The formal logic of legal decisions

The US Supreme Court ruled today that the ban on sex-based discrimination in Title VII of the 1964 Civil Rights Act protects employees from discrimination based on sexual orientation or gender identity. Justice Gorsuch, who is a textualist (i.e. believes that laws should only be interpreted according to the written words alone without taking into any consideration the intent of the writers), writes “An employer who fires an individual for being homosexual or transgender fires that person for traits or actions it would not have questioned in members of a different sex. Sex plays a necessary and undisguisable role in the decision, exactly what Title VII forbids.” I find this to be an interesting exercise in logic. For example, consider the case of a “man married to a man”. According to Gorsuch’s logic, this cannot be an excuse to fire someone because if you replace “man” with “woman” in the first instance then you end up with the the phrase “woman married to a man”, and since this is not sufficient for firing, the reason is not sex invariant. Dissenting legal scholars disagree. They argue that the correct logic is to replace all instances of “man” with “woman”, in which case you would end up with “woman married to a woman” and thus the reason for firing would be sex invariant. I think in this case Gorsuch is correct because in order to have complete sex invariance, the rule must apply for any form of exchange. The law should be applied equally in all the possible ways that one gender is replaced by the other.

A conservative legal argument for gun control

I am an advocate for gun control because, as I expounded in my previous post, of my inherent belief in the incompetence of all humans. A major impediment to gun control in the US is the 2nd Amendment of the Constitution, which states “A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.” The two key phrases of the 2nd Amendment are “well regulated Militia” and “right … to bear arms” and there has always been constant tension over what they exactly mean. The current Supreme Court, prior to Antonin Scalia’s death, held that the 2nd Amendment means that people can bear arms under any circumstance and this has led to the overturning of many gun control measures in cities like Washington DC and Chicago. However, this has not always been the case. Previous courts have put more weight into the “well regulated” part and allowed for some gun restrictions.

Although the right to bear arms is considered to be the conservative position, I actually think there is an equally compelling conservative argument for gun control. One of the things that conservatives argue for is that government should be less centralized and that individual states should be able to set their own laws, as long as they don’t violate the Constitution. Hence, gun control advocates should use a “States’ Rights” argument that communities should be able to establish their own interpretation for how “well regulated” and “right to bear arms” should be balanced. Instead of trying to fight for uniform federal gun control laws, they should argue that local laws should be allowed to stand, provided that they do not completely outlaw guns. So if Washington DC wants an assault weapons ban, that should be fine. If Chicago wants to limit magazine sizes in hand guns, that should also be okay. People in gun ravaged cities like Baltimore should not have to have gun laws that might be popular in states like Idaho be forced upon them. Depending on who fills the vacant position on the next Supreme Court this line or argument could be moot but I think it is one that gun control advocates should perhaps pursue.

Probability of gun death

The tragedy in Oregon has reignited the gun debate. Gun control advocates argue that fewer guns mean fewer deaths while gun supporters argue that if citizens were armed then shooters could be stopped through vigilante action. These arguments can be quantified in a simple model of the probability of gun death, p_d:

p_d = p_gp_u(1-p_gp_v) + p_gp_a

where p_g is the probability of having a gun, p_u is the probability of being a criminal or  mentally unstable enough to become a shooter, p_v is the probability of effective vigilante action, and p_a is the probability of accidental death or suicide.  The probability of being killed by a gun is given by the probability of someone having a gun times the probability that they are unstable enough to use it. This is reduced by the probability of a potential victim having a gun times the probability of acting effectively to stop the shooter. Finally, there is also a probability of dying through an accident.

The first derivative of p_d with respect to p_g is p_u - 2 p_u p_g p_v + p_a and the second derivative is negative. Thus, the minimum of p_d cannot be in the interior 0 < p_g < 1 and must be at the boundary. Given that p_d = 0 when p_g=0 and p_d = p_u(1-p_v) + p_a when p_g = 1, the absolute minimum is found when no one has a gun. Even if vigilante action was 100% effective, there would still be gun deaths due to accidents. Now, some would argue that zero guns is not possible so we can examine if it is better to have fewer guns or more guns. p_d is maximal at p_g = (p_u + p_a)/(2p_u p_v). Thus, unless p_v is greater than one half then even in the absence of accidents there is no situation where increasing the number of guns makes us safer. The bottom line is that if we want to reduce gun deaths we should either reduce the number of guns or make sure everyone is armed and has military training.

