I’m taking a class in probability this semester so I’ve been hearing a lot about “dependence and independence”, but it wasn’t until I finished Seven Habits that I realized that those definitions applied to the concepts in the book. If you wanted a definition that satisfies your left brain there’s no better place to look than math. So here’s my attempt at explaining the interpersonal concepts of dependence, independence, and interdependence.

First a few Definitions

The figures in this post are all Venn Diagrams. The circles are events, they’re all something the happens. An event could be “Nique goes to the grocery store” or “Nique cleans her room” or “It rains today”. The events in this post are labeled A and B, but they could be anything. Single letters just fit in the circles better than full sentences.

If circles overlap that means that events overlap. For instance if event A is “Nique goes to the grocery store today” and event B is “Nique buys strawberries today” those two events sometimes intersect. That is, sometimes I buy strawberries at the grocery store. But they don’t always overlap because sometimes I buy strawberries from the farmers market or I might pay to pick some at the U-pick fruit farms. In this case the overlap of the events is partial and that’s shown by the circles overlapping. If I only bought strawberries at the grocery store then event B would be completely inside event A. Event B would also be smaller than A since I can go to grocery store and not buy strawberries, but I can’t buy strawberries and not go to the grocery store. Make sense?

That should be enough to understand the rest of this article. (If it’s not, leave a comment or send me an email and I can revise it.)

Now onto how this applies to your social life.

Dependence

Figure 1: Dependence

The classic example of dependence is the parent-child relationship, so lets look at two related events: A: Mother feeds child; B: Child eats. A and B highly related events… so highly related in fact that they totally overlap. (Figure 1) It’s a little hard to see in the picture, but there are two circles there–one for A and one for B–they just superimposed on top of each other. The child is totally dependent on her mother. If A occurs (Mom feeds child) then B occurs (Child eats). If B doesn’t occur (Child doesn’t eat) then we know A didn’t occur either (Mom didn’t feed her).

This diagram can be applied to all sorts of situations. I’ll use three basic cases through out this post: the money borrower, the employee, and the drug addict. For dependence these situations could be visualized as follows:

• Money Borrower: Event A: Bank loans money to person.  Event B: Person gets to spend money
• Employee: Event A: Company’s Stock Price Goes up. Event B: Employee’s Stock Portfolio Goes up (employee invested heavily in company stock)
• Drug Addict: Event A: Drug of choice has been obtained by person. Event B: Person feels happy.

In each of these cases of extreme dependence, Event A always implies Event B, and vice versa.

Figure 2: Still Dependence

This isn’t the only form of dependence, though. Take a look at figure two. Believe it or not, that’s also dependence. Specifically it’s counter-dependence. If event A occurs we know that event B does NOT occur and vice-versa. This is a majorly important concept and is the source of a lot of confusion, so an example: Event A: Mom tells you to clean your room Event B: You clean your room. From Figure two we know that if A happens (Mom tells you to clean your room) B definitely didn’t happen (You definitely didn’t clean your room). The reverse works too. If you cleaned your room, Mom definitely did not tell you to. This is still dependence! How many times have we heard parents say, “I gave my teenager some advice, but it fell on deaf ears” or “My kid just won’t listen to me”? Chances are the kid actually is listening (listening intently) and then doing the opposite. The parent of a truly independent child is powerless, but I imagine that it’s quite likely the child is counter-dependent instead of independent.

The beauty of the Venn diagram is it clearly shows the confusion between counter-dependence and independence. The events are mutually exclusive. They look like they should be independent since they’re separate, but the dependence properties are exhibited just as strongly as in Figure 1. New probability students often get this concept of “mutually exclusive events are not independent” confused (I certainly did) so it seems inevitable when it’s applied to personal relationships it gets even more muddled.

Independence: The true “falling on deaf ears”

Figure 3: Independence

Figure 3 is the form of true independence. What it shows is that if Event A happens then Event B may or may not happen. Sometimes it will (the overlapping section) and sometimes it won’t (the non-overlapping section). Also, if we know Event A happened we know nothing about whether Event B happened or not. For instance, if A is still “Mom tells you to clean your room” and B is still “you clean your room”, if you are truly acting independently the knowing whether or not your mom asked you to clean your room doesn’t give us any information on whether or not you do it. You might do it or you might not. The factors it may or may not be dependent on do not include your mother telling you to do so.

