Prejudice -- By the Numbers

So apparently you can now download a video podcast of the entire Rachel Maddow show, complete with no commercial interruptions. That's just five different kinds of awesome in a nice tasty blend, but that's not the subject of this note. It was while watching Maddow's first podcasted show that I stumbled across a statistic that floored me -- exit polls suggesting that approximately 70% of African-American voters in California voted in favor of the anti-gay-marriage Proposition 8. As anyone who knows me can tell you, once I get ahold of one interesting number, I like to juggle it up with some other interesting numbers, and as it turns out, this is one really interesting number. Let's start by saying, in order to keep the examples easier, that nine in ten African-American voters in California voted for Barack Obama for President. (That's probably a bit on an underestimation, as exit polling suggests that about 94% of African-American voters in California voted for Obama, but as you'll see, underestimating this percentage won't change the conclusion.) Using a very simple statistical formula, if you know the percentage of one thing that happened, and you know the percentage of another thing that happened, you can determine the percentages of those two things happening together, assuming those two things are independent. For instance, let's matrix up the Obama vote among California blacks:

   1   2   3   4   5   6   7   8   9   0
1  x   x   x   x   x   x   x   x   x   .
2  x   x   x   x   x   x   x   x   x   .
3  x   x   x   x   x   x   x   x   x   .
4  x   x   x   x   x   x   x   x   x   .
5  x   x   x   x   x   x   x   x   x   .
6  x   x   x   x   x   x   x   x   x   .
7  x   x   x   x   x   x   x   x   x   .
8  #   #   #   #   #   #   #   #   #   +
9  #   #   #   #   #   #   #   #   #   +
0  #   #   #   #   #   #   #   #   #   +

The horizontal axis here represents the percentage of votes for Obama, while the vertical represents the percentage of votes for Prop 8. Each different marker, thus, represents one of the four possible outcomes: x - voted for Obama and in favor of Prop 8 (63) # - voted for Obama and against Prop 8 (27) . - voted for McCain and in favor of Prop 8 (7) + - voted for McCain and against Prop 8 (3) The total adds to 100, as you'd expect. What you wouldn't expect is that a significant majority of African-American voters who voted for Obama also appear to have voted in favor of Prop 8. Of course, it's not that simple -- I say 'appear to have voted in favor' because it's clearly not the case that these two outcomes are independent, as they would need to be for the numbers to be completely valid. All you have to do is look at the exit poll data for yourself to realize that support for Prop 8 wasn't exactly the same across party lines. But here's the thing that makes the numbers interesting -- let's say we tweak the numbers so that every McCain voter voted against the amendment. That allows us to change those three + votes into . votes, but it also messes up our original assumption, because now more than 70% of African-American voters are supporting Prop 8. To put the accounting right, we have to change three supporting votes for Obama to non-supporting votes, which then allows us to move three x votes into the # vote column, and leaves us with this: x - voted for Obama and in favor of Prop 8 (60) # - voted for Obama and against Prop 8 (30) . - voted for McCain and in favor of Prop 8 (10) Now the original assumptions are back in place, but we've still got African-American Obama supporters voting 2-to-1 in favor of the amendment. Unfortunately, there's no more juggling that can be done with the numbers -- unless you want to argue that the exit polls are simply wrong, this result is fairly close to the reality of the voting on this issue. (Two other points. Perhaps you can now see why underestimating African-American support for Obama wouldn't change the outcome, because now, for every voter we've identified as a McCain voter who actually voted for Obama, we can't actually change how they voted on Prop 8, and we're assuming *every* McCain voter voted for Prop 8. Changing McCain to Obama votes now only increases the margin of support for Prop 8 among Obama voters. Also, our assumption that every McCain voter voted in favor of Prop 8 is actually less realistic than our assumption that the support was identical by party affiliation -- while the same exit polls show that 64% of Democrats voted against the amendment, only 82% of Republicans said they voted for it. If that breakdown is similar to the breakdown among African-American voters for Obama and McCain, then again, we're identifying fewer Obama voters who voted for the amendment using our quick-and-dirty method than actually exist.) One more chart, for the benefit of those preparing to argue that white voters also voted in favor of Prop 8, which is absolutely true. For this chart, we'll assume that 60% of white voters voted for Obama, and that 60% voted in favor of Prop 8. To further show the case for racial equality, we'll use the same legend as in the charts above:

   1   2   3   4   5   6   7   8   9   0
1  x   x   x   x   x   x   .   .   .   .
2  x   x   x   x   x   x   .   .   .   .
3  x   x   x   x   x   x   .   .   .   .
4  x   x   x   x   x   x   .   .   .   .
5  x   x   x   x   x   x   .   .   .   .
6  x   x   x   x   x   x   .   .   .   .
7  #   #   #   #   #   #   +   +   +   +
8  #   #   #   #   #   #   +   +   +   +
9  #   #   #   #   #   #   +   +   +   +
0  #   #   #   #   #   #   +   +   +   +

x - voted for Obama and in favor of Prop 8 (36) # - voted for Obama and against Prop 8 (24) . - voted for McCain and in favor of Prop 8 (24) + - voted for McCain and against Prop 8 (16) Again, we know that these two positions are not truly independent, and that more than 60% of Republican voters voted in favor of the amendment. If we assume that the percentage of McCain voters in favor of Prop 8 is closer to 80% (as noted above), then we can move half of the 'against' votes into the 'for' category, and to balance the scales, move the same number of Obama voters from 'for' to 'against', leaving us with this: x - voted for Obama and in favor of Prop 8 (28) # - voted for Obama and against Prop 8 (32) . - voted for McCain and in favor of Prop 8 (32) + - voted for McCain and against Prop 8 (8) We now have a slight majority of white Obama voters voting against Prop 8. If you take into account that the actual percentage of white voters supporting Obama in California was closer to 50% than 60% (51%, according to this same exit poll), it becomes clear that white voters seemed more likely to vote against Prop 8 than to vote for Obama, which might be construed as prejudice in the opposite direction. The difference, however, isn't nearly as dramatic as that for the African-American voters noted above. Again, these are really just quick-and-dirty estimates based on one set of exit polls, and might not actually reflect the underlying reality. It would certainly be easy enough to simply dismiss the poll as flawed. The next question, for someone of a scientific mind, would be to ask if there is additional data that can either confirm or refute the hypothesis suggested by this data: that California African-American voters appeared significantly more prejudiced against gays and lesbians than their white voting counterparts in the 2008 election cycle.