Wednesday, October 22, 2008

What the Bradley Effect Might Look Like

There has been a lot of talk this year about the potential for the Bradley/Wilder* effect to play a role in this presidential campaign. In fact, this is the first time we have had the opportunity to discuss the phenomenon in terms of a legitimately viable candidate for the presidency during both the primary phase of the race and continuing into the general election. There also has not been any lack of opinions or research done as to whether the Bradley effect could play a role or whether it is even relevant in 2008. Just today Nate Silver at FiveThirtyEight linked to a Newsweek piece he had written to once again attempt to debunk the myth. And that's just the thing: given the current state of this race, this is the one unknown -- and some people, Silver included, argue that it really isn't -- that could affect the race enough to hand McCain the election.

...or could it?

I can buy Silver's argument that the Bradley effect is a myth in 2008. In fact, Dan Hopkins' paper on the Bradley effect has shown that over time the phenomenon has faded to the point of being minor at best. But Hopkins' research serves as something of a jumping off point. Whether there is or isn't a Bradley effect at play between now and November 4, we have data that indicates approximately what that effect may look like [...on average]. Across the 133 cases of minority or female candidates running for either a senate or gubernatorial position since 1989, the average effect was one percent. Now, that doesn't seem like that much, but let's look at how today's electoral college map would look if there was a uniformly distributed, 1% Bradley effect in the presidential race. [Again, the point of this exercise isn't to determine whether there is a Bradley effect, rather it is one to ascertain what the effect would look like on the electoral college map.]

[Click Map to Enlarge]

The obvious change is that several of the states on today's Watch List shift enough in that one percent move to change categories. Most consequentially, Florida, Nevada and Ohio move back into the McCain toss up category, handing the Arizona senator 52 electoral votes in the process. So even if there is just a one percent shift it turns a projected landslide into 2004. The electoral vote distribution would be the exact same 286-252 as four years ago, but Barack Obama would still garner enough electoral votes to win the presidential race. Is there a Bradley effect? Is there not a Bradley effect? Well, if it is only an average effect, then it could make things a bit more interesting come November 4.

Changes (Bradley Effect = 1%)
StateBeforeAfter
Colorado
Obama lean
Toss Up Obama
Florida
Toss Up Obama
Toss Up McCain
Indiana
Toss Up McCain
McCain lean
Minnesota
Strong Obama
Obama lean
Nevada
Toss Up Obama
Toss Up McCain
Ohio
Toss Up Obama
Toss Up McCain
Wisconsin
Strong Obama
Obama lean

There is a caveat to all this, though. Hopkins also draws a distinction between the presence of a Bradley effect when a candidate is already behind in the polls and when it is in place for a candidate who is the front-runner in one of these senate or gubernatorial races. Those front-runners also have some inflation in their pre-election poll numbers -- most tend to anyway. Hopkins makes the argument that those minority candidates who have pre-election poll leads have two effects to deal with: the Bradley effect and this front-runner effect [a bandwagon effect of sorts]. But within that line of argument, he splits the data into two samples -- those behind in the polls to begin with and those who fairly consistently clear the 50% barrier in those pre-election polls -- to make a broader point on the front-runner candidates. At the descriptive statistics level, Hopkins informs us that in those front-runner, Bradley effect races, African American candidates see a 1.9% disparity between what the polls say prior to an election and what the vote outcome will be. If we extend that basic finding to FHQ's electoral college map, we see a few additional changes to the map immediately above.

[Click Map to Enlarge]

What we find is that when it is assumed that there is a two point Bradley effect placed on the current electoral vote distribution, an additional set of states shift categories. But there are not any additional states that cross the partisan line. Virginia comes very close, but based on the strength of the post-Lehman polling in the state, Virginia remains within the Obama toss up category. And while the overall electoral vote distribution is unchanged, a handful of states are safer for McCain by virtue of the two point Bradley effect. Montana and West Virginia become strong McCain states and North Carolina shifts out of the toss up category and takes its fifteen electoral votes into McCain lean territory. New Hampshire remains blue, but is much more competitive as a result.

