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About that claim in the NYT that the immigration issue helped Hillary Clinton? The numbers don’t seem to add up.

Today I noticed an op-ed by two political scientists, Howard Lavine and Wendy Rahm, entitled, “What if Trump’s Nativism Actually Hurts Him?”:

Contrary to received wisdom, however, the immigration issue did not play to Mr. Trump’s advantage nearly as much as commonly believed. According to our analysis of national survey data from the American National Election Studies (a large, representative sample of the population of the United States), Hillary Clinton did better in the election than she would have if immigration had not been so prominent an issue. . . .

Hmmmm, that’s a surprise. I wonder whassup with that? They online version features a couple graphs:

And here’s some corresponding text in the op-ed, following the principle that a picture and a thousand words are better than two pictures or 2000 words:

We found that Mr. Trump did only slightly better than his Republican predecessors among anti-immigration whites. Among pro-immigration whites, however, Mrs. Clinton far outpaced John Kerry in 2004 and Barack Obama in 2008 and 2012. For example, Mr. Obama received the votes of 50 percent of pro-immigration whites in 2012, whereas Mrs. Clinton won the votes of 72 percent of that group in 2016 — a 22-point difference.

Among anti-immigration whites, by contrast, Mr. Trump improved only marginally on Mitt Romney’s showing, 79 percent to 71 percent. Perhaps most important — given the popularity of the “keep the same” position — is that immigration moderates swung 7 percentage points in Mrs. Clinton’s favor (Mr. Obama received 38 percent to Mrs. Clinton’s 45). . . .

Now I was curious, so I thought I’d check the numbers. According to the above graph, everyone is in one of the three categories of immigration attitudes (44% + 40% + 16% = 100%), so we can just take a weighted average to compute Hillary Clinton’s support among white voters in 2016:

whites for Clinton in 2016: .44*.21 + .40*.45 + .16*.72, which comes to 0.3876, that is, 39%.

And we can carefully read off the graph and do the same for 2012:

whites for Obama in 2012: .45*.29 + .42*.38 + .13*.50 = 0.3551, that’s 36%.

So, if you believe these numbers, then Clinton in 2016 did 3 percentage points better than Obama in 2012 among white voters.

What really happened? I don’t really know; all we have are surveys. Here’s what the exit polls say (here and here):


Taking total vote share, the exit polls have Clinton in 2016 doing 2 percentage points worse than Obama in 2012. As a proportion of two-party vote, their shares are almost identical, within rounding error (39.4% for Clinton, 39.8% for Obama).

I could be doing something wrong here—or maybe I’m just making a mistake trusting the exit polls here. But if we do believe that Clinton did worse, or no better than, Obama among white voters, then the numbers in that NYT op-ed just don’t add up.

In particular, there seems to be something wrong with the calculation, derived from the above graphs, that Obama had only 36% support among whites in 2012, given that the exit polls gave him 39% and our MRP analysis gave him 41% of the white vote in that year.

To say it another way: the op-ed’s conclusions are driven by two striking pattern in the above graph: the jump in Democratic support among pro-immigration voters, from 50% in 2012 to 72% in 2016, and the smaller but still substantial increase in Democratic support among immigration neutrals, from 38% to 45%. But these numbers imply that Clinton outperformed Obama by 3 percentage points among white voters—not a claim I’ve seen anywhere else.

And I’m not convinced by the claim in the op-ed that “Hillary Clinton did better in the election than she would have if immigration had not been so prominent an issue.”

So what happened with those goofy numbers? The researchers worked with a single survey, and surveys have sampling error. When, after an election is over, you use a survey to summarize election results, standard practice is to adjust to match the sample with the known vote totals: that’s what the exit polls do, and that’s what we do too. If you don’t make that adjustment, you get numbers that don’t add up to what actually happened.

Or maybe I just messed something up in my calculations. That’s an advantage of blogging—if I get something wrong, one of you is likely to correct me. A newspaper op-ed just sits there, with no one really taking responsibility for its correctness. This one looks so wrong, that I do think there’s a good chance that I’m just missing something obvious. If so, please let me know.

