A while back, the New York Times had an article on decision fatigue. It’s an esoteric look at the troubles behind making consistent decisions, and is worth a read.
Lack of consistency is always a worry when making decisions, more so in some decisions than in others. You may not care much about biases if you are making a decision that would cost you 100$, but when making a decision that could affect your life years down the line, you most definitely want to be wary of all the issues you can face.
Read the article. It’s quite good, though long in some parts. It’s why I believe that decision making isn’t a tactic you use. It’s a mentality. You always need to be prepared to make a decision, and have the in built logic that goes behind making a good decision.
As I’ve mentioned before, decision trees are an important element in normative decision making. Even if you don’t go through a complete mathematical analysis, decision trees help organize your thoughts. A few months ago, my brother had received several job offers, each of which had different pros and cons to them. Working through a decision tree helped him break the decision down, and ultimately, decide where he wanted to go.
The standard example used in decision analysis when demonstrating the power of decision trees is the “party problem.” I did not create this example. I also probably would not use decision analysis to decide where to throw a party, but it is a perfect example. As I have in the past, I will assume that you are risk-neutral. In a later post, I will start to elaborate more on being risk-averse and risk-seeking, but risk neutrality simplifies life. For now.
What is the Party Problem
Imagine you are planning on throwing a party. You want to invite friends, acquaintances, coworkers, and family. You want to have food, drinks, and music. You want to the party to be a success.
You can have the party indoors, outdoors in your wonderful garden, or in the patio. The best place to have the party is outdoors because your garden is spacious and dancing under the stars is spectacular. However, where you live there is a chance for rain, and having an outdoor party when it rains is definitely not fun.
What do you do? Where do you have the party?
Where to throw the party: A decision analysis approach
If the weather is clear, then in your opinion, the best place to have the party would be outdoors. The second best place is on the patio, which is covered but is open on the sides. The worst place to have the party would be indoors.
If it rains, the best place to have the party would be indoors. The second best place is on the patio, and the worst place would be outdoors.
In order to decide where you want to throw the party, you need three things.
1 – The chance that the weather will be rainy vs. sunny.
2 – The value you attach to having the party outdoors, on the patio, or indoors if it is sunny.
3 – The value you attach to having the party outdoors, on the patio, or indoors if it is rainy.
The chance of rain vs. sun
From your experience, you believe that there is a 40% chance of it being sunny, and a 60% chance of it raining. How you come up with these numbers is up to you and your beliefs. Maybe you research it with the weather bureau. Maybe you have a dog that barks more when it is about to rain. Maybe you have a sixth sense. The point is, this numbers will never be definitive. They will represent your beliefs and experiences.
What is your value if it is sunny or when it is rainy?
The best way to do this is to rank the prospects. Since you can have the party in three different places, and since it can either rain or be sunny (which are two possibilities), then the number of possible outcomes is 3×2 = 6. The possible outcomes are:
1 – Outdoors + Sunny
2 – Outdoors + Rainy
3 – Patio + Sunny
4 – Patio + Rainy
5 – Indoors + Sunny
6 – Indoors + Rainy
When dealing with this problem, you want to rank this outcomes, from best to worst. For you (and each person can have a different list), ordering the above list results in:
1 – Outdoors + Sunny (this is the best, and you assign a value of 1 to it)
2 – Patio + Sunny (this is ok, 0.95 times as good as the best)
3 – Indoors + Rainy (this is ok, but is 0.67 times as good as the best)
4 – Indoors + Sunny (you’d get upset here, since you’re indoors, so it is only 0.57 times as good as the best)
5 – Patio + Rainy (this is not good, but it’s better than the worst one. So you give it 0.32 times as good as the best).
6 – Outdoors + Rainy (this is the worst, and you assign a value of 0 to it)
(How do you assign the above numbers? Good question. I will discuss it in the next post. For now, think of it this way: let’s say you can pay an all powerful figure to make it any one of the prospects above. How much would you pay it to make it outdoors and sunny? You may be willing to pay it 100$. You do not want it to be outdoors and rainy, so you will pay 0$. However, indoors and rainy is still ok, but not great, in which case you are only willing to pay 57$ to guarantee that it will rain. You can do this for the rest. The actual approach to getting the above numbers is more sensitive. It is important to hone down on what numbers are good for you, especially in more important decisions.)
