Recall this analysis

We’re now several years into the trend of “data journalism,” and I’m still not sure whether I like it. On the one hand, it’s nice to see reporters writing about numbers; on the other hand, numbers typically aren’t their strong suit. Too often we get articles whose sole purpose seems to be to show off some colorful graphs.

Last Thursday, the San Francisco Chronicle published this article, entitled “If California was made up of just these 35 counties, Gavin Newsom would have been recalled.” That a similarly-titled article could be written about almost any election—”Some people voted for, others against”—didn’t prevent the Chronicle from going with this dog-bites-man story.

The article starts with this long bar chart of counties:

SF Chronicle bar chart

The counties are ordered according to their percent of Yes votes (in favor of recall), and the bars represent the cumulative percentage of Yes and No votes as we include the votes of each county in turn. If you think that’s a contrived and tortuous way to present the data, you’re not alone. The reporter, Nami Sumida, spent five paragraphs explaining it, and I’ll bet those paragraphs were written at the insistence of confused and math-averse editors.

The flip from cumulative Yes to cumulative No comes when we add the Ventura County vote. If you put the effort into counting down the list, Lassen through San Diego is 35 counties, hence the title of the piece.

If you’d like to see the numerical results for each county, the article gives them to you in a series of tables that look like this:

SF Chronicle table

The colors in this table made me see red. Or maybe green. Using the same color to represent contradictory data is just inexcusably sloppy work. Maybe if the editors hadn’t been so confused by the construction of the bar chart, they would have noticed that Sumida flipped the meaning of red and green in the middle of the article.

The article also includes this stylized map of California, with each of the counties represented by a hexagon in its approximate geographic location and the titular 35 counties tinted.1

SF Chronicle map

This use of equal-sized hexagons in place of actual geographic shapes has become a popular way to make colored maps without over-representing large areas. In this case, of course, it has the effect of under-representing populous areas, making it seem as if each county counts as much as every other county in the recall vote. This will be a surprise to both the 10,000,000 residents of Los Angeles County and the 1,200 residents of Alpine County.

You might look at the map and think that 35 counties had a majority of Yes votes. I wouldn’t blame you if you did. That’s normally how people use color when showing election results on a map. But six of these counties—San Diego, Mono, San Joaquin, Nevada, Orange, and San Bernardino—had a majority of No votes. It’s just that if you add their votes to the 29 counties that really did have a majority of Yes votes, you still end up with a Yes majority.

Are there other ways to take a subset of California’s 58 counties and get a majority of votes in favor of recall? God, yes. Even if we restrict ourselves to subsets of 35, there are \(8.8\times10^{15}\) (that’s 8.8 quadrillion) ways to combine 58 things, taking them 35 at a time. Only a small fraction of these combinations will yield a majority of Yes votes, but even a small fraction of 8.8 quadrillion is a big number. Taking the election results (as of October 1) from the California Secretary of State’s office and using the combinations function from Python’s itertools module, I wrote a short bit of brute force code and in a few minutes found over ten million combinations that did the trick.2 And you don’t have to use a subset of exactly 35 counties.

This is perhaps the weirdest thing about the article. It’s clearly intended to slice up California in a way to show that Newsom is unpopular across some large chunk of the state. What other purpose is served by including counties that voted to retain him? So why not go for the gusto? Why not work out the largest number of counties which, when added together, would have arrived at a majority for recall?

It isn’t hard to do. Instead of ordering the counties by their percentage of Yes votes, order them by their margin of Yes votes. Like this:

County Yes No Margin CMargin
1 Kern 117,584 73,781 43,803 43,803
2 Shasta 49,141 21,655 27,486 71,289
3 Placer 103,192 80,088 23,104 94,393
4 Tulare 63,680 40,640 23,040 117,433
5 El Dorado 58,062 39,743 18,319 135,752
6 Stanislaus 81,456 68,085 13,371 149,123
7 Tehama 15,958 6,186 9,772 158,895
8 Madera 25,638 16,233 9,405 168,300
9 Sutter 20,216 11,484 8,732 177,032
10 Kings 19,710 11,242 8,468 185,500
11 Riverside 362,958 355,630 7,328 192,828
12 Fresno 130,580 123,433 7,147 199,975
13 Yuba 14,839 7,784 7,055 207,030
14 Butte 42,703 35,707 6,996 214,026
15 Lassen 8,532 1,600 6,932 220,958
16 Calaveras 14,559 8,018 6,541 227,499
17 Tuolumne 15,832 9,850 5,982 233,481
18 Amador 12,895 6,957 5,938 239,419
19 Siskiyou 11,282 6,951 4,331 243,750
20 Glenn 6,317 2,479 3,838 247,588
21 Merced 29,926 27,517 2,409 249,997
22 Plumas 5,106 3,008 2,098 252,095
23 Mariposa 5,375 3,376 1,999 254,094
24 Colusa 3,977 1,996 1,981 256,075
25 Modoc 2,508 706 1,802 257,877
26 Del Norte 5,137 3,454 1,683 259,560
27 Inyo 4,128 3,496 632 260,192
28 Trinity 2,699 2,106 593 260,785
29 Sierra 1,064 616 448 261,233
30 Alpine 218 340 -122 261,111
31 Mono 2,186 2,719 -533 260,578
32 Lake 3,728 5,605 -1,877 258,701
33 San Bernardino 282,659 285,596 -2,937 255,764
34 San Benito 9,181 12,595 -3,414 252,350
35 Nevada 25,273 29,702 -4,429 247,921
36 Imperial 12,193 18,210 -6,017 241,904
37 Mendocino 11,870 21,852 -9,982 231,922
38 San Luis Obispo 47,882 59,364 -11,482 220,440
39 Humboldt 15,442 28,810 -13,368 207,072
40 San Joaquin 79,097 94,109 -15,012 192,060
41 Napa 17,747 37,134 -19,387 172,673
42 Yolo 24,273 51,405 -27,132 145,541
43 Santa Barbara 57,355 92,905 -35,550 109,991
44 Orange 547,685 586,457 -38,772 71,219
45 Solano 58,277 97,839 -39,562 31,657
46 Monterey 38,169 80,664 -42,495 -10,838
47 Ventura 136,389 182,158 -45,769 -56,607
48 Santa Cruz 24,188 86,669 -62,481 -119,088
49 Marin 22,701 105,508 -82,807 -201,895
50 Sonoma 45,443 142,866 -97,423 -299,318
51 Sacramento 218,432 327,482 -109,050 -408,368
52 San Mateo 64,250 226,891 -162,641 -571,009
53 San Diego 502,226 671,379 -169,153 -740,162
54 Contra Costa 128,259 321,242 -192,983 -933,145
55 San Francisco 47,053 292,180 -245,127 -1,178,272
56 Santa Clara 166,827 468,486 -301,659 -1,479,931
57 Alameda 108,081 465,901 -357,820 -1,837,751
58 Los Angeles 853,398 2,072,346 -1,218,948 -3,056,699

Each county’s CMargin column is the cumulative margin from the top of the list. By ordering them this way, the Yes margin gets nibbled away as slowly as possible as you move down the list. As you can see, if the Chronicle had ordered the counties this way, they could’ve written an article with the headline “If California was made up of just these 45 counties, Gavin Newsom would have been recalled.”

And we still wouldn’t be any smarter.


  1. And yes, they’re tinted green, another example of changing the meaning of colors mid-article. 

  2. How long would it take to check all 8.8 quadrillion combinations by brute force? I don’t know, but it’s likely to be hundreds of years, and I didn’t feel like waiting that long.