QUESTION 3

fill the blanks

According to EVR you ought not to buy an extended warranty

The principle of EVR says you ought not choose an action whose ............cost is greater than the..........value, which is the case in buying an extended warranty, because the real cost is set by the seller.

Even without knowing the probabilities, you know the expectation value of the extended warranty for the.........is the negative of your expectation value, since any outcome which is a positive for you as the buyer is a negative for them as the seller, while the price, which is your real .............., compensates them, which means the real cost to you is greater than your expectation value.

According to EVR you ought not to buy an extended warranty.

Look to :

3. According to EVR you ought not to buy an extended warranty

COLLAPSE

Top of Form

3.1 Introduction

We explained before how engineering requires normative decision making because real world problems do not have perfect solutions. One way solutions will be imperfect is because they cannot satisfy all the non-technical constraints.

But now we want to consider another reason. Engineers must make normative decisions because of risk or uncertainty. Technical expertise only gets one so far in predicting how well a solution to a problem will work out. Since we can never have perfect certainty, any engineer solving a problem is making a choice about what is an acceptable level of uncertainty. Acceptable (or adequate, good enough) is one of those normative ideas.

Uncertainty, therefore, means normativity. Dealing with uncertainty requires normative expertise.

Expectation value reasoning (or EVR) is a theory of normative ethics --- that is, a theory for choosing actions, for deciding on the best course of action.

The theory is described in more detail in the textbook, and in the previous quad. In this quad, we'll assume you understand the details. The point here is to put the theory to work, in arguing against a particular action. Namely, against buying an extended warranty (XW).

(This is just one argument, and one way to look at that decision.)

The skeleton of the argument is this: the theory of EVR includes a normative principle about what you should or should not do. According to that principle, buying an extended warranty is something you should not do. So, according to EVR, you should not buy an extended warranty.

That's just the skeleton. It's a valid argument, but without a fuller explanation of each of the premises in this argument the argument cannot be persuasive. No one can be persuaded by an argument if they do not understand the reasons given in that argument.

The rest of the quad, then, will explain the premises of the argument. Your job, in answering the short-answer question will be to reduce those explanations to three sentence form --- something which will have the same skeleton just given, but using more explanatory detail.

3.2 Expectation value reasoning is probability weighted cost benefit analysis

Expectation value reasoning (or EVR) is a theory of normative ethics --- that is, a theory for choosing actions, for deciding on the best course of action. It is designed to guide our decisions when faced with uncertainty. The theory is described in more detail in the textbook. In this quad, we'll assume you understand the details.

EVR actually falls under the big three categorization of consequentialism. It is a consequentialist theory since it requires you to evaluate actions through their consequences.

In the theory the consequences are called utilities. Each possible outcome, or consequence has a utility --- a measure of the benefit or, to put it simply, the ``goodness'' of that outcome.

But these are possible outcomes. This is the point. EVR is used when we cannot be certain about what the outcome will be. There is a range of them, or at least more than one.

The theory also takes into account the cost of an action. For this, there is not a range, and we don't consider this an outcome or consequence. It is fixed. You pay it if you choose the action, regardless of the outcome.

So EVR is a form of cost-benefit analysis. It takes into account the cost of an action or choice; as well as the benefits of that action. Except that, we are uncertain about which benefits because we are uncertain about the outcomes.

The way EVR works is to use the probabilities of each outcome to ``weight'' the benefits of those outcomes. Intuitively, the idea is that a high probability outcome with a low benefit should count the same in our decision making as a very very long shot, with a high benefit.

EVR just makes precise how to calculate those comparisons. EVR is a theory for doing cost benefit analysis when one is uncertain about which benefits one will gain. What you calculate is called the expected utility of an action. The expected utility is found by adding up, for each possible outcome of the action, the utlity (benefit) of that outcome multiplied by the probability of that outcome.

The expected utility is the ``benefit'', so to speak, with which EVR tells you to compare the cost.

3.3 The normative principle of EVR is: you ought not to choose any action with expected utility less than real cost

EVR is a theory of normative ethics. Normative ethics is about good decision making; it is about action. Any theory of normative ethics should contain a principle about action: a principle which describes how to decide what one ought or ought not to do.

In consequentialist theories, for example, the principle is you ought to choose the action which maximizes the good consequences. A principle of Virtue ethics may be that you ought to act with prudence and according to good character. Note that these principles are both about actions, and about the good. They are about good actions. So, they are theories of normative ethics.

