2000 supplied by ABCNEWS.com. Printable versions of the above graphic are available in JPG, TIFF and Adobe PDF formats. All graphics copyright 2000, Insightful Corp. May be used without permission provided attibution to Insightful/S-PLUS remains visible.

Buchanan scored 3407 votes in Palm Beach.  Using S-PLUS's "Robust MM Regression" statistical modeling technique, the expected number of votes for Buchanan in Palm Beach based on the Florida-wide Bush/Buchanan voting pattern is 761. If we assume that all 2646 extra votes cast for Buchanan were intended for Gore, this discrepancy is more than enough to swing the result of the razor-close Florida electoral college vote, and give Gore the presidency. The same analysis using the Gore/Buchanan voting pattern shown in the second graphic suggests 1997 extra votes to Buchanan in Palm Beach.

Consider the first graphic above (Bush/Buchanan votes in Florida counties).  With the exception of Palm Beach, the points approximately fall on a straight line, because the proportion of Buchanan voters to Bush voters is roughly the same in each county.  If Buchanan voting patterns compared to Bush voting patterns are the same in each county, it's reasonable to assume that for every Buchanan vote, Bush gets B votes. Mathematically, we assume for each county the following approximately holds true:

Buchanan Votes = Bush Votes / B

If we could determine the factor B, we could determine how many votes Buchanan would have expected to get in Palm Beach, by dividing the actual number of Bush votes in Palm Beach and dividing by B. Comparing this number with the actual Buchanan votes in Palm Beach allows us to estimate the number of misallocated votes.  We estimate the value of B to be 200.9.  Since Bush scored 152954 votes in Palm Beach after the first recount, this indicates that Buchanan ought to have scored 761 votes, 2646 fewer than he actually did score.

The Gore voting patterns may also be used to predict the Buchanan votes in Palm Beach, using the equation

Buchanan Votes = Gore Votes / G

Using the Buchanan/Gore data, we estimate the factor G to be 191.2.  Since Gore scored 269696 votes in Palm Beach, we estimate that Buchanan ought to have scored 1410 votes, 1997 fewer than the actual result.

We used S-PLUS's "Robust MM Regression" technique to estimate B and G.   This is an improved version of the "Ordinary Least Squares Regression" technique most commonly used for analyses such as this. This method is considered to be robust in the sense that unusually high or low data values (such as was observed for the Buchanan votes in Palm Beach) are less likely to influence the estimate of B or G. The robust regression line is shown in orange on the graphic. For comparison, using Ordinary Least Squares Regression, the values of B and G are 188.8 and 217.5 respectively, indicating 2597 (Bush data) and 2167 (Gore data) votes misallocated to Buchanan in Palm Beach.