Reason and Critical Thinking PART TWO February 26 2013 Rational Decision Making Conceptual parts of rational decision making 1 choice and 2 the fact that it is usually the case that of the choices we can make some are better than others 1 To make choices we need to consider options aka Possibilities for action or inaction The possibilities can be exhaustive and exclusive A list of possibilities is exhaustive if and only if all possible choices of the agent have been considered There is no possibility for choice the agent can make that has not been considered A list of possibilities is exclusive if and only if the agent can choose one and only one option Options which depend on earlier decisions can either be treated as further c choices or wrapped into one choice Decisions Under Uncertainty Rhonda 25 000 over 10 years wants to get money from starting accounting business Lou 25 000 over 10 years want to get money from lotto Has Low or Rhonda made better choices given that they have the same starting point and the same goal Distinguish decision under uncertainty from decisions under certainty Probability P E1 Probability of Events outcome of the choices we make Event 1 E1 coin coming up heads Event 2 E2 coin coming up tails P E1 5 1 2 50 P E2 5 1 2 50 These are exhaustive and exclusive All probability subjective P E H Conditional upon given H Background always with judgments but they drop out don t matter Anne knows that it is more likely to come up tails because head side is slightly heavier so she may say P E1 H 41 P E2 H 51 Clint thinks heads is his lucky side of the coin his judgments off the mark P E1 H 75 P E2 H 25 Combining Probabilities Sometimes we combine the probability judgments of different event in different ways These combinations seem to be backed up by rules of rationality It is irrational to believe that one has a better chance of studying for the exam going to the concert and getting a full night s sleep than doing each individually The odds favor accomplishing only one We can generalize from the particulars to see that generally the combination of getting three outcomes is less likely than each on its own First Law of Probability P E1 or E2 P E1 P E2 Since H s are the same they cancel out and you don t need them as long as same person is making the judgments Probability of this or that happening Event1 E1 coming up 3 1 6 Event 2 E2 coming up 4 1 6 P 3 or 4 1 6 1 6 2 6 1 3 Probability of an event not happening P E1 1 P E1 Second Law of Probability P E1 and E2 P E1 x E2 E1 P 3 and 4 1 6 x 1 6 1 36 Jar of Marbles 3 Red 3 Green E1 pulling out a red marble E2 pulling out a second red marble P E1 and E2 1 2 x 2 5 2 10 1 5 Third Law of Probability E1 Studying for the exam Always less than or equal to the probability of just one of the events A Getting an A on the Exam P A P A E1 x P E P A E x P E P A 2 3 x 1 2 1 3 x 1 2 P A 2 6 1 6 3 6 1 2 February 28 2013 Important to keep long term decisions in mind little and big decisions both matter Value Intrinsic value something has intrinsic value when it is valuable in itself it is not valuable as a means to some other value example happiness Instrumental value something has instrumental value when it is useful to obtaining something else that is of value Some things can be both intrinsically and instrumentally valuable For instance suppose you want to make a lot of money this makes sense if that is what you really want but also philosophers can grant that money can help you get other things which are of intrinsic value So everyone can agree that it is rational to want more money Expected Utility Rational decision making making the choices based on achieving your goals or getting the most value Dependent upon probabilities because the future is uncertain but probabilities are not all the benefits and costs can be of varying magnitudes or sizes Consider two different lotteries You can only play one With the first you have a 50 of winning 10 000 In the second you have a 70 of winning 100 Which to take Probabilities favor lottery 2 but it seems like lottery 1 is more rational in some sense We can compare something very probable but having small value with something very valuable but unlikely to happen and all other sorts of combinations We need a measure of this magnitude in the value that is somehow related to the rationality of the decision Utility that which represents a person s preferences Broome p 21 Mathematical function which serves as a measure of preferential strength The traditional view of rational decision making takes utility to be either equivalent or virtually perfectly correlated with one s good With full information and control the traditional view would say it would be easy to decide what to do do what you know will bring you the most utility However the world is full of uncertainty and events which over which we do not have complete control D1 Play lottery number 1 D2 Play lottery number 2 Exclusive Lottery 1 1010 and it costs 10 to play Lottery 2 1520 and it costs 20 to play Best Win Lottery 2 Preference Strength 1 Second Best Win Lottery 1 Preference Strength 7 Third Best Loose Lottery 1 Preference Strength 1 Worst Loose Lottery 2 Preference Strength 0 Lottery 1 60 chance of winning 40 chance of loosing Lottery 2 50 chance of winning 50 chance of loosing Expected utility P E x U E P E x U E Basically the third law of probability D1 6 x 1000 4 x 10 596 units or dollars D2 5 x 1500 5 x 20 603 Expected utility would say play lottery 2 With preference strength D1 6 x 7 4 x 1 46 D2 5 x 1 5 x 0 5 Expected utility would say play lottery 2 still If we change the probabilities you can run the same formula and see how it affects things March 19 2013 Review of Traditional Views of Rational Reasoning and Decision making Deduction Step by step process serial reasoning use premises to support conclusions conclude with certainty check for formal validity then check for soundness Induction Serial reasoning use premises to support conclusions premises must make argument strong do not make hasty generalizations do not have biased samples do not mistake correlation for causation Decision making Serial reasoning use probability theory to determine the likelihood of all possible outcomes must consider exhaustive list of all outcomes calculate expected utility to …