The Obama-Romney Debate and Geogaugy

Popular wisdom may say that Barack Obama lost the debate to Mitt Romney on eloquence, confidence and body language.  But looking at the text shows that he won hands down on what we like to call "geogaugy": numerical estimation of real-life quantities.  In this case, real-life money such as taxes and the federal deficit.

Here's one of the most striking exchanges between Obama and Romney; it's good to read it without taking into account Romney's well-studied body attitude, facial expression and vocal effects compared to Obama's in truth paler performance.

MR. ROMNEY: I will not, under any circumstances, raise taxes on middle-income families. I will lower taxes on middle-income families... let’s get to the bottom line. That is, I want to bring down rates. I want to bring down the rates down, at the same time lower deductions and exemptions and credits and so forth so we keep getting the revenue we need. 

Obama's response: 

PRESIDENT OBAMA: Now, Governor Romney’s proposal that he has been promoting for 18 months calls for a $5 trillion tax cut on top of $2 trillion of additional spending for our military. And he is saying that he is going to pay for it by closing loopholes and deductions.  The problem is that he’s been asked a — over a hundred times how you would close those deductions and loopholes and he hasn't been able to identify them.

Mr. Lehrer: All right.

PRESIDENT OBAMA: When you add up all the loopholes and deductions that upper income individuals can — are currently taking advantage of — if you take those all away — you don’t come close to paying for $5 trillion in tax cuts and $2 trillion in additional military spending.
 
BANG!  Shouldn't this be totally obvious?  Is Romney seriously fooling anyone? Loopholes are going to produce $7 trillion?

Romney tried to muddy the waters by claiming that he was not calling for a $5 trillion tax cut.

MR. ROMNEY: Let me - let me repeat - let me repeat what I said. I'm not in favor of a $5 trillion tax cut.  That's not my plan. My plan is not to put in place any tax cut that will add to the deficit. That's point one. So you may keep referring to it as a $5 trillion tax cut, but that's not my plan.

But this is foozling.  He certainly did propose a series of tax cuts that would add up to $5 trillion dollars over a period of about 10 years; his disclaimer does not concern the existence of the $5 trillion tax cut, but only the fact that it was not going to increase the budget deficit. What Obama said is correct. (Sadly, in spite of the cute little "never mind" comment, Obama did not take enough advantage of Romney's confusing these two issues and thereby denying his own proposed tax cuts.)

Kudos to President Obama for bringing meaning to those numbers by a little wise geogaugy.

PRESIDENT OBAMA: The fact is that if you are lowering the rates the way you describe, Governor, then it is not possible to come up with enough deductions and loopholes that only affect high-income individuals to avoid either raising the deficit or burdening the middle-class.  It's - it's math.  It's arithmetic. 

I would just say this to the American people. If you believe that we can cut taxes by $5 trillion and add $2 trillion in additional spending that the military is not asking for — $7 trillion, just to give you a sense, over 10 years that’s more than our entire defense budget — and you think that by closing loopholes and deductions for the well-to-do, somehow you will not end up picking up the tab, then Governor Romney's plan may work for you.

But I think math, common sense and our history shows us that's not a recipe for job growth. 
 
Let's see for a minute; this tax cut is supposed to cost $5 trillion, so what would that mean for individual middle-class wage earners?  Well, there are a roughly estimated 120 million households in the United States and a very roughly estimated half of them qualify as "middle-class".  Let's suppose that a normal middle-class household has two wage-earners in it, so we're talking about 120 million middle-class taxpayers in the United States.  Obviously, the tax cuts Romney is proposing are going to affect small businesses and not only households, but this is a rough estimation.  So if tax cuts for 120 million individual middle-class wage-earners are going to cost the government $5 trillion, that means that each individual would get a tax break of about $40,000 over the 10-year period under discussion.  So the tax cut would mean $4,000 dollars a year.  It's nice, but it's not life-changing.

As Obama says, it's very hard to imagine that closing loopholes that allow the rich to become richer is going to produce enough money to finance the $7 trillion expense.  But let's do Romney a favor, and suppose for a moment that it's true, or at least nearly true; maybe his tax cut will have to be a little more modest.  Then everything would be fine, right?

But wait - what about the $16 trillion U.S. budget deficit?  Isn't Romney also supposed to explain how he intends to find the money to balance that?

Well, here's how he does it: he explains that his tax cut for the middle class will create such economic stimulation that there will be millions of new jobs, and all of these newly employed people will pay taxes, thence providing the money to balance the budget!

MR. ROMNEY: My plan is not like anything that's been tried before. My plan is to bring down rates but also bring down deductions and exemptions and credits at the same time so the revenue stays in, but that we bring down rates to get more people working. My priority is putting people back to work in America...