Changes (Bradley Effect = 2%)
StateBeforeAfter
Montana
McCain lean
Strong McCain
New Hampshire
Obama lean
Toss Up Obama
North Carolina
Toss Up McCain
McCain lean
West Virginia
McCain lean
Strong McCain

Alright. Case closed. Even if there is a two point Bradley effect -- one that doesn't even attempt to separate the front-runner effect out -- Obama continues to hold enough of a lead in the electoral college to win the race. Yes, that's true, but there is one major problem with how we have set this up thus far. The assumption in both scenarios above is that the effect applies evenly to all states. It is safe to say that that just isn't the case. A Bradley effect in Idaho is likely going to be different from a Bradley effect in Georgia.

But how do we determine how the effect would vary from state to state? Well, it isn't a stretch to hypothesize that race is likely an important determinant of that variation. In fact, as an extension of the Schaller hypothesis we discussed a few days ago in the comments section, we can argue that the Bradley effect is higher in states where the African American population is high. Now, the Schaller argument is that the support for a minority candidate among white voters holds a negative relationship with the percentage of a state's population that is black; that as a state's percentage of African Americans increases, support among white voters -- for the Democratic candidate -- decreases. That doesn't necessarily jibe well with an idea that inadvertently puts social pressure on survey respondents to say they support a minority candidate when they don't. However, it could certainly be argued that it is in this situation, where the greatest potential for the Bradley effect resides. If there are more African Americans and thus greater interaction between the races, then there is, by extension, a greater potential for these social pressures to cause a discrepancy between pre-election poll numbers and the tally of votes cast.

What we can do, then, is weight two percent Bradley effect that Hopkins finds in the cases of African American candidates who are also front-runners in their senate or gubernatorial races. If two percent is the average Bradley effect in those situations, then how can we go about weighting or discounting states based on the percentage of their population that is African American? First, we can use the 2007 Census estimate of the population to determine that figure for each state (as recently as possible). We can then construct a weight by standardizing the Census data (by caluculating a z-score for each state's data) and applying it to the average Bradley effect from Hopkins. The result is a Bradley effect range from 1.05% in Montana to 4.28% in Mississippi based on a state's proportion of African Americans. If we then apply this Schaller Weighting structure to the electoral college map, we set yet another set of changes.

[Click Map to Enlarge]

Now Virginia switches over into the McCain toss up category and the Old Dominion's 13 electoral votes tighten the electoral college distribution even more. But a trio of states with lower relative African American populations -- Montana, New Hampshire and West Virginia -- now are not affected as greatly as they were when it was assumed that the Bradley effect was the same for all states. New Hampshire remains an Obama lean and both Montana and West Virginia stay in the McCain lean category.

Changes (Bradley Effect = Weighted by % Pop. Black)
StateBeforeAfter
Montana
Strong McCain
McCain lean
New Hampshire
Toss Up Obama
Obama lean
Virginia
Toss Up Obama
Toss Up McCain
West Virginia
Strong McCain
McCain lean

Essentially what has happened by assuming that there is an average Bradley effect of 2% that is weighted according to a state's African American population is that the race has been returned to its post-convention/pre-Lehman level, at least in terms of the electoral vote distribution. Obama would win by the slimmest of margins -- well, among the slimmest of margins -- if the votes were cast according to the map above.

While one and two percent effects don't seem like that much they have the effect of shifting the race back to where it was prior to the pre-economic collapse level. And the perception of that change has been that we have witnessed a pretty large shift in terms of the electoral college over the last month. Will there be a Bradley effect? I don't know, but there are certainly strains of arguments of both sides. Regardless, if there was a Bradley effect at play in 2008, and it was on par with what we have seen in other races -- on average -- over the last twenty years, it would have an impact but wouldn't necessarily change the outlook on what the outcome is likely to be on November 4.

