Results for “Tests”
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Bill Gates is Angry

But people aren’t getting their tests back quickly enough.

Well, that’s just stupidity. The majority of all US tests are completely garbage, wasted. If you don’t care how late the date is and you reimburse at the same level, of course they’re going to take every customer. Because they are making ridiculous money, and it’s mostly rich people that are getting access to that. You have to have the reimbursement system pay a little bit extra for 24 hours, pay the normal fee for 48 hours, and pay nothing [if it isn’t done by then]. And they will fix it overnight.

Gates is correct. If companies were paid for speed they would increase capacity and move immediately to a stack processing (LIFO) model, as I described yesterday.

The whole interview is worth reading. Gates is restrained but you can tell he is angry. Bill has had it with the FDA, Trump, Mark Zukerberg, stupid anti-vaxxers like Robert Kennedy (who he was forced to listen to to get access to Trump), Congress and much more. I don’t blame him one bit. I am angry too.

Stack-Push-Pop COVID Testing

A COVID test that doesn’t come back in a few days is close to useless and PCR tests are taking a long time to process:

NYTimes: Most people who are tested for the virus do not receive results within the 24 to 48 hours recommended by public health experts to effectively stall the virus’s spread and quickly conduct contact tracing, according to a new national survey by researchers from Harvard University, Northeastern University, Northwestern University and Rutgers University….People who had been tested for the virus in July reported an average wait time of about four days. That is about the same wait time for those who reported taking a test in April. Over all, about 10 percent of people reported waiting 10 days or more.

…“A test result that comes back in seven or eight days is worthless for everybody — it shouldn’t even be counted,” said Dr. Amesh Adalja, a senior scholar at the Johns Hopkins University Center for Health Security and a physician in Pittsburgh. “It’s not a test in any kind of effective manner because it’s not actionable.”

One seemingly severe but potential solution is to change how tests are processed. Right now it’s mostly first come, first-served but this means we can easily have a situation where everyone eventually gets a test result but all the results are useless because they take a week or more to process. I propose instead that any test that can’t be reported back in 3-4 days be thrown out immediately. Labs should focus only on processing tests that can be reported back quickly.

One way of thinking about this is to use a stack or last-in first-out (LIFO) model for testing. In a stack model the newest test request is pushed onto the top of the stack and the next test to be processed is popped off the top of the stack. One disadvantage of this model is that some test requests will never be processed (they should be removed from the bottom of the stack and returned as null results). Some people will be angry.

But the stack model of testing has a huge advantage over first-come, first-served. Namely, just as many tests will be completed as under the current model but the tests results will all come back faster and be much more useful. What would you rather have, guaranteed stale test results or fresh results with some possibility of a null return? Since a stale result is not much better than a null it seems obvious that the stack system is superior. Most importantly, faster, more useful tests will help to end the crisis by reducing the number of infections.

Addendum: See also my posts Pooled Testing is Super-Beneficial and Frequent, Fast, and Cheap is Better than Sensitive on other methods to improve testing.

The Hawaii bastion has fallen

“We must accept the new reality: The virus is widespread on Oahu,” said Anderson, noting that it’s becoming increasingly difficult for contact tracers to pinpoint the source of infection as the virus grows more and more prevalent.

Hawaii now has seen 2,448 positive cases of coronavirus since state health officials started reporting testing results in March. More than 500 of those cases were reported in the last seven days, and most of them are on Oahu.

Historically, about 1% to 2% of tests conducted in Hawaii have come back with positive COVID-19 results. But in recent days that percentage has crept up close to 5%.

“Any time it gets over 5%, there’s reason for concern,” Anderson said. “Some of the states where they’re having large outbreaks have high rates of over 10%. And, obviously, we don’t want to be there.”

The growing prevalence of COVID-19 in Hawaii could jeopardize the state’s ability to reopen public schools, bring college students back to campus and invite visitors to return to Hawaii, said Hawaii Gov. David Ige.

Here is the full story.  Of course it is much better to have cases now — when superior treatments are available — than back in March or April.  Still, the containment strategies that are supposed to work for the most part…do not in fact work.

Infected versus Infectious

As I said in my post Frequent, Fast, and Cheap is Better than Sensitive we shouldn’t be comparing virus tests head-to-head, as if all tests serve the same purpose. Instead, we should recognize that tests have comparative advantages and a cheap, fast, frequent testing regime can be better in some respects than a slow, infrequent but more sensitive testing regime. Both regimes can be useful when used appropriately and especially when they are used in combination.