 Mathematically there are - there are three ways that you can cut a deficit. One, of course, is to raise taxes. [OK but he's going to lower them instead.] Number two is to cut spending. [Right, cut spending on "Obamacare" and PBS, and close those loopholes, too.  Oh no, I forgot, that's just supposed to balance out the tax cut.] And number three is to grow the economy because if more people work in a growing economy, they're paying taxes and you can get the job done that way.

Get the rates down, lower deductions and exemptions to create more jobs, because there’s nothing better for getting us to a balanced budget than having more people working, earning more money, paying — (chuckles) — more taxes. That’s by far the most effective and efficient way to get this budget balanced.

Oh, okay.  Now, that makes sense: the tax cut will create jobs and these new working people will pay taxes and that will bring in lots of money to balance the budget. So let's see.  Unemployment in the U.S. right now is at over 20 million and I don't know how many millions of jobs Romney sees his tax cut of $3 or $4 thousand yearly actually creating, but let's be insanely optimistic and say his policies cut unemployment by a half, creating 10 million jobs.  

The 10 million newly employed people are all going to start paying taxes, which is great, because now in ten years these ten million people are going to pay for a $16 trillion deficit that the rest of the country's taxpayers' money is not sufficing to reduce.  That means that each of the 10 million newly employed people will be responsible for paying $1,600,000 worth of taxes to Romney's government in ten years - $160,000 a year each!  Bingo - problem solved!

Well, if Romney reduces unemployment to 0%, then each new employee only has to pay $80,000 of taxes a year....

Right.
 

Childhood obesity

New York "socialite" Dara-Lynn Weiss has taken a beating lately because she published an article in Vogue about putting her 7-year old daughter on a diet.

The main thrust of the criticisms that have been leveled at Dara-Lynn are, in summary, something like this:

(1) Children should be left to enjoy a happy childhood and not forced to become self-conscious about food at such a young age - teenage and adulthood will already bring enough psychological food-related problems to American women. Dara-Lynn's attitude is likely to produce an eating disorder in an innocent, happy child.

(2) In spite of the doctor's recommendation and Dara-Lynn's own remarks, her true reason for putting her child on a diet was not health-based, but appearance based: what she really wanted was for the little girl to to look and feel pretty. So really she was pandering to one of our shallower tendencies, namely to overrate the importance of looks and also the importance of what other people think of us.


(3) Dara-Lynn's methods, which contained many elements that may have been humiliating for the child, such as scolding her in front of others and publishing an article on her weight problems in a fashion magazine, may have created present and future psychological problems for the child concerning all kinds of aspects, such as her self-consciousness about her weight, her looks, her mother's love for her, or her relationship with her friends.

Reading over the dozens, even hundreds of angry comments reacting to her Vogue article, I want to break a lance in defence of Dara-Lynn.

To start with - and this is the easiest and simplest objection - those who say that children should be left free to enjoy their childhood and not be put on diets are in straightforward contradiction with every piece of medical information coming our way.

From Wikipedia (and Dara-Lynn quotes this in her article): "There are plenty of statistics available that prove child obesity in America is at epidemic levels. In the last 30 years the number of children who are overweight has tripled to 15%....The mixture of fast food diets along with sedentary lifestyles is creating a generation of children who are facing very adult health issues like high cholesterol, diabetes and heart disease." (If this blog entry is on the Maths on Trial blog at all, it's because this is STATISTICAL evidence that the problem faced by Dara-Lynn is a real and prevalent one!)

Is there really anyone out there who says that Dara-Lynn should have left her daughter to run straight into the jungle of health problems described here, when in fact, mother and daughter working together could actually do something about it? I don't know, but the "leave that poor child alone" attitude is really not convincing.Secondly, there's the psychological aspect directly concerning food. Many commentators say that Dara-Lynn's behavior, especially in the kind of social circles - Greenwich village intelligentsia - where she and her daughter live and move, are probably going to produce eating disorders in the child, and that in fact, these disorders are just as dangerous and actually more likely than the cholesterol and other problems cited above.

But, these comments ignore the fact that an obese child already has an eating disorder! In fact, I really don't believe that there is any difference between children who become fat because they are constantly hungry and have grown over the years to develop habits of eating very large portions and a large amount of carbohydrates, and grownups who behave the same way. Chronic overeating and the inability to recognize the signals of fullnes do form an eating disorder, whatever the age. Many adults fight with this disorder more or less all the time, and dream of some sadly non-existent simple and healthy form of appetite control to replace the missing awareness. Addiction to food, especially addiction to carbohydrates, exists. Everyone knows that little kids can suffer from this kind of eating disorder just as much as anyone else; most everyone probably even knows a kid who does. So a parent of a child with this problem is really caught between one eating disorder that already exists, and another one that may be more dangerous for the health, but on the other hand may not ever occur. Indeed, although some overweight people may go overboard in dieting and eventually become anorexic, the large majority will just manage to control their eating desires enough to reach a healthy weight, and then yo-yo up and down over the months and years as addiction battles with will-power. Yes, this is an eating disorder too, but it is less dangerous than obesity, not more, and it has its satisfactions, too, both when good things get eaten and when the diets reach their goal.