UPDATE: The discussion on this in the comments section has been instructive thus far. What if, as I said, the Schaller hypothesis and the Bradley effect don't naturally wed themselves? What if, as SarahLawrenceScott says, it is more a matter of perceptions in the whitest states that would drive a potential Bradley effect as opposed to those normalized perceptions in states with higher proportions of African Americans? Well, let's have a look. If we take the Census figures on the white populations in the states, we can construct a similar measure to the one above. Can we expect whiter states like New Hampshire to get tighter and plains and prairie states to potential move further into the McCain column?

[Click Map to Enlarge]

That's exactly what we see. All the changes on the previous hypothetical are reversed. Most consequentially, this brings Virginia back into the blue. But New Hampshire becomes much closer as does Colorado, which would be on the Watch List to cross the partisan line into McCain territory if there was the actual map. Also, Missouri and Iowa (roughly a couple of plains states, though folks in Missouri may disagree with that) and Montana and North Dakota move toward McCain. Missouri, Montana and North Dakota -- along with West Virginia -- become safer for McCain while Iowa is less so for Obama.

North Carolina has been a topic of conversation here at FHQ recently, and while the effect is lessened in this fourth scenario, it is still great enough to push the Tar Heel state into the McCain lean category.

Changes (Bradley Effect = Weighted by % Pop. White)
StateBeforeAfter
Iowa
Strong ObamaObama lean
Missouri
Toss Up McCain
McCain lean
Montana
McCain lean
Strong McCain
New Hampshire
Obama lean
Toss Up Obama
North Dakota
McCain leanStrong McCain
Virginia
Toss Up McCain
Toss Up Obama
West Virginia
McCain leanStrong McCain

The underlying conclusion is the same, though. Even if there is some Bradley effect, it is not likely to change the outlook for the election. Obama is in a good position to win on November 4 unless there is an above average Bradley effect involved. But as Hopkins suggests, after about 1996, these effects decreased in a noticeable way in the senate and gubernatorial races he examined.


*The basic concept is that a minority candidate's poll numbers run above where the electoral outcome ends up. Survey respondents feel a sort of social pressure to say that they are voting for the minority candidate when in actuality they are not.

I want take an opportunity to thank Del Dunn at the University of Georgia for planting the basis of the Schaller idea discussed above in my head in a water cooler conversation we had. In addition, I'd like to thank Anon3:58 and SarahLawrenceScott for their contributions to the updated version of the analysis.


Recent Posts:
The Electoral College Map (10/22/08)

Map Update Coming...

The Electoral College Map (10/21/08)

9 comments:

Anonymous said...

CBS pollster Kathleen Frankovic doesn't see [the Bradley effect] any more. In recent elections with black candidates - Deval Patrick's winning governor's race in Massachusetts, in Tennessee, Harold Ford losing his run for the Senate, both in 2006 - the polls were right-on.
Your weighting would be bizzare. By the extension weighting one would have to assume that it is less acceptable to say you are voting for McCain in Georgia and North Carolina than NH, CA,HI,DE,WI, etc. Bradley effect is NOT a measure of racism. It is a measure of secret racism, which according to that weighting is more common in South Carolina than Massachusetts.

Robert said...

Nice analysis, Josh. It is interesting that early on, the Republicans were playing up the Bradley effect to keep the ranks from being discouraged in a close race. Now it is to the Democrats advantage to play up a possible Bradley effect to keep their base energized and getting out to vote.

SarahLawrenceScott said...