Applying them to the examples listed above:

• Money Borrower: Knowing the bank lent him money (Event A) doesn’t tell us anything about whether or not he spent it (Event B)
• Employee: Knowing the the company stock price went up (Event A) doens’t tell us anything about whether or not his portfolio went up (Event B) (His portfolio doesn’t contain any of the company stock.)
• Drug Addict: Knowing that person obtained drugs does not give us any information on whether or not he’s happy.

In all these cases independence is clearly better than dependence. The person is in charge of his spending, his portfolio, his happiness, not the bank or the company or the drug. Granted he may be dependent on something other than those things (and probably is), but at least it’s dependent on institutions and things that definitely don’t have his best interest at heart.

Independence is an illusive concept. In fact, I’d say, true independence either doesn’t exist or is so useless that it might as well not exist. Think about it. Even if you lock yourself away from society, whether or not you eat will still be dependent on the quality of the land, your skills as a farmer or hunter or gatherer, and the weather and plenty of other factors. And even if you could make decisions without making use of external input you’d be acting randomly. Not exactly the most useful way to live.

Still, as in the case of the examples above, acting independently from people, things, and institutions that don’t have your best interest in mind is VERY useful. Methinks when people talk about wanting independence that’s what they really want: the freedom to disregard stuff.

So that’s independence. It’s better than total dependence since presumably you have a pretty good idea of what’s best for you. But asserting that you always know what’s best is not only arrogant it’s just downright wrong. Someone with different experience than you will have some useful information you simply don’t have. Acting independently of good information is an incredibly stupid way to live. The trick is to utilize the strengths of both independence and dependence (Yes, dependence can be useful. If it wasn’t all babies would be doomed.), and that brings us to our last concept:

Interdependence

Figure 4: Interdependence

Interdependence is when events are related, but neither mutually exclusive (Figure 2) nor identical (Figure 1). If mapped as a Venn diagram interdependence would look something like Figure 4. Yes, it’s the same picture as Independence in Figure 3. Venn diagrams can’t really be used to distinguish between independence and interdependence. [1] This confusion which may partially explain why interdependence is hard to see as being better than independence. The visual looks the same, and at least with independence we aren’t being affected by potentially harmful advice! Interdependence really is the better way, though. It’s the difference between putting your money in a mutual fund and putting it in a savings account. Yes, there’s more risk in a mutual fund but there’s also a high potential for gain. With a savings account your money is safe, but you won’t get much in the way of interest. With advice, yes there’s some risk in taking other people’s advice, but there’s a lot to be gained if advice is used wisely. Similarly acting independently of other people’s advice may be safer, but you won’t won’t gain their knowledge. There is a big difference between stocks and interdependence, though. With stocks you’re often better off picking an index fund which samples a whole bunch of funds rather than creating your own portfolio by hand. With interdependence picking and choosing advice consciously, manually, is the best way to use it. You’re more likely to learn that way. Also your own mind gives you a higher interest rate than a savings account.

So enough abstraction and imperfect analogies. What does interdependence look like? Let’s go back to the earlier examples:

• Money Borrower: Knowing the bank lent him money (Event A) might make him more likely to spend money (Event B), but he may also consider the advice a financial consultant beforehand (unlabeled Event C).
• Employee: Knowing the the company stock price went up (Event A) tells us that his portfolio is likely to have gone up (Event B) (His portfolio contains some company stock, but not exclusively company stock.)
• Drug Addict:Knowing that he obtained his drug of choice (Event A) tells us that he’s likely to feel happy, but there may be other unlabeled events that would lead him to feel not happy about it.

In a nutshell interdependence is allowing yourself to wisely be influenced by others. It looks like independence(at least when you see the figures) and sounds like dependence (being influenced by others), but really it’s the best of both. It’s using your ability to act independently to make good use of the collective knowledge of other people.

Hopefully now your analatical side has a better grasp on these terms.

[1] Technically Figures 1, 2, and 4 are all diagrams of dependence since all show differing levels of influence one event has on the other. Figures 1 and 2 show total dependence and Figure 4 is supposed to show partial dependence. So when you open your probability text book and it says that Venn diagrams can’t be used to distinguish indpendent and dependent events you’ll know why: interdependent events are really a subset of dependent events.