Eric Topol has a good graphic.

Image

As Topol also notes:

In order to get this done, we need a reboot at @US_FDA, which currently requires rapid tests to perform like PCR tests. That’s wrong. This is a new diagnostic category for the *infectious* endpoint, requiring new standards and prospective validation.

The FDA has sort-of indicated that they might be open to this.

Much, much too slow, of course. Matching a virus that grows exponentially against a risk-averse, overly-cautious FDA has been a recipe for disaster.

How to restart the baseball season sustainably

You may have read that a number of early games in the season have been cancelled due to many of the players testing positive for Covid-19.  There is talk of the season being unsustainable, but it seems a simple remedy has not yet been tried — dock a player 30 percent of his salary if he tests positive.  That should limit the degree of nightclubbing and carousing, keeping in mind that the already-infected are probably some of the worst offenders and they have been “taken care of.”  Furthermore, the players would have a strong incentive to monitor each other, not wanting to be on the receiving end of an infection from a teammate.

While that arrangement presumably runs counter to the collective bargaining agreement, that agreement can and should be revised if season cancellation is the true alternative.

If need be, the fines can be redistributed to the players who never test positive, thus keeping total compensation constant.

Incentives don’t always work, but if you haven’t even tried them something is amiss.  Do I hear “35 percent”?  “Forty”?  “Thirty-seven percent and three lashes”?

Frequent, Fast, and Cheap is Better than Sensitive

A number of firms have developed cheap, paper-strip tests for coronavirus that report results at-home in about 15 minutes but they have yet to be approved for use by the FDA because the FDA appears to be demanding that all tests reach accuracy levels similar to the PCR test. This is another deadly FDA mistake.

NPR: Highly accurate at-home tests are probably many months away. But Mina argues they could be here sooner if the FDA would not demand that tests for the coronavirus meet really high accuracy standards of 80 percent or better.

A Massachusetts-based startup called E25Bio has developed this sort of rapid test. Founder and Chief Technology Officer Irene Bosch says her firm has field-tested it in hospitals. “What we learned is that the test is able to be very efficient for people who have a lot of virus,” she says.

The PCR tests can discover virus at significantly lower concentration levels than the cheap tests but that extra sensitivity doesn’t matter much in practice. Why not? First, at the lowest levels that the PCR test can detect, the person tested probably isn’t infectious. The cheap test is better at telling whether you are infectious than whether you are infected but the former is what we need to know to open schools and workplaces. Second, the virus grows so quickly that the time period in which the PCR tests outperforms the cheap test is as little as a day or two. Third, the PCR tests are taking days or even a week or more to report which means the results are significantly outdated and less actionable by the time they are reported.

The fundamental issue is this: if a test is cheap and fast we shouldn’t compare it head to head against the PCR test. Instead, we should compare test regimes. A strip test could cost $5 which means you can do one per day for the same price as a PCR test (say $35). Thus, the right comparison is seven cheap tests with one PCR test. So considered a stylized example. If a person gets infected on Sunday and is tested on Sunday then both tests will likely show negative. With the PCR test the infected person then goes to work, infecting other people throughout the week before being the person is tested again next Sunday. With the cheap test the person gets tested again on Monday and again comes up negative and they go to work but probably aren’t infectious. They are then tested again on Tuesday and this time there is enough virus in the person’s system to show positive so on Tuesday the infected person stops going to work and doesn’t infect anyone else. Score one for cheap tests. Now consider what happens if the person gets tested on another day, say Tuesday? In this case, both tests will show positive but the person doesn’t get the results of the PCR test until next Tuesday and so again goes to work and infects other people throughout the week. With the cheap test the infected person learns they are infected and again stops going to work and infecting other people. Score two for cheap tests.

Indeed, when you compare testing regimes it’s hard to come up with a scenario in which infrequent, slow, and expensive but very sensitive is better than frequent, fast, and cheap but less sensitive.

More details in this paper.

Moskos on Surging Crime in NYC

Peter Moskos warns about rising crime in NYC in the NYDaily news.

