The purpose of this work was to determine how voters stand politically in Benton County Oregon. The "World's Smallest Political Quiz" was given to a self-selected sample of people. Bivariate densities were estimated from the sample for all Democrats, Libertarians, Republicans, and all other parties (including the non-aligned) in Benton County on a two dimensional field -- the dimensions being personal and economic issues. The number of voters in each party was obtained from the Benton County register of voters as of mid-September 2009. It was found that voters in Benton County tend to have libertarians tendencies. It appears that Republicans can win in Benton County by appealing to those libertarian tendencies.
The next (second) section discusses the World's Smallest Political Quiz and the sample of people taking the quiz. The third section discusses how the bivariate densities were estimated. The fourth section deals with the uncertainties in the samples showing the two dimensional means and confidence ellipses for each party and for the "average" voter. The fifth section contains the conclusions.
"World's Smallest Political Quiz"
The Benton County Republican Central Committee (BCRCC) gave the "World's Smallest Political Quiz" to all who would take it at the Benton County 2009 Fair. The fair was held between July 28th and August 1st. The questions asked and information about the quiz can be found on a flyer from the Advocates for Self-Government. The goal of the quiz is to determine where one stands politically.
(Images and graphs below are clickable for a larger view. Use your back arrow to return.)
The BCRCC makes no claims that the set of people taking the quiz was a random sample of Benton County voters. The sample was self selected; it consisted of people who stopped by the BCRCC booth and took the quiz. Forty Democrats, eleven Libertarians, 157 Republicans, and thirty-one people from other political parties, or who were not aligned with any party, took the quiz. The large number of Republicans relative to the other parties was not a surprise since the booth was a Republican booth. The sample is the only sample of this type that I know of; hopefully it is at least somewhat representative of the voters. The image to the right shows where all quiz takers are politically. The red dots are Republicans, the blue dots are Democrats, the green dots are Libertarians, and the yellow dots are all other parties and the non-aligned. As can be seen, the quiz results are shown in a two-dimensional field, the dimensions being personal issues and economic issues. The field is divided into Libertarian, Left, Centrist, Right, and Statist areas. The placement of the dots show where the quiz taker is located on those dimensions.
Not surprisingly, the Democrats tend to be on the Left and the Libertarians in the Libertarian area. The other/non-aligned tend to be in the Centrist and Libertarian areas. And, the Republicans tend to be in the Libertarian and Right areas. A few quiz takers seem to have political philosophies very different from their parties and may wish to rethink their political affiliations.
The densities were estimated using the procedures in Silverman, 1986. An adaptive bivariate normal kernel was used. The reader is referred to Silverman for the details. Densities were estimated for the Democrats, Libertarians, Republicans, and all other parties combined, including the non-aligned. The original data was in increments of ten. The test taker had two scores -- one for personal issues, the second for economic issues -- which varied from zero to 100 in increments of ten. I mapped this data from zero to 100 in increments of one so that the curves would be smoother. I also included a constant in the distribution that made the volume under the distribution equal to the number of voters in the party instead of making the volume equal to one. I did this to make the contours more informative -- they show the density in people in one of 10,201 one-by-one squares which is more informative than the height of the density as a fraction.
Densities by Party
The estimate of the density of the Benton County Democrats is shown in the chart below. The software package would not rotate the chart so that it would have the same orientation as the two-dimensional quiz field above.
The BCRCC makes no claims that the set of people taking the quiz was a random sample of Benton County voters. The sample was self selected; it consisted of people who stopped by the BCRCC booth and took the quiz. Forty Democrats, eleven Libertarians, 157 Republicans, and thirty-one people from other political parties, or who were not aligned with any party, took the quiz. The large number of Republicans relative to the other parties was not a surprise since the booth was a Republican booth. The sample is the only sample of this type that I know of; hopefully it is at least somewhat representative of the voters. The image to the right shows where all quiz takers are politically. The red dots are Republicans, the blue dots are Democrats, the green dots are Libertarians, and the yellow dots are all other parties and the non-aligned. As can be seen, the quiz results are shown in a two-dimensional field, the dimensions being personal issues and economic issues. The field is divided into Libertarian, Left, Centrist, Right, and Statist areas. The placement of the dots show where the quiz taker is located on those dimensions.Not surprisingly, the Democrats tend to be on the Left and the Libertarians in the Libertarian area. The other/non-aligned tend to be in the Centrist and Libertarian areas. And, the Republicans tend to be in the Libertarian and Right areas. A few quiz takers seem to have political philosophies very different from their parties and may wish to rethink their political affiliations.