 

 

 

Government shutdown

As of today, I am officially furloughed without pay since the NIH is officially closed and nonessential employees like myself are barred from working without pay by the Antideficiency Act of 1884. However, given that blogging is not considered an official duty, I can continue to post to Scientific Clearing House. Those who are not up on American politics may be wondering why the US government has shutdown. The reason is that the US fiscal year begins on Oct 1 and according to the the US Constitution, only Congress can appropriate funds for the functioning of government and they did not pass a budget for the new fiscal year by midnight of September 30. Actually, Congress has not passed a budget on time in recent years but has passed Continuing Resolutions that to keep the government going. So why have they not passed a budget or a CR this year? Well, currently the US government is divided with the Democratic party controlling the Senate and Presidency and the Republican party controlling the House of Representatives. All three entities must agree for a law to pass. Three years ago, the Democrats controlled the Congress, which includes both the House and Senate, and passed the Affordable Care Act, also known as Obamacare, which the President signed into law.   The Republicans took control of the House in 2011 and have been trying to repeal the ACA ever since but have been stopped by the Senate. This year they decided to try a new tactic, which was to pass a budget that withholds funding for the ACA. The Senate did not agree, passed a budget with the ACA and sent it back to the House, which then took out funding for the ACA again with some modifications and sent it back. This went on back and forth without converging to an agreement and thus we are closed today.

The problem with democracy

Winston Churchill once said that “Democracy is the worst form of government, except for all those other forms that have been tried from time to time.” The current effectiveness of the US government does make one wonder if that is even true. The principle behind democracy is essentially utilitarian – a majority or at least a plurality decides on the course of the state. However, implicit in this assumption is that the utility function for individuals match their participation function.

For example, consider environmental regulation. The utility function for the amount of allowable emissions of some harmful pollutant like mercury for most people will be downward sloping – most people would increase their utility the less the pollutant is emitted. However, for a small minority of polluters it will be upward sloping with a much steeper slope. Let’s say that the sum of the utility gained for the bulk of the population for strong regulation is greater than that gained by the few polluters for weak regulation. If the democratic voice one has in affecting policy is proportional to the summed utility then the smaller gain for the many will outweigh the larger gain to the few. Unfortunately, this is not usually case. More often, the translation of utility to legislation and regulation is not proportional but passes through a very nonlinear participation function with a sharp threshold. The bulk of the population is below the threshold so they provide little or no voice on the issue. The minority utility is above the threshold and provides a very loud voice which dominates the result. Our laws are thus systematically biased to protecting the interests of special interest groups.

The way out of this trap is to either align everyone’s utility functions or to linearize the participation functions. We could try to use regulation to dampen the effectiveness of minority participation functions or use public information campaigns to change utility functions or increase the participation functions of the silent majority. Variations of these methods have been tried with varying degrees of success. Then there is always the old install a benevolent dictator who respects the views of the majority. That one really doesn’t have a good track record though.

Beware the vampire squid

Before you take that job programming at an investment bank or hedge fund you may want to read Felix Salmon’s post and Michael Lewis’s article on the case of Sergey Aleynikov. He was a top programmer at Goldman Sachs, who was then prosecuted and convicted of stealing proprietary computer code. The conviction was eventually overturned but he has now been charged again for the same crime under a different law. According to Lewis, the code was mostly modified open source stuff that Aleynikov emailed to himself for future reference of what he had done and had little value outside of Goldman. Salmon thinks that Goldman aggressively pursued this case because in order for the directors of the programming division to justify their bonuses, they need to make it look like the code, which they don’t understand, is important. If Goldman Sachs had a public relations problem before, the Lewis article will really put it over the top. This case certainly makes me think that we should change the criminal code and leave cases of intellectual theft by employees to the civil courts and not force the taxpayer to pick up the tab. Also, what is the point for putting a harmless nonviolent programmer in jail for 8 years. We could at least have him serve his sentence doing something useful like writing code to improve city traffic flow. Finally, the open software foundation may have a case against Goldman and other firms who use open source code and then violate the open source license agreement. I’m sure it wouldn’t be too hard to find a backer with deep pockets to pursue the case.

Patent perspiration not inspiration

Little irks me more than the current state of US patent law. It stifles innovation and encourages patent trolls, the most famous being Nathan Myhrvold’s Intellectual Ventures. The main problem is that we are allowing patents for the wrong thing. Currently, patents are awarded for innovative ideas, which means you can try to patent fairly obvious ideas like a device that converts optical images into digital information, which amazingly enough is owned by one patent troll who is trying to extort money out of anyone who has ever used a scanner, including nonprofits (see here). This American Life had an episode devoted to this topic (see here). What we should do instead is to patent the effort and cost sunk into developing an idea into a product. Alex Tabarrok has been writing about this topic for a long time and has a nice paper giving the economic reasons of why this would be better (see here for reprint). You should only get patent protection in proportion to the costs you have incurred in developing the idea.