Violence in New York is up….In the last 28 days (through July 12), compared to last year, shootings have more than tripled (318 vs. 97). Last week was even worse. If the last 28 days become the new normal, 2021 will have more than 4,100 shootings, a level not seen in well over 20 years.

Undoubtedly bail reform, protests, looting, COVID-19, and the release of prisoners because of COVID all play a role, though how much is debate. What’s less known is how the NYPD has been methodically declawed by design.

Years of political advocacy have resulted in the intentional erosion of legal police authority. There is less prosecution. Most miscreant activities have been decriminalized. The city survived and even benefited from many reforms, but now the camel’s back is breaking.

…For many, this is a feature, not a flaw. A new breed of progressive prosecutors has battled to see who can prosecute the least. As a result, arrests in 2019 decreased 35% from 2016. Reducing incarceration is desirable, and New York has been doing so literally for decades without jeopardizing public safety.

More recently, since November, because of bail reform and COVID releases, the number of jailed inmates dropped another 40%. People are coming out of jail, and few are going in. Many applaud this because incarceration disproportionately affects Black and Brown people.

But so does non-enforcement and the rise in violence. In 2018 (the latest year with published data), 95.7% of shooting victims in New York City are Black or Hispanic. Just 4.3% of victims are white or Asian. When violence goes up, more Black and Hispanic people are shot.

A highly speculative version of the immunological dark matter hypothesis

The COVID-19 pandemic is thought to began in Wuhan, China in December 2019. Mobility analysis identified East-Asia and Oceania countries to be highly-exposed to COVID-19 spread, consistent with the earliest spread occurring in these regions. However, here we show that while a strong positive correlation between case-numbers and exposure level could be seen early-on as expected, at later times the infection-level is found to be negatively correlated with exposure-level. Moreover, the infection level is positively correlated with the population size, which is puzzling since it has not reached the level necessary for population-size to affect infection-level through herd immunity. These issues are resolved if a low-virulence Corona-strain (LVS) began spreading earlier in China outside of Wuhan, and later globally, providing immunity from the later appearing high-virulence strain (HVS). Following its spread into Wuhan, cumulative mutations gave rise to the emergence of an HVS, known as SARS-CoV-2, starting the COVID-19 pandemic. We model the co-infection by an LVS and an HVS and show that it can explain the evolution of the COVID-19 pandemic and the non-trivial dependence on the exposure level to China and the population-size in each country. We find that the LVS began its spread a few months before the onset of the HVS and that its spread doubling-time is \sim1.59\pm0.17 times slower than the HVS. Although more slowly spreading, its earlier onset allowed the LVS to spread globally before the emergence of the HVS. In particular, in countries exposed earlier to the LVS and/or having smaller population-size, the LVS could achieve herd-immunity earlier, and quench the later-spread HVS at earlier stages. We find our two-parameter (the spread-rate and the initial onset time of the LVS) can accurately explain the current infection levels (R^2=0.74); p-value (p) of 5.2×10^-13). Furthermore, countries exposed early should have already achieved herd-immunity. We predict that in those countries cumulative infection levels could rise by no more than 2-3 times the current level through local-outbreaks, even in the absence of any containment measures. We suggest several tests and predictions to further verify the double-strain co-infection model and discuss the implications of identifying the LVS.

That is a new paper from Hagai and Ruth Perets, another link here, via Yaakov.

Mood affiliation, the police, and rising crime rates

Had a thought on the discussion of rising crime over the last few months inspired by your MR posts on mood affiliation that I wanted to pass along:

There’s been a bit of discussion lately about increased shootings in major cities in the wake of the George Floyd protests, and the two main narratives trying to explain them have been “protests fueling higher tensions” and “cops backing off and not patrolling as much or doing their jobs”. Interestingly, the latter seems to be based on a model where fewer cops and patrols results in more crime, so you might naively expect people who hold that belief would be more likely to believe that simple defunding and reduction of police presence would lead to more crime generally.

But if you believe that mood affiliation predicts opinions better than factual consistency, then it matters more that the former position sounds like “cops to blame, cops bad”, while the second sounds more like “cops are important, cops good”. And most commentators care more about the correct affect towards the police, rather than consistent models of reality, so you largely have commentators that are pro-defund police, but blame their lack of presence for crime increases, or commentators that are pro-police, think defunding would lead to increases in crime, but are less willing to entertain the idea that recent increases in crime are caused by the choices of officers.

That is from an email by Benjamin Hawley.

