Reply #42: Empirical issue: Just how high is "too high" for minor candidates? [View All]

[AirAmFan]

Overall, Badnarik got 1886 votes, 0.28 percent of the Cuyahoga total, and Peroutka got 1751, 0.26 percent of the total. Within the Benedictine High cluster alone, Badnarik got 164 votes, 15.6 percent of the cluster total, and Peroutka got 225, or 21.3 percent.

Clearly the Benedictine percentages for minor candidates were "WAY too high". But precisely how many of those Badnarik and Peroutka votes at Benedictine should be considered erroneous?

This is a question about "statistical outliers". One of the most common ways of dealing with outliers is to calculate the mean and standard deviation and then consider any observation 3 or more standard deviations above the mean as an outlier, above any "reasonable" proportion that might by some stretch of the imagination be considered genuine. We can do these calculations later, but for now let's say that the excess vote for Badnarik in any cluster is (1-rB)*n(B), and the excess vote for Peroutka in any cluster is (1-rP)*n(P), where rB is a maximum reasonable proportion for Badnarik and rP is a maximum reasonable proportion for Peroutka. For the moment, let's arbitrarily set rB = 4*0.0028 = 0.0112, and arbitrarily set rP = 4*0.0026 = 0.0104. We can always change these values later, and analyze the sensitivity of miscount estimates to assumptions about these parameters.

Then for Benedictine High, the number of excess votes for Badnarik is tentatively (1-0.0112)*164 = 162.13, and the number of excess votes for Peroutka is tentatively (1-0.0104)*225 = 222.66.