The Innumerate American

19 Feb

In answering a question, scientists sometimes collect data that answers a different, sometimes yet more important question. And when that happens, scientists sometimes overlook the easter egg. This recently happened to me, or so I think.

Kabir and I recently investigated the extent to which estimates of motivated factual learning are biased (see here). As part of our investigation, we measured numeracy. We asked American adults to answer five very simple questions (the items were taken from Weller et al. 2002):

  1. If we roll a fair, six-sided die 1,000 times, on average, how many times would the die come up as an even number? — 500
  2. There is a 1% chance of winning a $10 prize in the Megabucks Lottery. On average, how many people would win the $10 prize if 1,000 people each bought a single ticket? — 10
  3. If the chance of getting a disease is 20 out of 100, this would be the same as having a % chance of getting the disease. — 20
  4. If there is a 10% chance of winning a concert ticket, how many people out of 1,000 would be expected to win the ticket? — 100
  5. In the PCH Sweepstakes, the chances of winning a car are 1 in a 1,000. What percent of PCH Sweepstakes tickets win a car? — .1%

The average score was about 57%, and the standard deviation was about 30%. Nearly 80% (!) of the people couldn’t answer that 1 in a 1000 chance is .1% (see below). Nearly 38% couldn’t answer that a fair die would turn up, on average, an even number 500 times every 1000 rolls. 36% couldn’t calculate how many people out of a 1000 would win if each had a 1% chance. And 34% couldn’t answer that 20 out of 100 means 20%.

If people have trouble answering these questions, it is likely that they struggle to grasp some of the numbers behind how the budget is allocated, or for that matter, how to craft their own family’s budget. The low scores also amply illustrate that the education system fails Americans.

Given the importance of numeracy in a wide variety of domains, it is vital that we pay greater attention to improving it. The problem is also tractable — with the advent of good self-learning tools, it is possible to intervene at scale. Solving it is also liable to be good business. Given numeracy is liable to improve people’s capacity to count calories, make better financial decisions, among other things, health insurance companies could lower premiums in lieu of people becoming more numerate, and lending companies could lower interest rates in exchange for increases in numeracy.

Town Level Data on Cable Operators and Cable Channels

12 Sep

I am pleased to announce the release of TV and Cable Factbook Data (1997–2002; 1998 coverage is modest). Use of the data is restricted to research purposes.

Background

In 2007, Stefano DellaVigna and Ethan Kaplan published a paper that used data from Warren’s Factbook to identify the effect of introduction of Fox News Channel on Republican vote share (link to paper). Since then, a variety of papers exploiting the same data and identification scheme have been published (see, for instance, Hopkins and Ladd, Clinton and Enamorado, etc.)

In 2012, I embarked on a similar such project—trying to use the data to study the impact of introduction of Fox News Channel on attitudes and behaviors related to climate change. However, I found the original data to be limited—DellaVigna and Kaplan had used a team of research assistants to manually code a small number of variables for a few years. So I worked on extending the data. I planned on extending the data in two ways: adding more years, and adding ‘all’ the data for each year. To that end, I developed custom software. The data collection and parsing of a few thousand densely packed, inconsistently formatted, pages (see below) to a usable CSV (see below) finished sometime early in 2014. (To make it easier to create a crosswalk with other geographical units, I merged the data with Town lat/long (centroid) and elevation data from http://www.fallingrain.com/world/US/.)

Sample Page
cable_factbook_example
Snapshot of the Final CSV
csv_snap

Soon after I finished the data collection, however, I became aware of a paper by Martin and Yurukoglu. They found some inconsistencies between the Nielsen data and the Factbook data (see Appendix C1 of paper), tracing the inconsistencies to delays in updating the Factbook data—“Updating is especially poor around [DellaVigna and Kaplan] sample year. Between 1999 and 2000, only 22% of observations were updated. Between 1998 and 1999, only 37% of observations were updated.” Based on their paper, I abandoned the plan to use the data, though I still believe the data can be used for a variety of important research projects, including estimating the impact of introduction of Fox News. Based on that belief, I am releasing the data.

The Value of Money: Learning from Experiments Offering Money for Correct Answers

10 Jul

Papers at hand:

Prior et al. and Bullock et al.


Two empirical points that we learn from the papers:

1. Partisan gaps are highly variable and the mean gap is reasonably small (without money, control condition). See also: Partisan Retrospection?
(The point is never explicitly commented on by either of the papers. The point has implications for proponents of partisan retrospection.)

2. When respondents are offered money for the correct answer, partisan gap reduces by about half on average.


Question in front of us: Interpretation of point 2.


Why are there partisan gaps on knowledge items?

1. Different Beliefs: People believe different things to be true: People learn different things. For instance, Republicans learn that Obama is a Muslim, and Democrats that he is an observant Christian. For a clear exposition on what I mean by ‘beliefs’, see Waters of Casablanca.