25 Comments

  1. Daniel Speyer says:

    NYT seems to be equivocating between “Americans” and “voters”. Those are very different categories. If, as anecdotes suggest, immigration drove turnout among Trump supporters, these graphs won’t show it.

  2. Copley says:

    … so a sloppy, anti-Trump political survey that the NY Times (and Washington Post today) really liked.
    Oh so difficult to imagine the newspaper editors’ mindset in eagerly publishing this stuff.

    Survey claims “a large, representative sample of the population of the United States”.
    Do you buy that? What was the Response Rate from the designated sample?

  3. yyw says:

    Even if all the numbers are correct, I don’t see how they can come to the absurdly strong conclusion “Hillary Clinton did better in the election than she would have if immigration had not been so prominent an issue.” There are so many alternative plausible explanations and interpretations for these numbers.

  4. Copley says:

    well, we’re discussing a very specific study here… not the general reputation of ANES.

    Apparently you have access to the full study.

    Please very briefly summarize that study’s methodology. It was likely a telephone survey with a single-digit response rate?
    Major “adjustments” were likely applied.

    • Andrew says:

      Copley:

      It looks like they just used the regular NES. But really you should ask the authors of the op-ed; it’s their study, and it looks to me like their numbers don’t quite make sense. Surveys like the NES can be useful, but you need to know their limitations, and you definitely want to adjust for known differences between sample and population.

    • Josh says:

      You can read about the ANES’s methodology, perhaps the most important survey in the study of American electoral studies, here:

      http://www.electionstudies.org/

      http://www.electionstudies.org/studypages/anes_timeseries_2016/anes_timeseries_2016.htm

      The 2016 ANES did not contain a telephone component. Rather, it combined a large face-to-face sample (as is done in all ANES Time Series surveys) with a separate online sample, both using probability based sampling. Per its methodology report the response rate was: “50 percent for the face-to-face mode and 44 percent for the Internet mode(AAPOR RR 1, the minimum
      —i.e., strictest—response rate”

  5. Terry says:

    Uh oh. A NYT op-ed. Before we take this too seriously, we should do some simple honesty checks.

    1. The data in the charts shows percentages that want immigration levels to decline, remain the same, or increase. An honest description of these people would be “pro-decreased-immigration”, “pro-current-immigration-levels”, and “pro-increased immigration”. But the authors characterize the first group as “anti-immigration”. This is dishonest. Almost everyone in this group is actually pro-immigration in that they are in favor of allowing a positive level of immigration. Analogously, when we talk about dieters, it is dishonest to say they are “anti-food”. Dieters are “anti-overeating” or “pro-calorie-reduction”.

    2. Note that the numbers show an overwhelming majority oppose increasing current levels of immigration (84%). Conversely, only a small group of extremists favor increasing immigration levels (16%). The authors ignore this obvious takeaway. Doesn’t fit the NYT narrative.

    3. The authors also ignore the obvious interpretation of the data. Hillary was seen as favoring looser immigration. (This is my recollection: that late in the campaign she basically said that if you can make it across the border, you are in. My recollection could be faulty though.) Since this is an extremist position, she was seen by many as an immigration extremist and that position hurt her. Trump was seen by many as being cautious about immigration and opposed to uncontrolled immigration. The NYT numbers clearly show that this was a mainstream opinion and so probably helped him.

    • Andrew says:

      Terry:

      In the few years leading up to 2016, it seems that immigration rates were decreasing; thus you could say that a majority of respondents—the 40% who preferred the current level of immigration and the 16% who preferred increased immigration—would have no reason to support a program of tightening existing immigration rules.

      Regarding the campaign, it was my impression that Clinton was supporting something similar to existing immigration policies, whereas Trump was supporting tighter rules. Hence it makes sense that, on that issue, Clinton would have the support of those who preferred the status quo or looser rules. But it could well be that voters who wanted a decrease in immigration levels felt more strongly about this issue, than did voters who supported the status quo.

