Study Guide COMM 402 Fall 2012 Exam 2 Lave March Chapter 4 What is the choice process being modeled in this chapter Decision Making Process Can be mundane decisions should I go home via Main St or should I try the shortcut or can be relatively consequential decisions should I drop out of school for a year Social scientists interested in developing and applying a model have assembled situations that involve an individual making a decision AND that the person making the decision cannot be certain about the outcome of the decision An individual makes a decision as if he were going through these steps 1 Examine all possible plans of action and see what possible outcomes can result from each 2 Judge how desirable each outcome is and how likely it is to occur as a result of following the particular plan of action 3 Choose the plan of action with the highest expected value How do you calculate Expected Value EV Expected Value The average payoff you would receive if you played the game a large number of times We use the word expected in a probability sense to designate an average amount of winning Value to decision maker of the various results possible from the different course of action Probability or likelihood that these results will actually occur Example from the book A die is rolled if it comes up with a 5 you win 12 if it comes up with any other number you win nothing Suppose we play the game 600 times We throw the die 600 times in succession and keep track of how much we win in total Since there are 6 sides to a die the chance of a 5 occurring is 1 in 6 or 1 6 In 600 throws we would expect the 5 to come up 100 times 1 6 times 600 and so you would win 1 200 12 X 100 For the other tosses you receive nothing Thus your total expected winnings are 1200 for the entire series of tosses or 2 per game is the average payoff or the expected value of the game Since the outcome of playing this game can only by 0 or 12 there is no way of winning the expected value of 2 in a single game We are using the word expected in a probability sense to designate an average amount of winning Calculating Expected Value 1 We shall designate all the possible outcomes of the game by using their values and use V as a symbol for them We can use subscripts to designate different outcomes Thus V1 is the value of outcome number 1 V3 is the value for outcome number 3 and so on In the game last described there were two outcomes which we designate V1 12 outcome number 1 is the occurrence of a 5 V2 0 outcome number 2 is the occurrence of any other number 2 We shall designate the probability of each outcome using P P1 1 6 the probability of outcome number 1 is equal to 1 6 P2 5 6 the probability of outcome number 2 is equal to 5 6 3 If we designate expected value as EV we can now write a formula for expected value as EV P1 V1 P2 V2 Or in the dice example we would have EV 1 6 X 12 5 6 X 0 EV 2 EV 2 0 If there are more than two outcomes we just add more terms to the formula and we have the general expression for the expected value of an alternative having n possible outcomes What is the numerical range of probability Why is probability limited to these numerical values When we talk about probability we are using the notion of relative frequency Ex When we say the probability of a head appearing is 0 5 we mean that if you flipped the coin many times a head would show up about or 50 of the time All probabilities must be within the range from 0 to 1 o 0 chance of occurring never something is certain not to occur o 100 chance of occurring every time something is certain to occur What are the two common mistakes people make when they apply probabilities in their decisions Notation P is the abbreviation for Probability P heads 0 5 means the probability of heads occurring is 0 5 If you add together the probabilities of all the possible outcomes associated with one situation they must equal 1 0 provided the outcomes are mutually exclusive That is to say out of all of the things they might occur at least one of them will occur Common Mistakes People Make 1 One of the most common errors people make when estimating probabilities is to assume that because there are two possible outcomes the probability of each of them is This works for coins because the two outcomes are equally likely But all two outcome situations do not have equally likely outcomes 2 Gamblers Fallacy you are never due for a certain outcome How do you draw a decision tree How do you use a decision tree to choose We use boxes to designate events or outcomes The lines connecting the boxes in the figure show all the possible connections or relations The number beside each line is the probability that the path will be followed The dollar values at the right hand side of the figure show the value associated with each between the boxes possible outcome You read the tree from left to right The die is rolled and each of the outcomes branches from that point and ends in a value associated with a final outcome A decision tree is a complete picture of the world one that shows all possible outcomes Each of the boxes in the tree is one possible outcome and I that one outcome can possible lead to other outcomes all of them will be shown branching off to the right If all the possible branches are shown one of them must occur Therefore the sum of the probabilities must equal 1 0 because the branches must be a complete description of the world Decision Trees Merely a graphical aid to seeing which outcome has the maximum Expected Value Must draw out the whole tree including all the contingent branches To simplify Start collapsing decision tree to the left until you end with only the branches representing the first choice The largest Expected Value predicts the first choice Continue the process Given the first choice collapse back to the next decision i e second choice And so forth Alternatively can just multiply probabilities along each branch and list the product at the end of the final branch point If a thing can happen N ways add up all N probabilities to estimate its likelihood How can a decision tree be simplified To simplify Start collapsing decision tree to the left until you end with only the branches representing the first choice The largest Expected Value predicts the first choice Example In this game Game C we first draw a card from a standard deck …