And this leads into the third reason for which I think that many of Dara-Lynn's critics are missing the beat: it is absurdly and even horridly wrong to pretend to believe or imagine that in a Western country at least, an obese child lives a happy, tranquil, psychologically undisturbed life until their parents cruelly interfere. If you don't believe me, have a look at the interview videos of Britain's new tenor star, Jonathan Antoine. He describes the suffering of growing up obese, and doesn't leave the slightest doubt that it is no enviable condition.

Wikipedia's page on obese children says it all: "Children who are obese also must confront the many psychological issues that being overweight creates. Overweight children often have low self-esteem, which is made worse when they are unable to participate in normal activities such as sports or on the playground... Obese children are teased, bullied and made to feel inferior on a number of levels."

So, maybe Dara-Lynn was not the one creating a worrying, humiliating psychological environment in the mind of her happy little girl. Maybe what she was actually trying to do was PROTECT the child from one. Yes, she started the diet, not just because the doctor said to, but because the little girl cried when a boy in school called her fat. But why is that a bad thing? All she was doing was waking up to the suffering her daughter was going to endure and was already starting to endure: exactly that psychological suffering from teasing and bullying expressed in the Wikipedia passage above.

How can a parent in Dara-Lynn's situation protect her little girl?

Should she just tell her that she has to live with it, ignore it, rise above it, and not listen to what other people say?

Should she teach her that being overweight is just part of "the way she is", and should be respected like any other physical or character trait?

What about teaching the girl that she can DO SOMETHING ABOUT IT? And helping her do it, and prove to herself that SHE CAN DO IT, that she can OVERCOME HER PROBLEMS?!

I have no connections to publishing in glossy magazines, but minus that aspect, if I were in Dara-Lynn's shoes, I think I would try to do the same thing that she did. I'd do it with love but also with strictness and a clear goal in mind. My own personal quirks, foibles and problems would play a role, as they do in all of my interactions with other people, all the time. I wouldn't be any more capable than she was to predict the long-term outcome. But I'd still do it. Good for her.

Laurence Tribe: Maths on Trial (7)

Tribe’s reaction to the use of Bayes’ theorem at trial

In this last post of the series, we continue to summarize Tribe’s objections to the use of Bayes’ theorem at trial, with our responses. Last time we discussed his first objection:

1….The Distortion of Outcomes

Today, we continue with the other three objections.

2….The End of Innocence: A Presumption of Guilt?

“At least in criminal cases, and perhaps also in civil cases resting on allegations of moral fault, further difficulties lurk in the very fact that the trier is forced by the Finkelstein-Fairley technique to arrive at an explicit quantitative estimate of the likely truth at or near the trial’s start, or at least before some of the most significant evidence has been put before him.” Tribe’s argument in this section is that the idea of forcing a juror to arrive at some kind of mathematical figure for the prior probability of guilt, before applying Bayes’ theorem to update that prior according to some new piece of numerical evidence, is fundamentally against the presumption of guilt, and that this injustice is not rectified even by setting the prior probability to an unreasonably low value.

Tribe stresses the importance of the juror listening to all of the evidence before “reaching any judgment, even a tentative one, as to his probable guilt”; he terms this one of the “intangible aspects” of our commitment to the proposition that “a man who stands accused of crime is no less entitled than his accuser to freedom and respect as an innocent member o the community”. Tribe admits that in reality, a juror listening to a trial may not actually be considering the accused as certainly innocent until a complete proof has been laid out before him; he may, in fact, swing backwards and forwards in his estimate of guilt as the trial proceeds, thus holding some vague idea of “prior probability of guilt” at all times. However, according to Tribe, these impulses must not be spoken or expressed, let alone called to the fore, out of respect for the presumption of innocence. “Society ought to speak of accused men as innocent, and treat them as innocent, until they have been properly convicted after all they have to offer in their defense has been carefully weighed,” and “Jurors cannot at the same time estimate probable guilt and suspend judgment until they have heard all the defendant has to say.”