      • Andrew’s take on the immigration preferences looks to be my own reading of the policy choices presented in different years leading up to the 2016 election.

        It also warrants the question of voter policy priorities during the lead up to the 2016 election.

        Sanders & Trump were able to capitalize on the ‘haves and have nots’ theme to suit their own constituencies. To suggest that the rhetorical zeal that each exhibited had resonance with voters.

      • David18 says:

        Andrew,
        There are two dishonesties in the immigration debate. One is the conflation of illegal aliens vs. legal immigrants.

        But second far, far less frequently discussed is that the level of immigration since 1970 has increase from less than 5% of the population to almost 14-15% today. The increase in the proportion of immigrants has brought about instability including economic instability for the working class who are generally the people to have their jobs displaced by generally “uneducated” immigrants, chiefly from Mexico.

        • Just as a general framework to the immigration debate, I would recommend Jerome Bruner’s Minding the Law & even Samuel Huntington’s Who Are We. Bruner’s draws on a series of race discriminatory cases brought before the Supreme Court, to illustrate the rhetorical conflict between established legal canon and stories on which judges/lawyers rely, to either impel or discourage specific appeals toward resolution of race discrimination cases. In short by way of ‘categorization’ of stories during the deliberative process. I mean to suggest that it’s this sort of examination of the dialectical process that we can gain more interesting and robust insights into the immigration questions that have been central particularly since the early 90’s.

          Samuel Huntiongton’s 1st few chapters of Who Are We, to which I’ve referred before, are also useful. They specifically focus on ‘identity’. Huntington represents, at least to me, the ethnocentric perspective about immigration.

          I’m sure there are many many books on the immigration debate. However few are as eloquently insightful, regardless of whether you agree with them or not.

          • David18 says:

            Sameera,
            I was hoping Andrew who wrote an entire book about these politics and whom is quantitatively oriented unlike many political scientists would have commented. I feel frustrated with many academics in political science because they tend to overanalyze instead of focusing on the main issue which is economic and that the working class in America has been suffering greatly from job and wage loss.

            You said:
            “Sanders & Trump were able to capitalize on the ‘haves and have nots’ theme to suit their own constituencies. To suggest that the rhetorical zeal that each exhibited had resonance with voters.”

            Democrats such as FDR, Truman, JFK, and LBJ used to focus on “bread and butter” issues of jobs and wages for the working class.

            The working class has been suffering from trade agreements (China in the WTO, Mexico with NAFTA) and from huge increase in uneducated immigrants since 1970 from less than 5% to about 14% of the population. There are an estimated 11 million illegal aliens whom employers love to hire since they don’t have to pay legal wages nor safe working environments saving lots of money and making even greater profits thus hurting the working class even more, especially in construction.

            As long ago as a decade before the election, Nobel Prize Economist and New York Times columnist Paul Krugman wrote:

            “Realistically, we’ll need to reduce the inflow of low-skill immigrants. Mainly that means better controls on illegal immigration.”

            But the Democrats totally ignored the wisdom of this left leaning Nobel Prize Winner whereas Trump followed his advice.

            The rest of the column is instructive. Had the Democrats listened to Krugman’s sound advice instead of leaving it to Trump to follow, they would have won easily.

            https://www.nytimes.com/2006/03/27/opinion/north-of-the-border.html

            Sanders also agreed with limiting immigration for economic reasons (correctly stating that was a Koch brothers notion) understanding the issue as Krugman had but the Democrats complained and made him change his position.

            Clinton lost the white woman vote to Trump, only won about one-third of the working class women and only won about half (51%) of white university educated women.

            Clinton and the Democratic Machine did not understand that working class parents were having trouble feeding and clothing their children and that increased immigration was making that worse (as Krugman has explained). Try to imagine if you can parents becoming desperate about how to feed, clothe, and house their children after they have lost jobs or had to take jobs that pay near minimum wage.

            Trump is totally a Democratic Party creation and thanks to the Democrats we will now have 2 conservative Supreme Court Justices as well as many lower court justices which will affect this country for years to come.

