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.




Implicit bias

The most dangerous form of bias is when you are unaware of it. Most people are not overtly racist but many have implicit biases that can affect their decisions.  In this week’s New York Times, Claudia Dreifus has a conversation with Stanford psychologist Jennifer Eberhardt, who has been studying implicit biases in people experimentally.  Among her many eye opening studies, she has found that convicted criminals whose faces people deem more “black” are more likely to be executed than those that are not. Chris Mooney has a longer article on the same topic in Mother Jones.  I highly recommend reading both articles.

Race against the machine

One of my favourite museums is the National Palace Museum (Gu Gong) in Taipei, Taiwan. It houses part of the Chinese imperial collection, which was taken to Taiwan in 1948 during the Chinese civil war by Chiang Kai-shek. Beijing has its own version but Chiang took the good stuff. He wasn’t much of a leader or military mind but he did know good art. When I view the incredible objects in that museum and others, I am somewhat saddened that the skill and know-how required to make such beautiful things either no longer exists or is rapidly vanishing. This loss of skill is apparent just walking around American cities much less those of Europe and Asia. The stone masons that carved the wonderful details on the Wrigley Building in Chicago are all gone, which brings me to this moving story about passing the exceedingly stringent test to be a London cabbie (story here).

In order to be an official London black cab driver, you must know how to get between any two points in London in as efficient a manner as possible. Aspiring cabbies often take years to attain the mastery required to pass their test. Neural imaging has found that their hippocampus, where memories are thought to be formed, is larger than normal and it even gets larger as they study. The man profiled in the story quit his job and studied full-time for three years to pass! They’ll ride around London on a scooter memorizing every possible landmark that a person may ask to be dropped off at. Currently, cabbies can outperform GPS and Google Maps (I’ve been led astray many a time by Google Maps) but it’s only a matter of time. I hope that the cabbie tradition lives on after that day just as I hope that stone masons make a comeback.

Discounting the obvious

The main events in the history of science have involved new ideas overthrowing conventional wisdom. The notion that the earth was the center of the universe was upended by Copernicus. Species were thought to be permanent and fixed until Darwin. Physics was thought to be completely understood at the end of the nineteenth century and then came relativity theory and quantum mechanics to mess everything up. Godel overthrew the notion that mathematics was infallible. This story has been repeated so many times that people now seem to instinctively look for the counterintuitive answer to every problem. There are countless books on thinking outside of the box.  However, I think that the supplanting of “linear” thinking with “nonlinear” thinking is not always a good idea and sometimes it can have dire consequences.

A salient example is the current idea that fiscal austerity will lead to greater economic growth. GDP is defined as the sum of  consumption, investment, government spending and exports minus imports. If consumption or investment were to decline in an economic contraction, as in the Great Recession, then the simple linear idea would be that GDP and growth can be bolstered by increased government spending. This was the standard government response immediately after the financial crisis of 2008. However, starting in about 2010 when the recovery wasn’t deemed fast enough instead of considering the simple idea that the stimulus wasn’t big enough, the idea that policy makers, especially in Europe, adopted was that government spending was crowding out private spending so that a decrease in government spending would lead to a net increase in GDP and growth. This is very nonlinear thinking because it requires a decrease in GDP to induce an increase in GDP. Thus far this idea is not working and austerity has led to lower GDP growth in all countries that have tried it.  This idea was reinforced by a famous, now infamous, paper by Reinhart and Rogoff, which claimed that when government debt reaches 90% of GDP, growth is severely curtailed. This result has been taken as undisputed truth by governments and the press even though there were many economists who questioned it.  However, it turns out that the paper has major errors (including an Excel coding error). See here for a summary.  This is case where the nonlinear idea (as well as conflating correlation with causation) is probably wrong and has inflicted immense hardship on a large number of people.


Cognitive dissonance

The New York Times has a story today describing how the American middle class are becoming more reliant on government aid, much to their chagrin.  However, the reaction of many of the people interviewed  is animosity towards government programs and support for culling them, even though that would hurt themselves economically.

New York Times: One of the oldest criticisms of democracy is that the people will inevitably drain the treasury by demanding more spending than taxes. The theory is that citizens who get more than they pay for will vote for politicians who promise to increase spending.

But Dean P. Lacy, a professor of political science at Dartmouth College, has identified a twist on that theme in American politics over the last generation. Support for Republican candidates, who generally promise to cut government spending, has increased since 1980 in states where the federal government spends more than it collects. The greater the dependence, the greater the support for Republican candidates.

Conversely, states that pay more in taxes than they receive in benefits tend to support Democratic candidates. And Professor Lacy found that the pattern could not be explained by demographics or social issues.

Cognitive dissonance is a term in psychology that describes the uncomfortable feeling when two conflicting thoughts are simultaneously held and the attempts to rationalize the inconsistency. The political dynamics currently playing out in the United States may be a giant manifestation of this phenomenon.  A telling aspect of the article was that many of the people interviewed acknowledged that they could not survive without government assistance but felt that they did not deserve such help and preferred that it be reduced rather than subjecting others to higher taxes to pay for it.   This rather honorable attitude serves as a stark contrast to the premise of the heavily debated new book of Charles Murray, Coming Apart (see New York Times review here) that argues that the economic travails of the white working class is due largely to a lapse in moral values.  What was also striking in the article was that there was no sense that the dire economic situation these people were facing was due to the fact that the economic game was stacked against them.  There was just a silent resignation that this is the way things are.  The American mythos of the self-reliant and self-made individual is a powerful metaphor that is firmly implanted in a large fraction of the population.  People will not always support policies that are in their economic interests.  This facility for self-denial is a large part of what makes us human.  How we obtained it is still an unresolved problem in evolutionary biology.