Thus, you now have the following decision tree:
Take a second and look at this decision tree. The main decision is to choose “Outdoors,” “Patio,” or “Indoors.” If you choose outdoors and it is sunny, then the outcome is 1. If you choose outdoors, but it rains, the value is 0. Choosing outdoors may be the best decision, even if a bad outcome is possible. So what is the best decision?
In order to answer that, you will need to solve the tree.
1 – Choosing outdoors will give you a value of 0.4*1+0.6*0 = 0.4. This is straighforward math, in that you simply multiply the chance of sun by the value of the outcome, and add it to the product of the chance of rain by the value of its outcome.
2 – Choosing patio will give you a value of 0.4*0.95+0.6*0.32 = 0.57.
3 – Choosing indoors will give you a value of 0.4*0.67+0.6*0.57 = 0.61.
The winner is indoors. Your best decision is to have the part indoors, even if none of the outcomes is the best!
Now, this decision really depends on the numbers you chose above. For example, if you live in sunny california, then the probability of sun is more like 0.99, whereas there is only a 0.01 chance of rain. Thus, your decision will be different (if you decide to do the math for that, the best decision for this would be outdoors). Since the numbers affect the best decision, is there a way to check those numbers? There is, and it is called sensitivity analysis. It is a bit complex at this stage, but I will look at that eventually. And the example for that will be the party problem.
I am a Netflix customer. It was an OK deal for me, since I only watch a few movies per month, but the convenience factor of being able to stream videos, versus going to a blockbuster or a redbox (even though the rentals would give me more movies for the same price), is simply worth the price. I had the unlimited streaming and 1 DVD at a time option, which cost around 10$ per month.
(I was also a Netflix stockholder, but decided to sell the stock a while back. The reasoning behind it, and whether it was a good decision at the time with a bad outcome (considering that the stock almost doubled since I sold it), could make an interesting blog post. If you are interested in that, please let me know.)
Last week, Netflix changed their pricing structure. It was a substantial change as well. If I wanted the same plan mentioned above, I will have to pay around 16 $. In my case, I usually only stream videos, so I canceled the DVD portion, and aren’t really affected by this. It was more of a surprise as opposed to anything else.
However, other people will get affected. 16 $ is basically 16 DVDs from redbox. Some people are going to cancel their netflix membership because it isn’t the ONLY supplier out there.
Some competition includes: Amazon (75$ for a prime account will give you unlimited streaming), Redbox, Blockbuster (and blockbuster express), Hulu / Hulu Plus, and cable. In reality though, any form of entertainment can be a Netflix replacement.
The executives who made the decision to increase prices by this much must be aware that they are going to lose customers. How many customers are they expecting to lose? Is the added revenue worth the loss? Is the revenue necessary to keep up with growing costs?
Decision-making is very real, and has serious consequences. Which is why normative analysis is so important.
When I first read about the increase, I was curious about how Netflix went about deciding the price increase. There are several reasons they would look into this.
1 – Content providers (for movies, such as Sony Pictures) are planning to increase their prices, which Netflix must deal with. Question: Does Netflix know how much the license prices will increase by? If yes, then it makes life easier. If no, then the correct way of factoring the uncertainty in is to have a distribution on the possible prices.
2 – Netflix sees the future of movies as streaming, as opposed to being delivered via a physical medium, such as DVDs. Question: How long does Netflix think it will take before DVDs will be phased out of our world? Do they think the quality of streamed videos can eventually compete with DVDs? Are they planning to have an online library of movies as comprehensive as the one they have on DVDs? I can’t see them having any form of certainty on any of these questions. Thus, they would be modeled as distributions. For example, there is a 20% chance that DVDs will be worthless in 5 years, a 40% chance they will be worthless in 10 years, and a 40% chance they will be worthless in 15 years. This can also be done for the other questions.
3 – What new competitors will come out in the future? Question: Did Netflix factor in this black swan concept into their model, if they had one? When making a decision tree, it is possible to factor in the unknown, which can affect your decision.
4 – Basic economics states that demand changes with a change in price. Question: How did Netflix model this? Was it a deterministic model, like what is taught in Economics 101 classes? Or did they factor in the uncertainty inherent in any industry? For example, at the current prices, Netflix has X customers. If they double the prices, they have a 10% chance of keeping X customers, a 50% chance of having aX customers, and a 40% chance of having bX customers. If they halve the price, they get a 20% chance of having cX customers, etc. Since I forsee this to have a serious effect on the bottom line, this would be something that should be modeled carefully, based on customer research. Maybe Netflix did do that. Maybe they didn’t.