Swedish update, and which places need to fear second waves?

Your recent question intrigued me. Do you have any new info/opinions on what’s happening in Sweden? Despite no mask wearing, continued indoor dining (at least judging from recent photos on instagram), their case AND death daily counts are plummeting (looks like an inverse exponential). This would also explain excess deaths returning to normal throughout US. Bizarrely, my cursory reading of Swedish newpapers online did not result in any recent articles discussing the dramatic decline in cases there!

One theory circulating is they achieved herd immunity on the math: 10x true seroprevalence (from CDC tests in US) * 2x true immunity (from Tcell things not measured by antibody tests that I don’t fully understand) * 0.75% reported case penetration * 2x for relatively low tests per capita rate = 30% true immunity (likely much higher in densest areas where spread would be much faster resulting in maybe >70% immunity in Stockholm). This puts them r0 < 1.

The nice thing about this hypothesis is that it’s easily falsifiable. If true immunity rates are 20x reported case load (dropping last 2x factor since test rate higher in US), then Florida should have just gotten to the 1.4% necessary to trigger similar immunity in dense cities and from now on, cases per day should follow an inverse exponential.

This would also explain why NYC has not seen a resurgence despite very similar reopening as SF and LA – they achieved dense herd immunity in May and thus the subsequent decline in reported cases was driven by herd immunity rather than more strict closures or mask compliance, reversing either of those factors now doesn’t reverse immunity. To be clear, I’m not disputing that distancing or mask wearing works – they do. But so does infecting everyone quickly. No value judgements on what’s the better policy decision here, just trying to make a predictive statement.

At least, one can hope!

That is my email from Mayank Gupta.  In my view, some version of this view is looking more true with each passing day.  We also are not seeing second waves in hard-hit northern Italy.  Still, many surprises remain and we should not leap to premature conclusions.

To be clear, I was and still am pro-lockdown (without regrets), pro-mask, pro-testing, and I believe Denmark followed a better path than did Sweden.  Long-term damage (rather than death) still may be a significant risk, and furthermore many parts of the world may be far more vulnerable than the United States.  Still, you need to put all of the moralizing and partisanship aside and ask what we are learning from the new data, and I think Mayank Gupta has put it (probabilistically) very well.  And see this related Atlantic piece, though I would have some quibbles with it.  And here is a bit more commentary on the new T-cell results.

In any case, always be prepared to revise!  I believe that within a month we will have a much better sense of these questions.

Addendum: You will note these hypotheses also significantly raise the probability of much earlier animal-to-human transmission, especially in Southeast Asia.  A very good baseline principle for reasoning is simply “Origins usually go back longer and earlier than what you first might think!”

Second addendum: If you go back to March, leading epidemiologist Michael Osterhalm argued: “We conservatively estimate that this could require 48 million hospitalizations, 96 million cases actually occurring, over 480,000 deaths that can occur over the next four to seven months with this situation.”  Covid-19 has been terrible, and the performance of the executive branch (and many governors) absymal, but do those look like good predictions right now?  (Hospitalizations for instance have yet to hit 250k.)  If not, why not?  How hard have you thought about this question?  (Added note: one correspondent suggests that Osterhalm misspoke and in fact meant 4.8 million hospitalizations — note that still would be off by quite a large margin, almost a factor of twenty.)

Fight the Virus! Please.

One of the most confounding aspects of the pandemic has been Congress’s unwillingness or inability to spend to fight the virus. As I said in the LA Times:

If an invader rained missiles down on cities across the United States killing thousands of people, we would fight back. Yet despite spending trillions on unemployment insurance and relief to deal with the economic consequences of COVID-19, we have spent comparatively little fighting the virus directly.

Economists Steven Berry and Zack Cooper have run the numbers:

By our calculations, less than 8 percent of the trillions in funding that Congress has allocated so far in response to the virus has been for solutions that would shorten or mitigate the virus itself: measures like increasing the supply of PPE, expanding testing, developing treatments, standing up contact tracing, or developing a vaccine. A case in point is the most recent House Covid-19 package. It calls for $3 trillion in spending; less than 3 percent of that total is allocated toward Covid testing. As Congress considers next steps, it’s imperative to shift priorities and direct more funding and effort toward actually ending the pandemic.

