I was relaxing the other night having what I like to call “a drink and a think” where I relax and ponder especially intractable problems. My mind may wander from the bizarre nature of black holes all the way to whether or not bees actually have knees. I’m not a big fan of bees so I tend not to question them given their often stinging rebuttals. I was a bit unfocused this night having done perhaps more drinking than thinking when my cat hopped onto the couch for a treat. He doesn’t drink or, near as I can tell, think overly much so he got a kitty treat then purred and kneaded himself into a little furry ball next to me.
That did shake a thought loose. We had just the one cat, yet I’ve heard that most people with only one will eventually decide to have more, at least two. I believe there was a 75% chance that a single cat owner would eventually have multiple feline friends begging for treats from them. I thought 75% was a pretty high odd, should I just go get another cat? If it was going to happen anyway, why put it off. I did like cats, they’re soft and sometime affectionate and the purring is certainly nice. But when I started thinking more than drinking, something started bothering me.
If 75% of all owners with just one cat get at least a second, does it follow that each individual owner has a 75% chance of increasing their feline residents? My drinking and thinking would have to move into research. I also considered anyone else I knew with only one cat and if they ever thought about getting another. As I would learn, this is an example of an Ecological Fallacy. It’s a pretty overbearing name, isn’t it? While this fallacy has its roots in statistics, it’s not so hard to explain. Rather simply it means that you can’t always apply the properties of a group to the individuals within that group. In my case it meant that while, as a group, owners of one cat were 75% more likely to get a second, the same was not true of any individual owner. I was comfortable with one feline friend and being old he didn’t like other animals so I was better off a one cat household. Other’s though, like those with multiple children who love animals might decide to have an equal child to feline ratio and get a few more.
This is an important fallacy, and application of logic, to keep in mind as you go about your day. As I write this summer is ending, fall is coming (I know, should be winter) and I’m seeing notes about getting my flu shot. Sometimes we will hear about the likelihood of contracting that nasty illness. Let’s say the medical community thinks there is a 60% chance to get it. As we learned above, this does not mean I have a 60% chance. I work remotely so I don’t have office exposure. I don’t have children so they won’t bring it home to me. Those facts may lower my chance. Others will have a higher likelihood. It’s only the population in general that has the 60% chance. I may still decide to get the vaccine as I like to be out amongst people, at holiday parties and shows. My risk of any reaction to the shot are very low while the possibility of avoiding the flu are high.
The US is coming up on an important election (even though all elections are important, aren’t they?) which means we see a lot of news talking about polling and knowing how communities, suburbs, cities, etc. will tend to vote one way or another. As I said, this fallacy has its roots in statistics and polling is all about stats even if they don’t tell you. Let’s say a report says that a particular community is 80% likely to vote for candidate A and only 20% for candidate B. If you live in a house with 10 people, this does not mean 8 of them will vote for A while 2 will vote B. Perhaps your household all has the same political ideals. Or perhaps the household likes to argue and is split down the middle. It’s important to always keep in mind that the poll represents a population (or a sample of the population, in reality) and does not know how any individual will vote. The take away is to ignore the polling and go cast your vote no matter what.
Let’s look at one more example to really drive this point home – sports! I know not everyone is a fan of the sports so I’ll keep this rather generic. Suppose you have a team that’s supposed to move some kind of object across a field better than another team, but they’re not doing too well. If the team is performing poorly it is easy to say that is because the team has all poor players. However, that isn’t at all true. A team is made up of a range of individuals. Perhaps there are a few that don’t run fast enough, but maybe one person is exceptionally quick. Maybe the leader can throw the ceremonial object really well, but the others aren’t as good at catching it. Genericizing sports is hard work! Its easy to ascribe the performance of the team as a whole to the individual members, but that is often not accurate.
I’m sure as you look around you’ll see more and more examples of the ecological fallacy. There is a strong desire to put people into groups and place certain attributes on that group. But that doesn’t mean the individuals will behave the same way. As a statistical fallacy, this isn’t always used to mislead (at least purposefully) but it is often misleading. As a member of a group with a given statistic you don’t necessarily have to conform to it. By understanding this fallacy, we can determine how to act, to vote and whether people can catch things and run. Now, if you’ll excuse me I saw some pictures of kittens and I might go become a statistic.