2. Systematic Lazy Guessing: The number one thing people lie about on knowledge items is that they have the remotest clue about the question being asked. And the reluctance to acknowledge ‘Don’t Know’ is in itself a serious point worthy of investigation and careful interpretation. (My sense is that it tells us something important about humans.) When people guess on items with partisan implications, they may use inference rules. For instance, a Republican, when asked about whether unemployment rate under Obama had increased or decreased, may reason that Obama is a socialist and since socialism is bad policy, it must have increased the unemployment rate.

3. Cheerleading: Even when people know that things that reflect badly on their party happened, they lie. (I will be surprised if this is common.)


The Quantity of Interest: Different Beliefs.
We do not want: Different Beliefs + Systematic Lazy Guessing


Why would money reduce partisan gaps?

1. Reducing Systematic Lazy Guessing: Bullock et al. use pay for DK, offering people small incentive (much smaller than pay for correct) to confess to ignorance. Estimate should be closer to the quantity of interest: ‘Different Beliefs.’

2. Considered Guessing: On being offered money for the correct answer, respondents replace ‘lazy’ (for a bounded rational human —optimal) partisan heuristic described above with more effortful guessing. Replacing Systematic Lazy Guessing with Considered Guessing is good to the extent that Considered Guessing is less partisan. If it is so, the estimate will be closer to the quantity of interest: ‘Different Beliefs.’ (Think of it as a version of correlated measurement error. And we are now replacing systematic measurement error with error that is more evenly distributed, if not ‘randomly’ distributed.)

3. Looking up the Correct Answer: People look up answers to take the money on offer. Both papers go some ways to show that cheating isn’t behind the narrowing of the partisan gap. Bullock et al. use ‘placebo’ questions, and Prior et al. timing etc.

4. Reduces Cheerleading: For respondents for whom utility from lying < $, they stop lying. Estimate will be closer to the quantity of interest: 'Different Beliefs.'

5. Demand Effects: Respondents take the offer of money as a cue that their instinctive response isn’t correct. Estimate may be further away from the quantity of interest: ‘Different Beliefs.’

Some Facts About PolitiFact

27 May

I assessed PolitiFact on:

1. Imbalance in scrutiny: Do they vet statements by Democrats or Democratic-leaning organizations more than statements Republicans or Republican-leaning organizations?

2. Batting average by party: Roughly n_correct/n_checked, but instantiated here as mean Politifact rating.

To answer the questions, I scraped the data from PolitiFact and independently coded and appended data on the party of the person or organization covered. (Feel free to download the script for scraping and analyzing the data, scraped data and data linking people and organizations to party from the GitHub Repository.)

Until now, Politifact has checked veracity 3,859 statements by 703 politicians and organizations. Of these, I was able to establish the partisanship of 554 people and organizations. I restrict the analysis to 3,396 statements by organizations and people whose partisanship I could establish and who lean either towards the Republican or Democratic party. I code the Politifact 6-point True to Pants on Fire scale (true, mostly-true, half-true, barely-true, false, pants-fire) linearly so that it lies between 0 (pants-fire) and 1 (true).

Of the 3,396 statements, about 44% (n = 1506) of the statements checked by PolitiFact are by Democrats or Democratic-leaning organizations. Rest of the roughly 56% (n = 1890) are by Republicans or Republican-leaning organizations. The average PolitiFact rating of statements by Democrats or Democratic-leaning organizations (batting average) is .63; it is .49 for statements by Republicans or Republican-leaning organizations.

To check whether the results are driven by some people receiving a lot of scrutiny, I tallied the total number of statements investigated for each person. Unsurprisingly, there is a large skew, with a few prominent politicians receiving a bulk of the attention. For instance, PolitiFact investigated more than 500 claims by Barack Obama alone. The figure below plots the total number of statements investigated for thirty politicians receiving the most scrutiny.
t30_total_investigated

If you take out Barack Obama, the percentage of Democrats receiving scrutiny reduces to 33.98%. More generally, limiting ourselves to the bottom 90% of the politicians in terms of scrutiny received, the share of Democrats is about 42.75%.

To analyze whether there is selection bias in covering politicians who say incorrect things more often, I estimated the correlation between the batting average and the total number of statements investigated. The correlation is very weak and does not appear to vary systematically by party. Accounting for the skew by taking the log of the total statements or by estimating a rank ordered correlation has little effect. The figure below plots batting average as a function of total statements investigated.

batting_average_total_investigated

Caveats About Interpretation

To interpret the numbers, you need to make two assumptions:

1. The number of statements made by Republicans and Republican-leaning persons and organizations is the same as that made by people and organizations on the left.

2. Truthiness of statements by Republican and Republican-leaning persons and organizations is the same as that of left-leaning people and organizations.