We feel that the proper method to counter Tribe’s worries and to allow jurors to keep all their thoughts about possible guilt, and their personal, intimate estimates of probability of guilt, silent and unspoken throughout the trial, is the presentation of a table such as the one given by Finkelstein and Fairley, in which many different values for the prior probability of guilt are entered, and the update according to the new evidence is calculated for each of them. In this way, the jury members are never required to explicitly formulate a probability of guilt at any stage; it is enough for them to place themselves loosely within the table, without being asked to specify where, or even to consider the entire set of output results and the meaning they indicate before coming to any final decision. This would certainly respect the duty of silence that Tribe describes.

We note as an aside that Tribe himself appears disturbed by the fact that the duty of silence is at the same time a call for lack of candor. In a few well-chosen words he expresses his obviously deeply held feeling that while a lack of candor should not be something that is required lightly, there are cases in which it serves a higher moral purpose. Lies or refusals to consider the full weight of the evidence are not required, merely a silence on the subject in respect for the presumption of innocence: “One need not say everything all at once in order to be truthful, and saying some things in certain ways and at certain times in the trial process may interfere with other more important messages that the process should seek to convey and with attitudes that it should seek to preserve.”

We respect and agree with this approach, but as explained above, Bayes’ theorem can be correctly presented and used at trial without undermining it.

3…The Quantification of Sacrifice

One extremely disturbing factor about the use of any mathematical method to determine guilt is that since the final probability, when all the evidence has been taken into account, is rarely likely to be equal to 1.0, it will, in cases of conviction, tend to be some concrete and convincing figure such as, for example, 0.98. Unfortunately, accepting such a figure as the probability of guilt can also be expressed as saying that one accepts that 2 people out of every 100 convicted are expected to be innocent. While there is no doubt that many innocent people are convicted each year, it is indeed disturbing to have an actual figure of the number of such people that one expects. “There is something intrinsically immoral about condemning a man as a criminal while telling oneself, “I believe that there is a chance of one in twenty that this defendant is innocent, but a 1/20 risk of sacrificing him erroneously is one I am willing to run in the interest of the public’s – and my own – safety.” Tribe wishes for any justice system to be structured in such a way as to avoid ever having to make such a proclamation with a specifically published figure. He considers that it is morally superior for a juror to express himself as being “very sure” or “as sure as possible” of guilt than to give an actual figure, which would prove his readiness to accept such or such a percentage of innocent sacrificial victims.

Naturally, there are miscarriages of justice in any justice system, but Tribe points out the vast moral difference between society’s recognizing the necessity of tolerating them, and the fact of its actually embracing a policy that juries “ought to convict in the face of this acknowledged and quantified uncertainty”. He prefers sticking to the notion of “guilt beyond a reasonable doubt”, which represents “a subtle compromise between the knowledge, on the one hand, that we cannot realistically insist on acquittal whenever guilt is less than absolutely certain, and the realization, on the other hand, that the cost of spelling that out explicitly and with calculated precision in the trial itself would be too high.”

Our response to this argument is that Bayes’ theorem should not, probably ever, be used to compute the probability of guilt. It should be brought in to establish certain factual subsidiary questions, such as the probability of its being the defendant or another person who left a certain print, was seen in a certain place, was present at a certain time, transported a certain object, and so forth. The actual final decision of innocence or guilt should and must be made by jurors without recourse to any numerical calculation.

4…The Dehumanization of Justice

Tribe’s final argument against the use of mathematical methods at trial is simply that they “threaten to make the legal system seem even more alien and inhuman than it already does to distressingly many…The need now is to enhance the community comprehension of the trial process, not to exacerbate an already serious problem by shrouding the process in mathematical obscurity.” Tribe worries that “guided and perhaps intimidated by the seeming inexorability of numbers, induced by the persuasive force of formulas and the precision of the decimal points to perceive themselves as performing a largely mechanical and automatic role, few jurors could be relied upon to recall, let alone to perform, this humanizing function, to employ their intuition and their sense of community values to shape their ultimate conclusions.”

Our response to this is that with the advent of DNA analysis, mathematics at trial is here to stay. It is perhaps not yet fully understood that the statistical analyses used on DNA are no different than many other cases and situations where Bayes’ theorem can be applied. The public has grown used to seeing DNA analyses presented at trial over the decades since Tribe wrote his article, and juries deal with the situation competently enough in the main, having expert witnesses explain the issues to them in layman’s terms, and not, generally, forgetting to employ their common sense.

It seems to us that what is needed is a general education aimed at the public, so that little by little, the notions used there, which are not more difficult than much of the mathematics seen at school, become familiar and trustworthy to the public at large, from which juries are drawn. We believe that this is the only way in which Tribe’s profound moral and social concerns can be reconciled with the fact that mathematics at trial is here to stay. We also believe that such a general public education is a legitimate and reasonable aim to work towards, which is the whole purpose of this blog.