The First Derivative of the Wisdom of Crowds

February 2, 2019
Posted by Jay Livingston

If this is Superbowl weekend, then the Socioblog’s fancy must be turning to thoughts of the wisdom of crowds vs. the smart money.  It’s a question I have returned to several times since the first year this blog was on the field. (See. for example, this post about the 2010 Superbowl.)

The “wisdom of crowds” is like the Ask-the-Audience option in “Who Wants to Be a Millionaire.” The “smart money” is like Phone-a-Friend — a friend who knows a lot about the subject.

The trouble with the wisdom of crowds is that sometimes the crowd is wrong, as it was in the 2007 NFC championship game between the Bears and the Saints that I blogged about at the time (here.)

Now, a trio of academics — John McCoy (marketing), Dražen Prelec (management), and  H. Sebastian Seung (neuroscience) — has a variation that allows you to derive the right answer from the crowd even when the crowd is wrong. You might call it the first derivative of crowd wisdom.

Is Philadelphia the capital of Pennsylvania? 

Suppose you don’t know, and you ask the crowd.

The correct answer is no. The capital is Harrisburg. But many people think it is, because Philadelphia is a large, populous city. Most people know about Philadelphia. When you ask that question to a crowd of people, as we did with MIT students, only about a third of the crowd gets the correct answer.*

Yes is the popular answer. The crowd, by two-to-one, says Yes, Philadelphia is the capital. The crowd is wrong. The capital of Pennsylvania is Harrisburg. So much for the wisdom of crowds.

Wait, not so fast, say McCoy and his colleagues. Let’s also ask another question: “What percent of people do you think will answer No to this question?” The average estimate is 23%. But in fact, 33% answer No. This makes No a “surprisingly popular” answer, surprising in that more people than expected say No. It’s as though you are taking the first derivative of crowd wisdom rather than the wisdom function itself.

If you went with the popular answer, you’d say Yes and be wrong. But if you go with the derivative — the “surprisingly popular” answer —  you’ll get it right.

McCoy sees applications of this to all kinds of forecasts — the market for some product, the price of gold, voting, He doesn’t mention the Superbowl. Right now, about 25% of bettors think that the Rams will win or that they will lose by 2 points or less. But suppose we asked all bettors, “What fraction of people do you think are betting the Rams?” If they guessed that only 10% of them are backing the Rams, then the Rams would be the “surprisingly popular” choice, and you would be a fool not to put down a grand to win $1250. Alas, I know of no such surveys. Besides, I don’t trust Belichick.

Two other thoughts:
First, McCoy’s makes the concept harder to understand by choosing an example where No is right. “Is No the correct answer?” “Yes, No is right.”

Second, I was stunned that two-thirds of MIT students did not know the capital of fifth most populous state in the country. Look, people, we’re not asking about Pierre or Carson City. This is not rocket science. And now I get the feeling that at MIT a question about rocket science might have gotten a higher proportion of correct answers.

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*From an interview with McCoy on a Wharton School podcast. An article by Prelec, Seung, and McCoy in Nature is here behind a paywall.

Michel Legrand — 1932 - 2019

January 28, 2019
Posted by Jay Livingston

As a callow youth, I dismissed Michel Legrand as a guy who wrote pretty tunes and scores. In fact, he did write 200 or more scores for movies and TV. Then I heard Legrand Jazz (1958) with his arrangements for three different groups — 1. a big band, 2. a group centered on Ben Webster and four trombones, and 3. the core of Miles Davis’s 1958 sextet (Miles, Coltrane, Bill Evans, Paul Chambers), Phil Woods instead of Cannonball, plus a few other instruments including flute and harp.

The tunes were  eleven jazz classics, from Dixieland (Louis Armstrong’s “Wild Man Blues” ) through swing (Benny Goodman, “Stompin’ at the Savoy”) to bebop (Dizzy’s “Night in Tunisia”). The arrangements were “far out” for the time, and even 60 years later, they hold up well.

Legrand later described the recording session with the Miles.