This pricing change has a very real effect on the Netflix business model.
There are multiple outcomes of this change, which can be lumped into two categories. Netflix will either come out better, or will suffer. Given all the information Netflix has on customers and the industry, some of which can be answered by looking deeply at the questions above, did they make a good decision?
Unfortunately, that isn’t something we can answer, because we don’t know the information they used when making the decision. It may be the best thing Netflix has done.
It may also be the worst. Time will tell. In the meantime, we can all work on making good decisions, regardless of what the outcome is. If you work in a corporation, your customers and stockholders depend on it.
While doing some research on decision analysis, I came across a paper written by Professor Ron Howard, entitled:
Speaking of Decisions: Precise Decision Language.
When I took courses with Prof. Howard, one of the things I greatly enjoyed, besides the life-changing content of the classes, was how he shares and explains ideas. He uses a semi-Socratic method in his discussions. Although this paper has some technical components, it is a great read. If there are any concepts you would like to have explained in more detail, let me know,
The Harvard Business Review recently ran an article on decision making. It is an excellent read on some of the differences between intuitive and normative decision making (the authors refer to these two groups as System One and System Two, respectively), as well as the issues you face when making decisions. For example, the authors (one of whom is a Nobel Prize winner) write that:
Though there may now be far more talk of biases among managers, talk alone will not eliminate them. But it is possible to take steps to counteract them. A recent McKinsey study of more than 1,000 major business investments showed that when organizations worked at reducing the effect of bias in their decision-making processes, they achieved returns up to seven percentage points higher. (For more on this study, see “The Case for Behavioral Strategy,” McKinsey Quarterly, March 2010.) Reducing bias makes a difference.
Seven percent is no joke.
I haven’t discussed biases on this blog yet, though this article is a reminder that I should touch on this. Sometimes, psychological blocks and twists results in bad decision making, and it is important to keep these in mind when involved in decision analysis.
A pdf version of the article linked above is available here.
Not to wax philosophical prose on you, but your PIBP and PISP, which were discussed in detail in the last few posts, are related in more than just their definitions. The PIBP and PISP are duals, because of a concept called the (instantaneous) cycle of ownership.
What is the cycle of ownership? The term is quite intuitive. If you sell your car, and then immediately buy the same car back again, you’ve created a cycle of ownership, since the ownership of the car cycles back to you. If you buy something and then sell it again, you’ve also created a cycle of ownership.
Formally defined, a cycle of ownership means selling (buying) an item and then instantaneously buying (selling) this item, without transaction costs. The instantaneous transfer makes it impossible for any information to change. For example, if you buy a car, you won’t have time to discover that it’s a lemon, in which case everything changes.
The figure below shows how the cycle is formed.
Now, we know that if you buy something, you have a PIBP – or a personal indifference buying price. If you’ve paid for a car with your PIBP, then your life becomes YOU + CAR – PIBP. Once you sell your car, you sell if the bid is equal to or higher than your PISP. If you sell it with your PISP, then your life becomes YOU – PIBP + PISP. However, because this is instantaneous, and there is no transaction cost, then you’re back to the original point in your life, which means that YOU – PIBP + PISP = YOU! And thus, your PISP and PIBP are both equal, around a cycle of ownership (this is assuming that there are no transaction costs – otherwise, you’d need to factor them into the equations above, and the PISP won’t be exactly equal to the PIBP).
This also works the other way around. Assume you are selling a computer that you own. Before selling it, your life is represented by YOU. After selling it (with at least your PISP), your life becomes YOU – COMPUTER + PISP. If you immediately buy it back again, and pay your PIBP, your life becomes YOU + PISP – PIBP, which is equal to – you guessed it – YOU!. Thus, again, with this cycle of ownership, your PIBP is equal to your PISP.
Why is this true only if there are no transaction costs?
In the real world, you usually pay someone a fee for buying or selling an item. A perfect example is buying and selling stocks, in which you pay your broker a fee. In the example above, buying the car results in YOU + CAR – PIBP – COST, where COST is the transaction cost you paid the dealer. Selling the car results in YOU + PISP – PIBP – COST – COST, which will not be equal to YOU if PISP and PIBP are equal (unless COST is equal to zero).
Why is this instantaneous?