Bivariate Densities of Parties
The densities were estimated using the procedures in Silverman, 1986. An adaptive bivariate normal kernel was used. The reader is referred to Silverman for the details. Densities were estimated for the Democrats, Libertarians, Republicans, and all other parties combined, including the non-aligned. The original data was in increments of ten. The test taker had two scores -- one for personal issues, the second for economic issues -- which varied from zero to 100 in increments of ten. I mapped this data from zero to 100 in increments of one so that the curves would be smoother. I also included a constant in the distribution that made the volume under the distribution equal to the number of voters in the party instead of making the volume equal to one. I did this to make the contours more informative -- they show the density in people in one of 10,201 one-by-one squares which is more informative than the height of the density as a fraction.
Densities by Party
The estimate of the density of the Benton County Democrats is shown in the chart below. The software package would not rotate the chart so that it would have the same orientation as the two-dimensional quiz field above.
As can be seen there are two modes in this distribution. The primary mode is at the approximate coordinates 30 and 70. The secondary mode is at 50 and 80. The center contour of the primary mode is 20 people per square meaning that at the very center there are at least 20 people per square but less than 24 people per square. the center contour of the secondary mode is 12 people per square but less than sixteen people per square. The reader may estimate the number of people within a contour. As can be seen, the primary mode is in left area and below the statist-libertarian line and the secondary mode is close to the libertarian area..
The estimate of the density of the Benton County Libertarians is shown in the chart below.
As can be seen there are several modes -- which are all over the place -- in this distribution. The sample was composed of eleven people claiming to be libertarians but looking at the distribution, I wonder how many really were Libertarians. However, there are only 298 registered Libertarians in Benton County so they don't affect the big picture much.
The estimate of the density of the Benton County Republicans is shown in the chart below.
As can be seen, there are two modes. The primary mode is located at 95 and 60 and the secondary mode is located at 80 and 40. This density estimate is probably the best of the four in that the sample had 157 data points. The primary mode is clearly in the libertarian area and the secondary mode is on the left side of the right (conservative) area -- and close to the libertarian area. It appears that Benton County Republicans are not really conservative; they tend to be libertarian.
The estimate of the density of all other parties and the non-aligned is shown in the chart below.
This is the most interesting chart of the four charts. This group is arrayed down the center of the field with the primary mode located at 80 and 50 and the secondary mode located at 85 and 80. Moreover, there are many people in the centrist area. This group tends to be libertarian and to the right of the center of the field. It is the group that Republicans need to attract.
Density of All Voters
The chart below shows the estimate of the density of all voters in Benton County. The chart is the sum, square-by-square, of the four charts above.
The reader will notice that the primary and secondary modes are where the primary and secondary modes are for the Democratic party. The tertiary mode, at 80 55, is the sum of the Republican modes and the Other primary mode -- with a little help from Libertarians.
It is clear that the left dominates in Benton County. The right -- people to the right of the line running from 0,0 to 100,100 constitute only 43% of Benton County. It is also clear that on the libertarian-statist divide, the libertarians dominate. 70% of the people fall above the libertarian-statist line.
Since we only need 50% plus one vote, the question is where to draw the line on the issue field to include 50% (+) of the voters. If one draws a line where the sum of the coordinates equals 117, the voters on the libertarian side of that line equals 50% of the electorate. If one draws two lines where the value of the economic issue coordinate is greater than 40 and the sum of the coordinates is equal to 112.5, 50% of the voters are on the libertarian side of those lines.
Median Voter Theorem
According to the median voter theorem, assuming everyone votes, the candidate who captures the median wins. If a candidate alienates voters and they don't vote -- shifting the median away from themselves, the candidate captures the median of those who do vote. This theorem applies to one or more dimensions. (The reader is referred to Hinch, 1997, for more information.) The trick is for a candidate to pick positions that are closer to the median than the opponent but not so far from the positions of the more extreme voters on the candidate's side that the more extreme voters don't vote. The medians for the economic and personal dimensions are 52 and 65 respectively -- a point on the line where the sum of the coordinates equals 117.