Congenial Invention and the Economy of Everyday (Political) Conversation

31 Dec

Communication comes from the Latin word communicare, which means `to make common.’ We communicate not only to transfer information, but also to establish and reaffirm identities, mores, and meanings. (From my earlier note on a somewhat different aspect of the economy of everyday conversation.) Hence, there is often a large incentive for loyalty. More generally, there are three salient aspects to most private interpersonal communication about politics — shared ideological (or partisan) loyalties, little knowledge of, and prior thinking about political issues, and a premium for cynicism. The second of these points — ignorance — cuts both ways. It allows for the possibility of getting away with saying something that doesn’t make sense (or isn’t true). And it also means that people need to invent stuff if they want to sound smart etc. (Looking stuff up is often still too hard. I am often puzzled by that.)

But don’t people know that they are making stuff up? And doesn’t that stop them? A defining feature of humans is overconfidence. And people often times aren’t aware of the depth of the wells of their own ignorance. And if it sounds right, well it is right, they reason. The act of speaking is many a time an act of invention (or discovery). And we aren’t sure and don’t actively control how we create. (Underlying mechanisms behind how we create — use of ‘gut’ are well-known.) Unless we are very deliberate in speech. Most people aren’t. (There generally aren’t incentives to be.) And find it hard to vet the veracity of the invention (or discovery) in the short time that passes between invention and vocalization.

The technology giveth, the technology taketh

27 Sep

Riker and Ordershook formalized the voting calculus as:

pb + d > c

where,
p = probability of vote ‘mattering’
b = size of the benefit
d = sense of duty
c = cost of voting

They argued that if pb + d exceeds c, people will vote. Otherwise not.

One can generalize this simple formalization for all political action.

A fair bit of technology has been invented to reduce c — it is easier than ever to follow the news, to contact your representative, etc. However, for a particular set of issues, if you reduce c for everyone, you are also reducing p. For as more people get involved, less does the voice of any single person matter. (There are still some conditionalities that I am eliding over — for instance, reduction in c may matter more for people who are poorer etc. and may have an asymmetric impact.)

Technologies invented to exploit synergy, however, do not suffer the same issues. Think Wikipedia, etc.

Unlisted False Negatives: Are 11% Americans Unlisted?

21 Aug

A recent study by Simon Jackman and Bradley Spahn claims that 11% of Americans are ‘unlisted.’ (The paper has since been picked up by liberal media outlets like the Think Progress.)

When I first came across the paper, I thought that the number was much too high for it to have any reasonable chance of being right. My suspicions were roused further by the fact that the paper provided no bounds on the number — no note about measurement error in matching people across imperfect lists. A galling omission when the finding hinges on the name matching procedure, details of which are left to another paper. What makes it to the paper is this incredibly vague line: “ANES collects …. bolstering our confidence in the matches of respondents to the lists.” I take that to mean that the matching procedure was done with the idea of reducing false positives. If so, the estimate is merely an upper bound on the percentage of Americans who could be unlisted. That isn’t a very useful number.

But reality is a bit worse. To my questions about false positive and negative rates, Bradley Spahn responded on Twitter, “I think all of the contentious cases were decided by me. What are my decision-theoretic properties? Hard to say.” That line covers one of the most essential details of the matching procedure, a detail they say the readers can find “in a companion paper.” The primary issue is subjectivity. But not taking adequate account of the relevance of ‘decision theoretic’ properties to the results in the paper grates.

Partisan Retrospection?: Partisan Gaps in Retrospection are Highly Variable

11 Jun

The difference between partisans’ responses on retrospection items is highly variable, ranging from over 40% to nearly 0. For instance, in 1988 nearly 30% fewer Democrats than Republicans reported that the inflation rate between 1980 and 1988 had declined. (It had.) However, similar proportions of Republicans and Democrats got questions about changes in the size of the budget deficit and defense spending between 1980 and 1988 right. The median partisan gap across 20 items asked in the NES over 5 years (1988, 1992, 2000, 2004, and 2008) was about 15 points (the median was about 12 points), and the standard deviation was about 13 points. (See the tables.) This much variation suggests that observed bias in partisans’ perceptions depends on a variety of conditioning variables. For one, there is some evidence to suggest that during severe recessions, partisans do not differ much in their assessment of economic conditions (See here.) Even when there are partisan gaps, however, they may not be real (see paper (pdf)).

Estimating Hillary’s Missing Emails

11 Apr

Note:

55000/(365*4) ~ 37.7. That seems a touch low for Sec. of state.

Caveats:
1. Clinton may have used more than one private server
2. Clinton may have sent emails from other servers to unofficial accounts of other state department employees

Lower bound for missing emails from Clinton:

  1. Take a small weighted random sample (weighting seniority more) of top state department employees.
  2. Go through their email accounts on the state dep. server and count # of emails from Clinton to their state dep. addresses.
  3. Compare it to # of emails to these employees from the Clinton cache.

To propose amendments, go to the Github gist