A cycle of ownership is looked at during an immediate buy and sell transaction. With every passing second, your life changes – you may have lost some money, or you may have bought something, or you may get paid at your job, in which case your PISP and PIBP also change. The totality of your life’s value, or your wealth, is important, and allowing the passage of time not only allows your wealth to change, but also gives you the chance to obtain more information, in which you will evaluate things differently. For example, if you sell a car, the new owner may discover some issues with it you hadn’t realized.
Play around with this idea in your head for a while. Internalize it. It’s important to understand it properly, if you are to be a consistent decision maker.
Recently, Ossama Bin Laden was killed. As I was reading articles on the raid, which most of you have probably also done, I came across one on CNN with the following headline:
I found that fascinating. Very few people admit that the decisions they took could have had bad outcomes, which is exactly what decision analysis deals with. Remember, decision analysis, which is the topic of this blog, doesn’t guarantee that only good outcomes arise.
Decision analysis guarantees that you consistently take good decisions. Every good decision can result in a bad outcome.
Just a short note and reminder that everything we do is a decision, and every decision is based on uncertainty. Even when you are president.
In the last post, I discusses what your PIBP is, in addition to going over a few simple qualitative examples. Your PIBP is your personal indifferent buying price. Since the opposite of buying is selling, we can also define your PISP.
Your PISP is your Personal Indifferent Selling Price. This is the amount of money you would be indifferent to accepting when selling a certain item. There are different ways to understand this (although all essentially boil down to the same concept). One interpretation of this is: if someone were to offer you 1 cent less than your PISP, then you would not sell this item. If someone were to offer you 1 cent more than your PISP, you would definitely sell it. An alternative interpration is: if someone were to offer you an amount exactly equal to your PISP, then you would not care if you 1) sold the item and took the money OR 2) kept the item and didn’t take the money. In other words, Your life would not change if you do one or the other.
In discussing your PIBP, I used a simple decision tree. Something similar can be drawn for your PISP, but I will leave it to you. How would you draw the decision tree for this? Since it is a trivial exercise (hint, see the post on the PIBP), let’s look at it from another perspective.
Let’s say you want to sell your couch. The value of your current life – or your state of happiness – or how complete you feel – or however you want to phrase the current status of your life – includes this couch. If you could package everything in your past, present, and future, such that “YOU” becomes one entity, then you would have something along the lines of the image below.
Of course, the “YOU” I’m referring to can be broken down into a million things. How exactly you break it down is very personal, but one such way is:
Note that your couch is included. Even if you really despise it. The value of your current life includes this couch. If you sell your couch in return for something (such as money), then the value of your life (post-selling the couch) becomes:
Depending on how much money you are given for the couch, one of the lives presented in the above two pictures may be more appealing. Your PISP is the value that would make you not care which of the above two lives you lived. Now, as in the case of your PIBP, your PISP doesn’t have to be positive. For example, don’t you pay someone to take your garbage from you?
Everything you own or have or use or know has a selling point that you would be hesitant about accepting. If you have a pair of old shoes, you would jump on anyone that gave you 10,000$ for them, but would probably keep them if they only offered 1$.
Look around you. What do you see? A pair of jeans? A computer? Maybe even your car? Can you think of a rough number for each as your PISP? You want to train yourself to calculate approximate values of your PISP for almost anything you think of. You can also attach value to items that have emotional significance. You have a basketball signed by Michael Jordan? You definitely won’t accept 10$ for it, but what if another fan offered you 1 million $. What if your wife gave you a gift that doesn’t have much material value, but makes you smile everytime you look at it. Maybe you wouldn’t even accept 1 million $ for it (although, if you don’t accept that because you’re afraid of her screaming at you, then you have other things to worry about), but if someone offered you 100 million $, what would you do? Even your time has a PISP attached to it. If you consult, you may not “sell” your time for anything less than 200 $. However, working pro bono as a volunteer could compensate for that because you get value from that (though not in real money).
Next up – the reason the title states that the PISP is the dual of your PIBP, is that they form a cycle of ownership. I’ll elaborate more on that later.
I have briefly mentioned what the PIBP is in a much earlier post, but as I’m cycling through some of the topics again, and have elaborated on decision trees in the last couple of posts, it is worth delving into this again.
Your PIBP is your “Personal Indifference Buying Price.”
Yes, that’s a complicated technical term. The meaning is much less complicated. Let’s say you come across a pair of jeans that has the most vibrant you’ve seen, fits great on you, and looks amazing. Furthermore, it only costs 1$.