            Simply implementing eVerify nationally so that employers must hire those who are legally allowed to work here would make a substantial difference to the working class.

            The Democrats can win over Trump, but the only way to do so is to focus on the “bread and butter” issues of jobs and wages which it seems to me they are unlikely to do ignoring the advice of Krugman. I have not seen any indication at all that Democrats have learned from losing to Trump — if anything they appear to be more strident, less eager to help working class mothers and fathers house, feed, and clothe their children.

            I check the Amazon reviews of the two books you mentioned, but neither brought up the economic issues. Did they discuss them?

            • David18 says:

              Regarding the Koch brothers, Sanders made the comment that increased immigration is a Koch brothers notion and it is indeed true that the Koch brothers want increased immigration for lower wages. Unfortunately Democratic policy is aligned with Koch brothers wishes.

  6. Copley says:

    Hmmm … seems unusually difficult to pin down the specific methodology of this particular study/survey under discussion. Odd that neither NY Times or WashPost included a URL to this study– apparently readers are supposed to track down the study authors & interview them about their methodology. Prof Gelman makes a vague reference to some “online version” of this study, but without any link.

    @Josh: your NES links are rather unhelpful — they are 2016 general and unclear summaries of NES protocols. Apparently they ultimately use some type of internet panel survey for final data? Guess you can’t find the actual study either.

    Why all the mystery here?

    • Andrew says:

      Copley:

      I agree with you that the news articles should link to the original study. Beyond that, I don’t know what your problem is. When I wrote in my above post about an “online version,” I was referring to the online version of the newspaper op-ed, for which I did find a link. If you want to learn more about the survey, you can google it just like anyone else can. There’s no mystery.

  7. Terry says:

    Is the op-ed’s analysis capable of proving anything at all?

    Ignore for a second that Hillary got a smaller vote of the share than Obama and assume instead she got the same share.

    If we divide the electorate into three categories, then it is mathematically certain that an increase in any one group’s vote for one of the candidates must be offset by a decrease in some other group’s vote for the other candidate. (As Andrew notes, the vote percentages have to sum to one.) So doesn’t this “analysis” always “prove” that there was no net effect?

    Now, consider that that Hillary got a lower share of the vote than Obama. Shouldn’t the “analysis” show that the immigration question “hurt” Hillary because the net shift was negative?

    This latter point seems to be what Andrew is keying in on. I agree it is a problem, but it seems to be a symptom of a deeper problem.

  8. Terry says:

    Another fundamental problem with the analysis is that voters are switching between the categories over time, so the average voter (or the character of each pool) is changing over time. The op-ed talks about the groups as if they are an unchanging pool of voters over time, so all the interpretations are flawed.

  9. Terry says:

    The more I look, the more stunningly dishonest the authors seem.

    Notice how the author’s carefully omit that the “anti-immigration” group is almost 4 times larger than the “pro-immigration” group. Hence, they characterize Trump’s 8% improvement on the larger group as “only slightly better” while Hillary’s 22% improvement among the smaller group is characterized as “far-outpacing Kerry”. This gives the misleading impression that Hillary gained more votes than Trump did. Of course, when you take into account the size of the groups and look at the number of actual VOTES involved, you get a very different story. Trump’s vote gain appears (to me anyway) to be larger than Hillary’s vote gain (it is hard to tell what the actual numbers are).

    How can anyone trust anything these people say?

    We found that Mr. Trump did only slightly better than his Republican predecessors among anti-immigration whites. Among pro-immigration whites, however, Mrs. Clinton far outpaced John Kerry in 2004 and Barack Obama in 2008 and 2012. For example, Mr. Obama received the votes of 50 percent of pro-immigration whites in 2012, whereas Mrs. Clinton won the votes of 72 percent of that group in 2016 — a 22-point difference.

    Among anti-immigration whites, by contrast, Mr. Trump improved only marginally on Mitt Romney’s showing, 79 percent to 71 percent.

    • Terry says:

      To be fair, most editorials are this dishonest. This is not something specific to the NYT.

      But knowing this, we should not give these extrusions any benefit of the doubt. Our default prior should be an assumption of dishonesty.