I agree with anonymous. I think your weighting by African-American population is most likely backward. The Schaller hypothesis suggests more racial polarization when the sizes of the racial groups are more comparable (perceived competition, not interaction, could be the driver). In that environment, people are used to voting against people from the other racial group, or at least against people they support. In an all-white state, they rarely have an opportunity to vote against a black candidate. Therefore there could be more hesitation to tell a pollster you're planning to do so. (By the way, I disagree with some characterizations of the Bradley effect. Although it is about race, it's not necessarily about "secret racism." In any Bradley effect scenario, we're talking about a situation where the respondent feels social pressure to say they're considering the black candidate. If the respondent gives in to that pressure, it doesn't necessarily follow that they're voting against the black candidate because they're black. They could be voting against them, or--gasp!--for the other candidate, for "legitimate" reasons. But they don't want to tell a pollster that, because they're afraid of seeming racist.)

Nate Silver's analysis seems to confirm the notion that the Bradley effect, if it exists, is more extreme in states with low African-American populations. He argues that it may be due to a reverse Bradley effect in which blacks feel pressure to say they'll vote for the white candidate, but it's also possible that what he's seeing is two effects: a larger Bradley effect in states with lower African-American populations, coupled with a generic overperformance by Obama everywhere due to a superior ground game.

So--could you do one more analysis, where you weight the effect by the size of the white population, rather than the size of the African-American population? Presumably New Hampshire will flip, but North Carolina will not. Hmm...sound familiar from the primaries?

Josh Putnam said...

Sure, I can add that.

Josh Putnam said...

Alright, the Bradley effect update is up.

Now I'm off to update the actual electoral college map.

Anonymous said...

Check out the new polls out today.
Look at Ohio in particular.
What are everyone's thought on these Ohio polls?
Seems to me they are way out of line.

Here is the link.
http://www.realclearpolitics.com/epolls/2008/latestpolls/index.html

Robert said...

Anon,

Nate talked about the Big Ten polls in his post at FiveThirtyEight

http://www.fivethirtyeight.com/2008/10/am-polls-show-surprisingly-large-leads.html

These polls tend to slant Democrat just like Big Ten fans tend to overrate their capacity for turning out decent football teams. Having said that, if the National polls are an indicator of what is happening in the states, you should expect some major shifting in the battleground states towards Obama. I see now that McCain has recently discovered that George W. Bush was not a good President. His discovery may be a little too late for him, just like his discovery that the fundamentals of our
economyhttp://politicalticker.blogs.cnn.com/2008/10/23/mccain-lashes-out-at-bushs-record/

Jack said...

Now that Blogger's working again — and I'm home from the chess club — I'll post.

First off, could you explain the following sentence? "And that's just the thing: given the current state of this race, this is the one unknown -- and some people, Silver included -- that could affect the race enough to hand McCain the election." The part between the dashes [pardon my lack of knowledge of the technical term] doesn't seem to make sense to me.

Some of those Big Ten and Quinnipiac polls that Robert mentions - the +11 PA, +13 WI and IA and +29 IL from Big Ten and the Quinnipiac +13 PA and +5 FL results, seem reasonable. But the others are odd. If they're right, I could fail my midterms and still be a very happy man.

Josh (and any others), what do you think of the idea - which I've read about periodically on other sites - of the reverse effect in which African-Americans are reluctant to say they are voting for Obama? Personally, I'm skeptical about both effects.

Josh Putnam said...

Jack,
The easy answer is that I was up too late last night finishing that up and screwed the point up. I'll fix it.

And thanks for pointing it out.

The above reason is why I'm going to call it a night shortly and finish plowing through all these polls in the morning. I'd rather do it right than not. Our readers deserve that much.

Only 12 more days and I can hibernate until 2010.

Just a sneak peek:
Montana is now on the Watch List to switch to a McCain toss up.

Indiana is one-thousandth of a point from being on the Watch List to switch to an Obama toss up.

Ohio is off the list, but remains a toss up on the Obama side. That it is off the list really says something.

Pennsylvania is now a strong Obama state.

Georgia holds pat as does Florida, though the latter is not as vulnerable to an immediate switch over as it was entering the day.


Blogger has been kind of funky today. I'm sorry if it was any inconvenience to anyone. I knew something was amiss when my handy-dandy "F" favicon by the URL was replaced by the boring Blogger "B".