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.