Would you buy it? Chances are, unless your a bum living on the streets of San Francisco, you probably would. What if it cost 10$? Probably. 20$? Probably. 50$? You’d start thinking about it. 100$? You’d think about it even more. 500$? Probably not. 1000$? Unless it’s studded with diamonds, I think it’s safe to say that you would not buy it.
When you buy this pair of jeans, you gain the jeans, but you give up some money. The question you would ask yourself, is which do you prefer:
1 – Having the jeans but parting with the money you spent on it.
2 – Not having the jeans.
The decision you face is denoted by the following tree (click to enlarge):
Your PIBP – personal indifference buying price – is the price where (value of jeans) = (amount paid for jeans). This bring an important notion in decision analysis to the forefront:
Value is not the same as price.
In order to calculate your PIBP, it is important to understand this. It comes with practice. Furthermore, if the (value of jeans) equals the price, then you do not care whether you buy the jeans or not. If the price is slightly less than the value, you’ll snap it up. And if it is more than the value, then you will move on. It makes decision making that much easier.
Why is it important?
Different people will have different answers, but the most important facet of the PIBP to me is that it allows you to remove emotion from decision making. When I go to buy a car, it is easy to be impressed by a super cool car, and be swayed by the salesperson to pay more.
However, if I give this some thought before hand, I can figure out what value different cars offer to me. And I can put a number to this value, which then allows me to either negotiate, or to look for different salespeople that will offer me a price less than this value.
This isn’t theoretical. This has immediate applications in your daily life. You want to buy a computer? Attach a number to the value that a computer offers you. Want to pay for education? Do the same.
Interestingly, your PIBP can be negative. Would you pay for rotten food? If you do have rotten food, then you (I hope) throw it away! Let’s say I come up to you and offer you some rotten food, if you pay me 10$. Deal or no deal?
What if I charge you 0$ – or give it to you for free? You’d probably say no deal as well. It’s too much hassle to take the food and then to walk to the trash can to throw it away.
What if I pay you 100$? I bet you’d say deal, since you would take the rotten food, pocket the 100$, and throw the food away.
In this example, your PIBP was less than 0. Think about it. And then, think about how you can apply this your life.
As I was preparing another post on whether you should buy a house or rent one, I realized that I have not really discussed the concept of uncertainty.
What is uncertainty?
A non-mathematical description of uncertainty is “How sure are you that something will happen?”
For example, I’d say most of us are sure that the sun will rise tomorrow (although in probabality theory, even that isn’t a certainty, and if people are interested, I can expand on this in a later post).
However, if you flip a coin, do you know for certain whether it will land heads or tails?
How about if you go watch a movie? Are you certain that it will be either good or bad?
If you invest in a stock, are you 100% sure that it will double in value? If you are, call me!
How many times have you watched the weather report, only to discover the next day that the report was completely wrong?
There are countless examples of how uncertain we are about things … and honestly, that’s because basically everything can be modeled with uncertainty.
How does uncertainty affect our decisions?
Let’s say you have an important meeting, and you usually walk to work. If it is always sunny, then I highly doubt you will take a jacket and umbrella. However, what if it is in winter, and it’s forecast that there is a 50% chance of rain? Will you take an umbrella, even if it may not rain?
You probably will.
Now, what if you drive to work, and the road you usually take is blocked because of an accident. Although you haven’t reached that road yet, you think there is a good chance that traffic has completely stopped. If you take it, and if the accident hasn’t been cleared yet, you’ll be late to a meeting. Will you take the road?
We face these decision all the time, and our decision changes because of some uncertainty. Because you are uncertain of weather it will rain or not, you change your usual decision to not take an umbrella, just in case. Likewise, you don’t take the road you usually drive on, just in case it’s blocked.
Why does any of this even matter?
It matters, because how uncertain you are – or, on the flipside, how certain you are – of something changes how you act. In other words, it changes your decision.
If you knew it was going to rain for sure, you might pay 20$ to take a taxi.
If you knew it was going to be sunny for sure, you might just walk, thus saving 20$ and getting some exercise.
If you weren’t sure, would you take the taxi? Would you walk? What exactly would you do?
Whether you walk or take the taxi depends on how unsure you are. And that, is where decision analysis, and the use of decision trees, comes in.
If you have any questions, don’t hesitate to contact me.