  10. Curious says:

    I think the authors could have framed it better, but it looks to me like their primary claim is consistent with the following:

    Conditional on being White and having an ‘Immigration Policy Preference’ that is contrary to Trump’s policy of reducing the rate of immigration, the percentage of these voters that voted Democrat increased 15% between 2004 and 2016.

    2004: 61% of white voters that opposed more restrictive immigration voted for the Democrat candidate, John Kerry.
    2016: 76% of white voters that opposed more restrictive immigration voted for the Democrat candidate, Hillary Clinton.

    This seems consistent with a causal explanation grounded in Trump’s decision to use restrictive immigration as a wedge issue. In 2016, if a voter was against reducing the rate of immigration into the U.S., they were increasingly likely to vote for a Democrat.

    # R code is below

    # Voters by Party
    y2004_dem = 59028444
    y2004_rep = 62040610

    y2016_dem = 65845063
    y2016_rep = 62984828

    # Total Voters
    total_2004 = y2004_dem + y2004_rep
    total_2016 = y2016_dem + y2016_rep

    # Pct White Voters
    pct_white_2004 = 0.792
    pct_white_2016 = 0.733

    # Number of White Voters
    num_white_2004 = total_2004 * pct_white_2004
    num_white_2016 = total_2016 * pct_white_2016

    # Number of White Voters by Party
    num_white_2004_dem = 0.42 * num_white_2004
    num_white_2004_rep = 0.58 * num_white_2004

    num_white_2016_dem = 0.37 * num_white_2016
    num_white_2016_rep = 0.58 * num_white_2016

    # Immigration Policy Preference of All White Voters
    white_anti_immigration_pct_2004 = 0.48 # Reduce rate
    white_current_immigration_pct_2004 = 0.43 # Maintain rate
    white_pro_immigration_pct_2004 = 0.09 # Increase rate

    immigration_pref_pct_2004 = c(white_anti_immigration_pct_2004, white_current_immigration_pct_2004, white_pro_immigration_pct_2004)

    number_immigration_pref_white_2004 = immigration_pref_pct_2004 * num_white_2004
    number_immigration_pref_white_2004

    num_white_anti_immigration_2004_dem = number_immigration_pref_white_2004[1] * 0.28
    num_white_current_immigration_2004_dem = number_immigration_pref_white_2004[2] * 0.38
    num_white_pro_immigration_2004_dem = number_immigration_pref_white_2004[3] * 0.50

    num_white_immigration_pref_2004_dem = num_white_anti_immigration_2004_dem + num_white_current_immigration_2004_dem + num_white_pro_immigration_2004_dem
    num_white_2004_dem

    num_white_anti_immigration_2004_dem/num_white_immigration_pref_2004_dem
    num_white_current_immigration_2004_dem/num_white_immigration_pref_2004_dem
    num_white_pro_immigration_2004_dem/num_white_immigration_pref_2004_dem
    (num_white_current_immigration_2004_dem + num_white_pro_immigration_2004_dem)/num_white_immigration_pref_2004_dem

    white_anti_immigration_pct_2016 = 0.44
    white_current_immigration_pct_2016 = 0.40
    white_pro_immigration_pct_2016 = 0.16

    immigration_pref_pct_2016 = c(white_anti_immigration_pct_2016, white_current_immigration_pct_2016, white_pro_immigration_pct_2016)

    number_immigration_pref_white_2016 = immigration_pref_pct_2016 * num_white_2016
    number_immigration_pref_white_2016

    num_white_anti_immigration_2016_dem = number_immigration_pref_white_2016[1] * 0.21
    num_white_current_immigration_2016_dem = number_immigration_pref_white_2016[2] * 0.45
    num_white_pro_immigration_2016_dem = number_immigration_pref_white_2016[3] * 0.72

    num_white_immigration_pref_2016_dem = num_white_anti_immigration_2016_dem + num_white_current_immigration_2016_dem + num_white_pro_immigration_2016_dem
    num_white_2016_dem

    num_white_anti_immigration_2016_dem/num_white_immigration_pref_2016_dem
    num_white_current_immigration_2016_dem/num_white_immigration_pref_2016_dem
    num_white_pro_immigration_2016_dem/num_white_immigration_pref_2016_dem