Berry and Copper point to the vaccine plan that I am working on as an example of smart spending:

…a group of prominent economists, including Nobel Laureate Michael Kremer, has proposed spending a $70 billion dollar vaccine effort. The proposed expenditure is both much larger than anything proposed by the White House or Congress and also quite cheap compared to the potential benefits.

…[Similarly] Nobel Laureate Paul Romer and the Rockefeller Foundation have each sketched out $100 billion plans to increase testing. We say: Let’s fund both, allocating half the funds directly to states, who can spend to activate the vast capacity of university labs, and also fund Romer’s plan to scale up $10 instant tests for true mass testing. We could create a $50 billion dollar challenge prize that rewards the first 10 firms that develop effective treatments for Covid-19 — $5 billion each. We could fund Scott Gottlieb and Andy Slavitt’s bipartisan $50 billion contact tracing proposal. We could allocate $100 billion to fund the libertarian leaning Mercatus Center’s proposal for advanced purchase contracts to procure massive quantities of PPE.

What makes this all the more confounding is that spending to defeat the virus will more than pay for itself! As I said in my piece in the Washington Post (with Puja Ahluwalia Ohlhaver):

Economists talk about “multipliers” — an injection of spending that causes even larger increases in gross domestic product. Spending on testing, tracing and paid isolation would produce an indisputable and massive multiplier effect.

Who gains by killing the economy and letting people die? Yes, it’s possible to spin some elaborate conspiracy about someone, somewhere benefiting. But in talking with people in Congress the message I hear is not that there’s a secret cabal with a special interest in economic collapse and dying constituents. In a way, the message is worse. Multiple people have told me that things move slowly, no one is stepping up to the plate, leadership is absent. “Who is John Galt?,” they sigh. Ok, they don’t literally say that, but that sigh of resignation is what it feels like in the United States today at the highest levels of government.

Pooled Testing is Super-Beneficial

Tyler and I have been pushing pooled testing for months. The primary benefit of pooled testing is obvious. If 1% are infected and we test 100 people individually we need 100 tests. If we split the group into five pools of twenty then if we’re lucky, we only need five tests. Of course, chances are that there will be some positives in at least one group and taking this into account we will require 23.2 tests on average (5 + (1 – (1 – .01)^20)*20*5). Thus, pooled testing reduces the number of needed tests by a factor of 4. Or to put it the other way, under these assumptions, pooled testing increases our effective test capacity by a factor of 4. That’s a big gain and well understood.

An important new paper from Augenblick, Kolstad, Obermeyer and Wang shows that the benefits of pooled testing go well beyond this primary benefit. Pooled testing works best when the prevalence rate is low. If 10% are infected, for example, then it’s quite likely that all five pools will have at least one positive test and thus you will still need nearly 100 tests (92.8 expected). But the reverse is also true. The lower the prevalence rate the fewer tests are needed. But this means that pooled testing is highly complementary to frequent testing. If you test frequently then the prevalence rate must be low because the people who tested negative yesterday are very likely to test negative today. Thus from the logic given above, the expected number of tests falls as you tests more frequently (per test-cohort).

Suppose instead that people are tested ten times as frequently. Testing individually at this frequency requires ten times the number of tests, for 1000 total tests. It is therefore natural think that group testing also requires ten times the number of tests, for more than 200 total tests. However, this estimation ignores the fact that testing ten times as frequently reduces the probability of infection at the point of each test (conditional on not being positive at previous test) from 1% to only around .1%. This drop in prevalence reduces the number of expected tests – given groups of 20 – to 6.9 at each of the ten testing points, such that the total number is only 69. That is, testing people 10 times as frequently only requires slightly more than three times the number of tests. Or, put in a different way, there is a “quantity discount” of around 65% by increasing frequency.

Peter Frazier, Yujia Zhang and Massey Cashore also point out that you could also do an array-protocol in which each person is tested twice but in two different groups–this doubles the number of initial tests but limits the number of false-positives (both tests must be positive) and the number of needed retests. (See figure.).

Moreover, we haven’t yet taken into account the point of testing which is to reduce the prevalence rate. If we test frequently we can reduce the prevalence rate by quickly isolating the infected population and by reducing the prevalence rate we reduce the number of needed tests. Indeed, under some parameters it’s possible to increase the frequency of testing and at the same time reduce the total number of tests!