Everyone said to me: “Miles will come to the meeting and stand near the door, keeping his trumpet in his closed case. He will listen for five minutes, and if he likes music, he will sit down, open his case, and play. If he does not like, he will leave and he will never again contact you.” I was so afraid that I had flare-ups of sweat! I started rehearsing with the orchestra. The door opened, and Miles listened by the door for five minutes. Then he sat down, opened his case and began to play. After the first catch, he asked me, “Michel, is my game [playing] suitable?” That is how it all began.

Here is that group playing Fats Waller’s “Jitterbug Waltz.”

The record went out of print and out of sight. I rarely met anyone, jazzers included, who knew of it. It was something of a collector’s item. Somewhere along the line, I lost my copy and wound up paying the equivalent today of about $75 for a used copy. Eventually, the album was re-issued as a CD, and now you can stream it anytime, anywhere.

Flashback Tuesday — MLK - AOC Edition

January 22, 2019
Posted by Jay Livingston

Alexandria Ocasio-Cortez was on Colbert last night. Colbert asked her about accusations that she was divisive. Said AOC:

Today is Martin Luther King day, and people called Martin Luther King divisive in his time. We forget that he was wildly unpopular when he was advocating for the Civil Rights Act.

She was right, sort of. King’s “unfavorables” were in the 40-45% range in the years AOC is talking about, much lower than Trump’s “unfavorables” today. But the favorable/unfavorable ratio did not turn positive until after he had been assassinated.

Here is part of a blog post I did seven years ago. The latter part of the post, about Reagan and Buckley, is not exactly relevant, but I’m leaving it in as a corrective to possible inaccuracies about them too.

*     *     *     *     *     *     *    

In August, Gallup (here) published some of their polling from the 1960s. The contrast with opinions today, when only 4% are unfavorable, is remarkable.

(Click on the chart for a larger view.)

(Note: these results include all races. The data for Whites only would surely show a higher percent unfavorable and a lower percent favorable.)

Except for 1966, the total favorable and unfavorable are fairly close.  (The change in 1966 is a result of King’s opposition to the Vietnam war.  He was right about that too.)  But of those with strong opinions, the “highly unfavorables” always outnumber the “highly favorables.” 

The unfavorables weren’t just those rabid Southern whites so familiar from the historical news footage. The same ideas could be found among seemingly temperate, sophisticated, and intellectual conservatives. Affable Ronald Reagan opposed the Civil Rights Act of 1964 and the Voting Rights Act of 1965. 

In 1957, William F. Buckley, Jr. supported the suppression of black votes in the South

The central question that emerges . . . is whether the White community in the South is entitled to take such measures as are necessary to prevail, politically and culturally, in areas in which it does not predominate numerically? The sobering answer is Yes – the White community is so entitled because, for the time being, it is the advanced race.  (The full article is excerpted by Brad DeLong here.)

That was before the rise of the Civil Rights movement.  Six years later, when Dr. King had come to prominence, a black church in Birmingham was firebombed.  Four young girls died.  Here is how Buckley’s National Review responded.

The fiend who set off the bomb does not have the sympathy of the white population in the South; in fact, he set back the cause of the white people there so dramatically as to raise the question whether in fact the explosion was the act of a provocateur – of a Communist, or of a crazed Negro. Some circumstantial evidence lends a hint of plausibility to that notion, especially the ten-minute fuse (surely a white man walking away from the church basement ten minutes earlier would have been noticed?). And let it be said that the convulsions that go on, and are bound to continue, have resulted from revolutionary assaults on the status quo, and a contempt for the law, which are traceable to the Supreme Court’s manifest contempt for the settled traditions of Constitutional practice. [emphasis added]

The suggestion that the firebombing was committed by “a communist or a crazed Negro” is a fantasy of pure desperation and wish-fulfillment.  Note also NR’s concern for “the cause of white people.”  As for the church bombing, the beatings, the tortures, the murders, and other acts of terrorism (“convulsions” as the NR calls them), committed against blacks and civil rights workers, just blame it all on the Supreme Court. 

All this would be laughable if the events were not of such grave importance and if the commentary were from some obscure, racist corner.  But National Review, then as now, was the main voice of intellectual conservatism. 