    (num_white_current_immigration_2004_dem + num_white_pro_immigration_2004_dem)/num_white_immigration_pref_2004_dem
    (num_white_current_immigration_2016_dem + num_white_pro_immigration_2016_dem)/num_white_immigration_pref_2016_dem

    • Andrew says:

      Curious:

      But, as detailed in the above post, their numbers don’t seem to add up when comparing 2012 to 2016. So I think something’s wrong there.

    • Terry says:

      Conditional on being White and having an ‘Immigration Policy Preference’ that is contrary to Trump’s policy of reducing the rate of immigration, the percentage of these voters that voted Democrat increased 15% between 2004 and 2016.

      This seems consistent with a causal explanation grounded in Trump’s decision to use restrictive immigration as a wedge issue. In 2016, if a voter was against reducing the rate of immigration into the U.S., they were increasingly likely to vote for a Democrat.

      This is a long way from showing that Hillary was not hurt by the immigration issue.

      People who agreed with her immigration position were more likely to vote for her, while people who agreed with Trump’s immigration position were less likely to vote for her. This is pretty obvious stuff and does not show that immigration was a wash. We need to know how many people were influenced by immigration to know that.

      I still don’t see how the analysis can prove anything at all. If Hillary’s vote percentage was similar to Obama’s, then any shifts within voter subgroups (any voter subgroups at all, not just subgroups based on immigration) has to be approximately a wash in order to add up to the same total percentage for the Democrat. (It should even be a slight negative for Hillary since her vote percentage was smaller than Obama’s.) This is just simple math.

      The results you give are completely consistent with immigration being a huge negative for Hillary. For instance, Hillary may have lost 10% of the electorate to Trump because of her immigration position. But, another issue, say moral repugnance, could have cost Trump 10% of the electorate. The two factors together are a wash, even though immigration was a huge negative for Hillary.

      To prove their case, the authors have to tell us what Hillary’s percentage would have been absent the immigration issue. They don’t do this. They just show that all factors, taken together, were a wash. But we already knew this without dividing the electorate into subgroups because we already knew her total vote percentage.

    • Curious says:

      As Andrew pointed out the accuracy of these numbers is dependent on whether the Immigration preference numbers are correct (I don’t have access to the survey data). That said, if 2012 is added, there is ~ 4% positive change between 2012 and 2016 for Whites against more restrictive immigration and voted Democrat.

      # Voters by Party
      y2004_dem = 59028444
      y2004_rep = 62040610

      y2012_dem = 65915795
      y2012_rep = 60933504

      y2016_dem = 65845063
      y2016_rep = 62984828

      # Total Voters
      total_2004 = y2004_dem + y2004_rep
      total_2012 = y2012_dem + y2012_rep
      total_2016 = y2016_dem + y2016_rep

      # Pct White Voters
      pct_white_2004 = 0.792
      pct_white_2012 = 0.733
      pct_white_2016 = 0.733

      # Number of White Voters
      num_white_2004 = total_2004 * pct_white_2004
      num_white_2012 = total_2012 * pct_white_2012
      num_white_2016 = total_2016 * pct_white_2016

      # Number of White Voters by Party
      num_white_2004_dem = 0.42 * num_white_2004
      num_white_2004_rep = 0.58 * num_white_2004

      num_white_2012_dem = 0.41 * num_white_2012
      num_white_2012_rep = 0.59 * num_white_2012

      num_white_2016_dem = 0.37 * num_white_2016
      num_white_2016_rep = 0.58 * num_white_2016

