Reason and Critical Thinking PART TWOFebruary 26, 2013 Rational Decision MakingConceptual 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 others1) To make choices, we need to consider options (aka. “Possibilities” for action or inactionThe 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 cchoices, or wrapped into one choiceDecisions 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 headsEvent 2= E2= coin coming up tailsP (E1)=.5=1/2=50%P (E2)=.5=1/2=50%These are exhaustive and exclusive All probability subjectiveP (E|H)|= Conditional upon givenH= 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 markP (E1|H)=75%P (E2|H)=25% Combining ProbabilitiesSometimes we combine the probability judgments of different event in different waysThese 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 oneWe can generalize from the particulars to see that, generally, the combination of getting three outcomes is less likely than each on its ownFirst Law of ProbabilityP (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= 1/6Event 2= E2= coming up 4 = 1/6P (3 or 4)=(1/6)+(1/6)= (2/6)= (1/3) Probability of an event not happeningP (~E1) = 1 – P (E1) Second Law of ProbabilityP (E1 and E2) = P (E1) x (E2|E1)P (3 and 4)= (1/6) x (1/6)= (1/36)Always less than or equal to the probability of just one of the events Jar of Marbles3 Red, 3 GreenE1= pulling out a red marbleE2= pulling out a second red marbleP (E1 and E2) = (1/2) x (2/5) = (2/10) = (1/5) Third Law of ProbabilityE1= Studying for the examA= 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 ValueIntrinsic 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 UtilityRational decision-making: making the choices based on achieving your goals, or getting the most valueDependent 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 strengthThe traditional view of rational decision-making takes utility to be either equivalent or virtually perfectly correlated with one’s goodWith 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 1D2= Play lottery number 2(Exclusive) Lottery 1= $1010 and it costs $10 to playLottery 2= $1520 and it costs $20 to playBest: Win Lottery 2= Preference Strength 1Second Best: Win Lottery 1= Preference Strength .7Third Best: Loose Lottery 1= Preference Strength .1Worst: Loose Lottery 2= Preference Strength 0 Lottery 1: 60% chance of winning; 40% chance of loosingLottery 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= 603Expected utility would say play lottery 2 With preference strengthD1= (.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, 2013Review of Traditional Views of Rational Reasoning and Decision-makingDeduction- Step by step process (serial reasoning); use premises to support conclusions; conclude with certainty; check for formal validity, then check for soundnessInduction- 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 causationDecision-making- Serial reasoning; use