Confidence Ellipses
The density charts above do not capture the uncertainties created by the different, and limited, numbers of data points. Therefore, I plotted mean positions and confidence ellipses of those means for each group -- Democrats, Libertarians, Republicans, and Others/NA. I also plotted the mean, and median, and confidence ellipse for the "average" voter. The details on plotting confidence ellipses can be found in Johnson, 1988.
Group Plots
The chart to the left shows where each group -- Democrats, Republicans, Libertarians, and Other/NA -- stands as a group. The plot shows the means of personal and economic issue scores and the 95% confidence ellipse1 of the means for each group.The mean location for the Libertarians is in the Libertarian area but the confidence ellipse is quite large reflecting the small sample. The location of the other/non-aligned mean is not unexpected. However, the mean other/non-aligned location may well be in the libertarian area. I suspect that the location of these two sets of means reflects the Libertarian streak that runs throughout Oregon.
The mean location for the Republicans is in the Libertarian area, not the Right area. The confidence ellipse is relatively small reflecting the relatively large sample. There is a reasonable probability that the mean location is in the Centrist area but it is probably not in the Right area which tells us that the Benton County Republicans are probably a libertarian-centrist group, not a right wing group. The mean location of the Republicans is very close to that of the Libertarians.
The mean location for the Democrats is on the Left, but not on the far left. However, there is a significant probability that the mean location is in the Centrist area and a small probability that the mean location is in the Libertarian area.
Average Voter Plot
The chart to the right shows the mean, median, and 95% confidence ellipse of the "average" voter. The average voter was estimated by simulating the position of a linear combination of Democrats, Republicans, Libertarians, and Other/NA using the fraction of voters in each group as the weights for each group. The simulation was done 10,000 times. A reference on simulation is Naylor, 1966. I plotted the median of the simulations because the probability distributions of the scores of each group were truncated bivariate normal distributions and I did not know what effect the truncations -- variables range from 0 to 100 -- would have. Obviously, the truncations did not have much effect.The mean-median point of the average voter is 55, 63 -- in the libertarian left quadrant of the centrist area -- which is close to the median (52,65) of the density plot for all voters. The major and minor axes of the ellipse are 25 and 23 respectively. There is a significant amount of uncertainty in the location of the mean-median. The sum of the mean-median scores is 118; for all practical purposes equal to the 50% dividing line between libertarian-statist discussed above.
Conclusions
Assuming that this sample is at least somewhat representative, the Benton County voter is probably more libertarian than statist. Moreover, the average voter is probably not on the far left, or the far right. However, the Democrats are clearly to the left of everybody else. Another way of describing the data may be to say that Republicans, Libertarians, some Democrats, and Others/NA seem to share many values, while many Democrats are alone in statist-left-field. Generally speaking, Democrats outnumber Republicans. Republicans and Others/NA outnumber Democrats. It seems reasonable that candidates who are positioned at the intersection of Republicans, Libertarians, and Other/NA -- economic dimension of about 70 and personal dimension of about 60 -- could capture more than 50% of the electorate, including the more libertarian Democrats, not alienating many of the more extreme elements of the Republican Party, and easily winning in Benton County. Such a candidate might even win in Corvallis.
References
- Hinch M.J. & M.C. Munger. Analytical Politics. Cambridge University Press. Cambridge UK. 1997. 253p.
- Johnson R.A. & D.W. Wichern. applied Multivariate Statistical Analysis. Prentice Hall. Englewood cliffs, NJ. 1988. 607p.
- Naylor, T.H., J.L. Balintfy, D.S. Burdick & K. Chu. Computer Simulation Techniques. John Wiley & Sons, Inc. New York. 352p.
- Silverman, B.W. Density Estimation for Statistics and Data analysis. Chapman and Hall. London and New York. 1986. 175p.
1The 95% confidence ellipses are actually a bit greater than 95% because the means are bounded by 0 and 100. I could have estimated that area but did not because it would not really shed more light on the situation.