      # Immigration Policy Preference of All White Voters

      # 2004
      white_anti_immigration_pct_2004 = 0.48 # Reduce rate
      white_current_immigration_pct_2004 = 0.43 # Maintain rate
      white_pro_immigration_pct_2004 = 0.09 # Increase rate

      immigration_pref_pct_2004 = c(white_anti_immigration_pct_2004, white_current_immigration_pct_2004, white_pro_immigration_pct_2004)

      number_immigration_pref_white_2004 = immigration_pref_pct_2004 * num_white_2004
      number_immigration_pref_white_2004

      num_white_anti_immigration_2004_dem = number_immigration_pref_white_2004[1] * 0.28
      num_white_current_immigration_2004_dem = number_immigration_pref_white_2004[2] * 0.38
      num_white_pro_immigration_2004_dem = number_immigration_pref_white_2004[3] * 0.50

      num_white_immigration_pref_2004_dem = num_white_anti_immigration_2004_dem + num_white_current_immigration_2004_dem + num_white_pro_immigration_2004_dem
      num_white_2004_dem

      num_white_anti_immigration_2004_dem/num_white_immigration_pref_2004_dem
      num_white_current_immigration_2004_dem/num_white_immigration_pref_2004_dem
      num_white_pro_immigration_2004_dem/num_white_immigration_pref_2004_dem
      (num_white_current_immigration_2004_dem + num_white_pro_immigration_2004_dem)/num_white_immigration_pref_2004_dem

      # 2012
      white_anti_immigration_pct_2012 = 0.44
      white_current_immigration_pct_2012 = 0.40
      white_pro_immigration_pct_2012 = 0.16

      immigration_pref_pct_2012 = c(white_anti_immigration_pct_2012, white_current_immigration_pct_2012, white_pro_immigration_pct_2012)

      number_immigration_pref_white_2012 = immigration_pref_pct_2012 * num_white_2012
      number_immigration_pref_white_2012

      num_white_anti_immigration_2012_dem = number_immigration_pref_white_2012[1] * 0.21
      num_white_current_immigration_2012_dem = number_immigration_pref_white_2012[2] * 0.38
      num_white_pro_immigration_2012_dem = number_immigration_pref_white_2012[3] * 0.50

      num_white_immigration_pref_2012_dem = num_white_anti_immigration_2012_dem + num_white_current_immigration_2012_dem + num_white_pro_immigration_2012_dem
      num_white_2012_dem

      num_white_anti_immigration_2012_dem/num_white_immigration_pref_2012_dem
      num_white_current_immigration_2012_dem/num_white_immigration_pref_2012_dem
      num_white_pro_immigration_2012_dem/num_white_immigration_pref_2012_dem

      # 2016
      white_anti_immigration_pct_2016 = 0.44
      white_current_immigration_pct_2016 = 0.40
      white_pro_immigration_pct_2016 = 0.16

      immigration_pref_pct_2016 = c(white_anti_immigration_pct_2016, white_current_immigration_pct_2016, white_pro_immigration_pct_2016)

      number_immigration_pref_white_2016 = immigration_pref_pct_2016 * num_white_2016
      number_immigration_pref_white_2016

      num_white_anti_immigration_2016_dem = number_immigration_pref_white_2016[1] * 0.21
      num_white_current_immigration_2016_dem = number_immigration_pref_white_2016[2] * 0.45
      num_white_pro_immigration_2016_dem = number_immigration_pref_white_2016[3] * 0.72

      num_white_immigration_pref_2016_dem = num_white_anti_immigration_2016_dem + num_white_current_immigration_2016_dem + num_white_pro_immigration_2016_dem
      num_white_2016_dem

      num_white_anti_immigration_2016_dem/num_white_immigration_pref_2016_dem
      num_white_current_immigration_2016_dem/num_white_immigration_pref_2016_dem
      num_white_pro_immigration_2016_dem/num_white_immigration_pref_2016_dem

      (num_white_current_immigration_2004_dem + num_white_pro_immigration_2004_dem)/num_white_immigration_pref_2004_dem
      (num_white_current_immigration_2012_dem + num_white_pro_immigration_2012_dem)/num_white_immigration_pref_2012_dem
      (num_white_current_immigration_2016_dem + num_white_pro_immigration_2016_dem)/num_white_immigration_pref_2016_dem

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