We can do better yet if we group individuals whose risks are likely to be correlated. Consider an office building with five floors and 100 employees, 20 per floor. If the prevalence rate is 1% and we test people at random then we will need 23.2 tests on average, as before. But suppose that the virus is more likely to transmit to people who work on the same floor and now suppose that we pool each floor. Holding the total prevalence rate constant, we are now likely to have a zero prevalence rate on four floors and a 5% prevalence rate on one floor. We don’t know which floor but it doesn’t matter–the expected number of tests required now falls to 17.8.

The authors suggest using machine learning techniques to uncover correlations which is a good idea but much can be done simply by pooling families, co-workers, and so forth.

The government has failed miserably at controlling the pandemic. Tens of thousands of people have died who would have lived under a more competent government. The FDA only recently said they might allow pooled testing, if people ask nicely. Unbelievably, after telling us we don’t need masks (supposedly a noble lie to help limit shortages), the CDC is still disparaging testing of asymptomatic people (another noble lie?) which is absolutely disastrous. Paul Romer is correct, testing capacity won’t increase until we put soft drink money behind advance market commitments and start using techniques such as pooled testing. Fortunately or sadly, depending on how you look at it, it’s not too late to do better. Some universities are now proposing rapid, frequent testing using pooling. Harvard will test every three days. Cornell will test frequently. Delaware State will test weekly. Lets hope the idea spreads from the ivory tower.

Sweden fact of the day

Cases in the Nordic country have declined sharply over the past few days and on Tuesday only 283 new cases were recorded.

That contrasts with a torrid month of June when daily numbers ran as high as 1,800, eclipsing rates across much of Europe, even as deaths and hospitalisations continued to decline from peaks in April.

At the same time:

…weekly numbers for tests have more than doubled since late May, putting the country in the same bracket as extensively testing nations such as Germany.

Here is the full article.  Who again has the best model of this?  Anyone?  How about no one?  Here is a NYT piece on Sweden, dated July 7, it doesn’t even mention any of this.

Here is the steadily declining Swedish death rate.  No need to point out that Denmark and Norway, with their early and swift responses, did much better yet.  I am interested in what is the best way to model why Sweden is not doing much worse.

Thursday assorted links

Can Philosophy Make People Generous?

Schwitzgebel and Rust famously found that professors of ethics are no more ethical than other professors. Peter Singer being perhaps a famous exception to the rule. In follow-up research Schwitzgebel and psychologist Fiery Cushman tried to find philosophical arguments to change people’s willingness to donate to charity. They were unable to find any. But perhaps they just weren’t good at coming up with effective philosophical arguments. Thus, they challenged moral philosophers and psychologists to a contest:

Can you write a philosophical argument that effectively convinces research participants to donate money to charity?

By a philosophical argument they meant an argument and not an appeal to pity or emotion. No pictures of people clubbing baby seals. The contest had 100 entrants which were winnowed down in a series of tests.

The test had people read the arguments and then decide how much of a promised payment they would they like to give to charity. An average of $2.58 was contributed to charity (of $10) in the control group (no argument). The best argument increased giving by 54% to $3.98. Not bad.

Here’s the argument which won:

Many people in poor countries suffer from a condition called trachoma. Trachoma is the major cause of preventable blindness in the world. Trachoma starts with bacteria that get in the eyes of children, especially children living in hot and dusty conditions where hygiene is poor. If not treated, a child with trachoma bacteria will begin to suffer from blurred vision and will gradually go blind, though this process may take many years. A very cheap treatment is available that cures the condition before blindness develops. As little as $25, donated to an effective agency, can prevent someone going blind later in life.

How much would you pay to prevent your own child becoming blind? Most of us would pay $25,000, $250,000, or even more, if we could afford it. The suffering of children in poor countries must matter more than one-thousandth as much as the suffering of our own child. That’s why it is good to support one of the effective agencies that are preventing blindness from trachoma, and need more donations to reach more people.

Now here’s the kicker. The winning argument was submitted by Peter Singer and Matthew Lindauer. Singer is clearly screwing with Schwitzgebel’s research!

You can read some of other effective arguments here. I don’t think it’s an accident that the winning argument was the shortest and also the least purely philosophical. I’m not saying Singer and Lindauer cheated, but compared to the other arguments the Singer-Lindauer argument is concrete and by making people think of their own children, likely to arouse emotion. That too is a lesson.