Eugene Volokh, in an appreciation of Buckley (here), notes that it wasn’t until the late 1960s, after the passage of the major civil rights laws and probably after the King and RFK assassinations, that Buckley and NR finally gave up defending segregation.  Volokh also says, approvingly,

Buckley tried very hard to create a genial and friendly image for conservatism as opposed to one that projected anger, intolerance, and rage.

Michael Harrington put it somewhat differently:

William Buckley is an urbane front man for some of the most vicious emotions in this country.

Confidence Games

January 19, 2019
Posted by Jay Livingston

Timing is crucial in comedy. In can be important in survey research as well. If you ask about satisfaction with government, and you take your survey at a historical moment when the Republican party controls the government, don’t be surprised if Republicans are more satisfied than Democrats. But also don’t write up your findings to imply that this means that Republicans have a deep and abiding faith in American institutions.

We’ve been here before, not with “satisfaction,” but with something similar — happiness. People who make claims about the relation between happiness and political views — people like Arthur Brooks, for example — often don’t bother to look at which party was holding sway at the time the survey they’re using was done. But that context matters a lot, especially now that the country has become so partisan and polarized, with people remaining loyal to their party the way sports fans are loyal to their team. In a post two years ago inspired by a Brooks column, I put it this way

When you’re talking about the relation between political views and happiness, you ought to consider who is in power. Otherwise, it’s like asking whether Yankee fans are happier than RedSox fans without checking the AL East standings. [the full post is here.]

I had a similar reaction to a recent thread on Twitter about who has lost confidence in American institutions. The answer is: everybody. But some more than others.  Patrick Egan of NYU looked at the “confidence” items in the General Social Survey and created these graphs showing the average confidence in twelve different institutions.

(Click on an image for a larger view.)

Confidence has dropped among all categories. But the steepest decline has come among non-college Whites. Their overall level of confidence is the lowest of any of these groups. They are also the strongest supporters of Donald Trump. This reinforces the image of the core Republican constituency — Trump’s staunchest supporters — as dissatisfied, even resentful. They have lost confidence in traditional American institutions, and they acclaim the strong outsider who could bring sweeping changes.

In response, Joshua Tucker posted a link to a report he was co-author on — the American Institutional Confidence Poll (AICP) from the Baker Center for Leadership & Governance at Georgetown University. The AICP found that demographic characteristics didn’t make much difference. Politics did. Here is AICP’s Number One Key Finding:

Why the discrepancy between the GSS data the AICP conclusions? I wondered if it might be the sample. It wasn’t.

The interviews were conducted online from June 12 to July 19, 2018, by the survey firm YouGov. The sample includes 3,000 respondents from the U.S. general population. Additionally, the poll includes samples of 800 African-Americans, 800 Latinx Americans, and 800 Asian Americans.

Their sample, as they note elsewhere, is larger than that of most political surveys, plus the  oversampling of smaller populations they want to have good data about. No problem there.

But what about the timing? We know that on November 1, 2016, Democrats were much more likely than were Republicans to say that the economy looked good. Two weeks later, those positions were reversed. The economy did not change in those two weeks. The occupancy of the White House did.

The AICP survey was done last summer, months before the midterm elections, when the GOP controlled the White House, the Senate, the House, and the Supreme Court. That seems like kind of an important fact, but to find it, you have to scroll down to the methodology notes at the end of the report. 

Even in the GSS graphs, Egan has drawn a trend line that smooths out these shifts that are possibly caused by electoral changes. Egan also has lumped together twelve institutions. Separating them in to categories (e.g,. government, non-government) might allow us to see even sharper demographic differences.

The AICP, on the other hand, does report about confidence in specific institutions, twenty in all. The authors conclude that “confidence in institutions is largely driven by party affiliation.” They neglect the corollary: who has confidence in which institution can shift quickly when an election changes the party in power. This volatility makes it a bit misleading to talk about confidence in “institutions” as though people were thinking about them in the abstract. For example, the authors say, “The executive branch is the institution in which Democrats have the least confidence, while Republicans rank it the fourth highest.” Surely this difference is not about what people think of “the executive branch.” It’s about Donald Trump. These days, isn’t everything?