(Note also that, although they're not written explicitly as if-then statements, they are equivalent to one. E.g. if an action is prudent and one which an honest person would do then you ought to do that action.)

EVR is also a theory of normative ethics. It has a normative principle. It is a form of consequentialist normative ethics, so it's principle is that you ought to maximize good consequences.

But EVR is also a form of cost benefit analysis. In cost benefit analysis an action ``makes sense'' if the benefits outweigh the costs. If the benefits are greater than the costs than the action would increase good consequences.

But what if you're uncertain about what the outcome of your actions will be? How do you weigh the consequences of what you only predict will be the outcome, especially if there are range of possible outcomes, all with different consequences?

The normative principle of EVR is based on a long term view of utilities. Rather than think of utilities (or benefits or consequences) in a simple way, EVR instead considersexpectedutilities. Expected utilities are utilities weighted by the probability that that will be the outcome. If you add all of the expected utilities together, for all of the possible outcomes of an action, you will get theexpectation valuefor that action. According to the EVR decision making theory, it's not simply that the benefit must outweigh the cost in order for an action to be good, as in cost benefit analysis. In EVR, the expectation utility must outweigh the cost.

As a simple example, let's say you're playing a game where you toss coin. You win two dollars for heads; you lose only 50 cents for tails. The expected utility for heads is one dollar. The expected utility for tails is negative 25 cents. The expectation value of playing the game is 75 cents.

Since you win 4 times as much as you lose, and you should win just as often as you lose, you might be able to convince someone to pay a dollar or even two dollars to play this game. But in fact, according to EVR, any price over 75 cents is a bad choice.

What makes the principle of EVR a sound principle is that, if you consistently follow expectation value reasoning then, over time, you will maximize your benefits, your good consequences. That's the point of including the probabilities. You might not get the best outcome everytime, but if you've calculated the probabilities right, the sum of your outcomes over time --- the good, the not so good, and even the negative --- will be greater than your costs over that same run of choices.

So the principle of EVR can be stated in two ways: anought to' version, and anought not to' version.

According to EVR you ought to choose any action with expected utility greater than the real cost of that action.

Or

According to EVR you ought not to choose any action with expected utility less than the real cost of that action.

It is the second version that is relevant to the argument against buying an extended warranty. The principle is justified by the theory. We just have to show now that the principle applies to buying an extended warranty. That is, we have to explain why someone should believe that the expected utility of buying an extended warranty is less than the cost of buying that warranty.

3.4 Buying an extended warranty has expected utility less than real cost

If you buy an extended warranty there are two possible outcomes you need to consider. You will either use the warranty, or you will not.

If you use the warranty it will probably be worth it. There will be some hassle replacing the item, maybe even some shipping or administration costs, but all that will still be less of a cost than buying a replacement device would have been.

The problem is, you can't be certain that you will use the warranty. If you do not, then you've just thrown your money away.

How do you decide? EVR gives you a theory for that, and we've just described the principle in subsection 2 of this quad: If the expected utility is less than the cost of buying the extended warranty then we ought not to buy it.

There are several factors to take into account in calculating the expected utility of this action. We would need to know the probability that the device will break, the cost of replacement, and the cost of the extended warranty, not to mention all the other things we might want to take into account, like convenience of using the warranty, delays.

It would seem you can't use EVR if you can't assign numbers to these factors. And even if you could for any one particular example, the argument here is that, in general, and in principle, no matter what the device is, you ought not to buy the extended warranty.

The key is to recognize that there is a reason the company is trying to sell you the extended warranty. Their reason is also based in EVR. We can assume the company is acting rationally (they're still in business, after all), and that they are making money off of selling these. They are making money because their expected utility of selling an extended warranty is greater than the cost. In the long run, for the company, the benefits outweigh the costs.

Now, to see that the reverse is true for you, you just need to see that the costs and the benefits are reversed for you. The benefits for the company are the price of the warranty, but the price of the warranty is a cost to you. Replacing the device, which is a benefit to you, is a cost to the company.

So, in the calculation you make to find the expected utility, your numbers will all be the negative of the company's numbers. And if those numbers mean that the benefits outweigh the costs for the company, negative numbers will mean that the costs outweigh the benefits for you.

Mathematically: if $B > C$ then $-B < -C$.