A Panel of 9 and Impartiality
Suppose there was a panel of 9 individuals, voting either “Yea” or “Nay” on a particular proposal. All things being equal, what would be the probability that any one particular individual would cast the deciding vote, either on the Yea side or the Nay side? To calculate this would not be very realistic, considering it would be based on each individual’s vote being totally random. But it does give us a reference point. Much of statistics is this comparison, determining whether some phenomenon is significantly different from, or similar to, a simply random occurrence.
As discussed in our Miscellaneous Math section, probability is defined as:
ρ = # of desired outcomes # of total possible outcomes
First, we need to figure out how many total possibilities of voting scenarios there are. The number of each scenario would be a combination; for example, in a 6 – 3 vote, the order of the voters in the winning or losing block does not matter (though it would obviously be different from a 3-6 "losing" vote).
Voting scenarios # of combinations
“Yea”-“Nay”
9 – 0 1
8 – 1 9
7 – 2 36
6 – 3 84
5 – 4 126
4 – 5 126
3 – 6 84
2 – 7 36
1 – 8 9
0 – 9 1
Total 512
As for casting the deciding vote, we focus on the 5- 4 and 4 – 5 scenarios. Controlling for one particular individual, this number would be a combination of 8 voters taken 4 at a time. This calculates to a total of 70 scenarios where one voter would be the “decider” in a 5 – 4 vote, the same number for casting the decisive vote in the 4 – 5 split. This is a total of 140 ways where any one particular person could be the deciding voter out of 512 possible scenarios, or 27.3%.
Now let’s compare this to one of the most powerful panels of 9 humans in the U.S., the Supreme Court; “humans” being the key word. Their votes are clearly not random, but neither are they impartial with respect to a political ideology. With the exception of (former) Justice Anthony Kennedy, there is little argument that these high court judges tend to vote in ideological blocks. (We also acknowledge that 1/3 of their 2014-2015 votes were unanimous 9-0 decisions, so there was considerable agreement as well.) Considering the clear partisan divide on several issues, how can we test the hypothesis that Justice Kennedy was relatively impartial?
Note that measuring impartiality is difficult, and perhaps irrelevant since humans are not inherently inclined to be impartial, and socialization serves to cement biases. Adam Smith implied that reason – which we have to work at – encourages us in a complex society to see things from other points of view and correct our unequal sentiments. Political scientists can more easily measure the public’s perception of a judge’s impartiality, or lack thereof. Many state and local judges are elected, run on a party ticket, and collect campaign contributions. Federal judges are appointed by the President. Either way, loyalty to a party ideology among judges has increased over time, thus influencing impartiality.
First let’s examine the 2014-2015 term, with the number of each vote count and their percent of the total cases that were decided with an oral argument.
Panel votes # % of total cases
5-4 decisions 26 34.7% (17 liberal, 8 conservative, 1 split)
9-0 decisions 25 33.3%
6-3 decisions 11 14.7%
7-2 decisions 6 8%
8-1 decisions 5 6.7%
6-2 decisions 2 2.6%
Justice Kennedy was part of the majority in 21 of those 26 “5-4” decisions, which justified his status as being the pivotal swing voter. In 13 of those deciding votes, he sided with the liberal block, and in 7 he sided with the conservative block. While it may seem that Justice Kennedy leaned to the liberal block as to the number of cases, note that he sided with the conservative block in 87.5% of the cases they “won,” while siding with the liberal group in 76.4% of their “winning” cases.
What is interesting is that his 21 deciding votes represent 28% of the total votes. This might suggest reasonable impartiality in that it is similar to the 27.3% probability of any judge being the “decider” if the votes were completely random. For example, if judges flipped a coin to decide yes or no for every proposal they were presented, they would clearly not be using bias. If every judge looked at each case individually, on its own merit, based on legal interpretations, without preconditioned ideological loyalties, we could ideally see a range of voting scenarios similar to the random distribution, particularly as the variety of cases in increased.
While books have been written trying to interpret or predict a judge’s legal beliefs, such numbers could demonstrate how we might measure their behavior or performance. Or at least confirm their ideological leanings. For example, while Justice Ginsberg could be considered the “decider” in all 17 of the liberal-leaning “5-4” votes (still less than 28%), she was predictably not the decider in any one of the 8 split-decisions that leaned to the conservative block. As with all of our analyses, it is not about who or what is right or wrong or good or bad. Justice Kennedy is interesting here in that he appeared to be the least loyal to a political ideology; perhaps a relatively impartial judge. Could this be what was originally intended, or a refreshingly novel concept?
RKL for Maximatican.com