Ideas are cheap; turning them into successful businesses is the hard part. Me, and probably everyone else, had the idea for Google Glass years if not decades ago. I had no idea how to make it work, nor did I put any effort in trying to do so. I just thought it would be great to have a projection screen built into glasses. Actually, my full idea was that it would project an image onto the retina with the focus set at infinity so I wouldn’t have to strain my eyes to read it. I don’t think anyone should be able to patent such an idea. We should encourage lots of companies to come up with ways of implementing eyeglass projection systems and let them battle it out in the marketplace. In some sense, fashion should be our model. You can’t patent fashion so designers must constantly innovate to keep ahead of the imitators. If anything, there is too much innovation in fashion. Given that we are now on the wrong side of the “Tabarrok Curve“, the argument that abolishing patents would stifle innovation is no longer valid. This is one issue that both liberals and libertarians should agree on. If we are to get any laws passed at all this congressional term, we should get patent reform.

 

Genes can no longer be patented

The US Supreme Court ruled today that human genes cannot be patented. Here is the link to the New York Times article. The specific case regards Myriad Genetics, which held a patent that controlled the rights to all tests for the BRCA1 and BRCA2 genes implicated in breast cancer. The patent essentially blocked most research on the BRCA genes. The immediate effect will be that genetic testing will become cheaper and more widespread. People will argue that not allowing genes to be patented will discourage further innovation. I doubt it. Most discoveries, like genes, come from basic federally funded research. Any company can now develop a test for any newly discovered gene. Patent law has been broken for decades and this is just one small step to correcting it.

What’s your likelihood?

Different internal Bayesian likelihood functions may be why we disagree. The recent shooting tragedies in Colorado and Wisconsin have set off a new round of arguments about gun control. Following the debate has made me realize that the reason the two sides can’t agree (and why different sides of almost every controversial issue can’t agree) is that their likelihood functions are completely different. The optimal way to make inferences about the world is to use Bayesian inference and there is some evidence that we are close to optimal in some circumstances. Nontechnically, Bayesian inference is a way to update  the strength of your belief in something (i.e. probability) given new data. What you do is to combine your prior probability with the likelihood of the data given your internal model of the issue (and then normalize to get a posterior probability). For a more technical treatment of Bayesian inference, see here. I posted previously (see here) that I thought that drastic differences in prior probabilities is why people don’t seem to update their beliefs when faced with overwhelming evidence to the contrary.  However, I’m starting to realize that the main reason might be that they have completely different models of the world, which in technical terms is their likelihood function.

Consider the issue of gun control.  The anti-gun control side argue that “guns don’t kill people, people kill people’ and that restricting access to guns won’t prevent determined malcontents from coming up with some means to kill. The pro-gun control side argues that the amount of gun violence is inversely proportional to the ease of access to guns. After all, you would be hard pressed to kill twenty people in a movie theatre with a sword. The difference in these two viewpoints can be summarized by their models of the world.  The anti-gun control people believe that the distribution of the will of people who would commit violence looks like this

where the horizontal line represents a level of gun restriction.  In this world view, no amount of gun restriction would prevent these people from undertaking their nefarious designs.  On the other hand, the pro-gun control side believes that the same distribution looks like this

in which case, the higher you set the barrier the fewer the number of crimes committed. Given these two views of the world, it is clear why new episodes of gun violence like the recent ones in Colorado and Wisconsin do not change people’s minds. What you would need to do is to teach a new likelihood function to the other side and that may take decades if at all.

 

 

Is a mandate a tax?

The health care law is currently under debate in the US Supreme Court.  At question is whether it is constitutional to impose an individual mandate to buy health insurance nationally.  I think the mandate is a perfect example of how the phrasing of logically equivalent statements can make all the difference.  In other words  “A is equal to B” and “A is not not equal to B” may both be logically equivalent but can have profound differences in the law and politics.  In the current law, everyone is obliged to have health insurance.  If they choose not to have insurance they are forced to pay a penalty.  The fact that one is compelled to engage in a commercial activity seems to be offensive to a majority of the US population.  However, congress has the right to impose a tax.  Hence, the mandate law could have been rephrased as “Everyone is assessed a health care tax and if you have health insurance, then you get a tax credit”.  This is logically equivalent to the mandate law but should have no constitutional problem since we currently pay taxes for social security and medicare.  I have never quite understood why the government doesn’t use this argument to justify the law so if anyone could explain this to me I would greatly appreciate it. It probably has more to do with the political anathema of taxation then anything else.

One last thing – there is a rationale for why a mandate is necessary, which I don’t think everyone fully appreciates.  The health care law aims to prevent people from being denied health care coverage because of pre-existing conditions.  If you make this a law then you have a free rider problem where people can simply sign up for insurance when they get sick.  This would then make insurance prohibitively expensive for everyone else.  The only way to prevent the free rider problem is to make everyone have insurance even when they are healthy and thus the mandate.  So, if you don’t want your insurance company to deny you a liver transplant because you forgot to report that you had  a broken collar-bone when you were six, then you are stuck with the mandate.  The other options are a single payer system like Canada or a fully nationalized health system like the UK but they were political nonstarters.