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Making decisions - Sequence of Gambles

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Sequence of Gambles

Consider the choice among pairs of casino gambles that are the staple of the most basic studies of decision making then think about an important personal decision how good is the analogy between gambling choice and your decision situation. Is life really a sequence of gambles?

a. Identify the decision.

b. Discuss the analogy between the gambling choice and your decision situation. Provide, at a minimum, three constructive points.

c. State your position regarding this statement: Is life really a sequence of gambles?

d. Provide three constructive statements supporting your decision.

This is comparing gambling to a personal decision.

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Solution Preview

RESPONSE:

a. Identify the decision.

You wrote: "My personal decision was filing a complaint with the Human Rights Board concerning one of my bosses and I had to weigh the pro and cons to think of this: was a good decision to make? As it turned out I made a good choice because I won the case. I can't figure out the analogy of that other than being treated unfairly on the job.
I don't know anything about gambling what is the analogy in that?"

You are right, being treated unfairly on the job doesn't have anything to do with the analogy to gambling; however, your decision to file a complaint does--as we will look at in the next question.

b. Discuss the analogy between the gambling choice and your decision situation. Provide, at a minimum, three constructive ...

Solution Summary

By responding to the questions and by example, this solution addresses the question: Is life really a sequence of gambles?

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Models of Decision Making

There are three (3) parts to this project. Your research paper should address each one fully and thoroughly.

Part 1: Review each situation (there are FIVE scenarios within the activity) and identify the applicable decision concept (you may select from any theory, principle, model, etc. from our learning in Unit 2) that you believe to be present. Make sure you also explain (for each concept identified) "how" and "why" you arrived at your conclusion. In other words; what information helped you select each concept for each situation? Be sure you separate your findings and support for each of the different scenarios (don't put all your findings & support in a single block paragraph).

Part 2: Look at the different decision concepts you identified in part 1. What do you think those different concepts imply about how people make decisions?

Part 3: Do the decisions we make always need to be rational? Under what circumstances are we (decision makers) likely to make irrational choices?

Make sure you reinforce your work with suitable references from the text book and other authoritative and credible references, which must enhance the quality of your response. In the process please use correct APA citation style.

Activity #1

If you were given a choice, which of the following gambles would you prefer?

$1,000,000 for certain
A 10 percent chance of getting $2,500,000, an 89 percent chance of getting $1,000,000, and a 1 percent chance of getting $0.
Answer:

Most people choose the sure outcome, but the alternative choice has an expected value greater than $1,000,000. The alternative expected value once calculated is as follows: EV = (.10)($2,500,000) + (.89)($1,000,00) + (.01)($0) = $1, 140,000 compared to the certain $1,000,000 in selection A.

If you were given a choice, which of the following gambles would you prefer?

An 11 percent chance of getting $1,000,000 and an 89 percent chance of getting $0.
A 10 percent chance of getting $2,500,000 and 90 percent chance of getting $0.
Answer:

Most people select Alternative B reasoning that there is little difference between a 10 or 11 percent chance of winning, but there is large difference in expected value. The problem is this: If you chose A in the first scenario you should also select A here. Likewise if you selected B in the first scenario, you should also select B here. The two choice situations offer the identical alternatives except for the addition of an 89 percent chance of winning $1,000,000. How did you do?

Activity #2:

Suppose you consider the possibility of insuring some property against damage (e.g. fire or theft). After examining the risks and the premium you find that you have no clear preference between the options of purchasing insurance or leaving the property uninsured.

It is then called to your attention that the insurance company offers a new program called probabilistic insurance. In this program you pay half of the regular premium. In case of damage, there is a 50 percent chance that you pay the other half of the premium and the insurance company covers all of the losses; and there is a 50 percent chance that you get back your insurance payment and suffer all of the losses.

For example, if an accident occurs on an odd day of the month, you pay the other half of the regular premium and your losses are covered; but if the accident occurs on an even day of the month, your insurance payment is refunded and your losses are not covered.

Recall that the premium for full coverage is such that you find this insurance barely worth its cost. Under these circumstances, would you purchase probabilistic insurance?

Answer:

80 percent of students that responded to this item in a study conducted by Kahneman and Tversky indicated that they would not purchase probabilistic insurance. People apparently would rather eliminate risk than merely reduce it, even if the probability of a catastrophe is diminished by an equal amount in both cases (as is the case here).

Activity #3:

How much money would you pay to play a game in which an unbiased coin is tossed until it lands on Tails, and at the end of the game you are paid ($2.00)k where k equals the number of tosses until Tails appears? In other words, you would be paid $2.00 if Tails comes up on the first toss, $4.00 if Tails comes up on the second toss, $8.00 if Tails comes up on the third toss, and in general:

Tosses Until Tails 1 2 3 4 5 ... K
Payoff in Dollars 2 4 8 16 32 ... 2K

Answer:

The expected value of this game (the average payoff you would expect if the game were played an endless number of times) is infinite, yet very few people are willing to pay large sums of money to play. Mathematician Daniel Bernoulli arrived at a solution to this paradox, however, by reasoning that the value, or utility,. of money declines with the amount won (or already possessed). Specifically, he argued that "a gain of one thousand ducats is more significant to a pauper than to a rich person though both gain the same amount." By assuming that the value of additional money declined with wealth, Bernoulli was able to show that the expected utility of this game is not infinite after all.

Activity #4

If you were given a choice which of the following would you prefer?

A 1 in 1000 chance of winning $5000.00
A sure gain of $5.00.
Answer:

Of the 72 respondents that originally made this choice, nearly three in four chose the first alternative. Thousands of people make much the same choice each day when they purchase lottery tickets.

If you were given a choice which of the following would you prefer?

A 1 in 1000 chance of losing $5000.00.
A sure loss of $5.00
Answer:

Of the 72 respondents that originally made this choice more than four out of five preferred the sure loss. Researchers Kahneman and Tversky explained this almost overwhelming preference in terms of a tendency of most people to overweight the chances of a large loss - a tendency that greatly benefits the insurance industry.

Activity #5:

You are the chair of a faculty search committee consisting of five other members: Ann; Bob; Cindy; Dan; and Ellen. Your task is to hire a new professor and the top three preferences have already been determined to be Joe Schmoe, Jane Doe, and Al Einstein. Suppose you know everyone else's preferences, as shown in the table, and you want to control the balloting so that Al Einstein is chosen.

Ann Bob Cindy Dan Ellen
Joe Schmoe 1 1 2 3 3
Jane Doe 2 3 3 1 1
Al Einstein 3 2 1 2 2

What should you do?
Call for a direct vote between Schmoe and Einstein followed by a direct vote between Einstein and Doe
Call for a direct vote between Schmoe and Doe followed by a direct vote between Schmoe and Einstein
Call for a direct vote between Einstein and Schmoe followed by a direct vote between Doe and Einstein
Why can the person setting the agenda have complete control over the outcome?
Answer to question A:

If you selected #1 you are incorrect. This would serve to get Jane Doe hired. Reexamine the committee members' preferences and use a strategy that avoids direct votes between Al Einstein and Jane Doe.

If you selected #2 you are correct. This strategy avoids direct votes between Einstein and Jane Doe and would effectively serve to get Al Einstein selected.

If you selected #3 you are incorrect. This would serve to get Jane Doe hired. Reexamine the committee members' preferences and use a strategy that avoids direct votes between Al Einstein and Jane Doe.

Answer to Question B:

Because the committee's preferences are intransitive with a majority rule based on pairwise comparisons, the person setting the agenda has complete control over the outcome.

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