Mẹo Hướng dẫn Which of the following decision criterion would likely be employed by a pessimistic decision maker? 2022

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There are four types of criteria that we will look .

Nội dung chính

    Example: A bicycle shopStates of NaturePayoff TableOpportunistic Loss TableExpected Value CriterionMaximax
    CriterionMaximin CriterionMinimax CriterionPutting it all together.Practice ProblemWhich criterion is known as the criterion of pessimism?Which method is to be used for pessimistic decision maker?Which of the following decision criterion would likely be employed by an optimistic decision maker?Which of the following is a pessimistic decision criterion Mcq?

Expected Value (Realist)Compute the expected value under each action and then pick the action with the largest expected value. This is the only method of the four that incorporates the probabilities of the states of nature. The expected value criterion is also called the Bayesian principle.Maximax (Optimist)The maximax looks the best that could happen under each
action and then chooses the action with the largest value. They assume that they will get the most possible and then they take the action with the best best case scenario. The maximum of the maximums or the “best of the best”. This is the lotto player; they see large payoffs and ignore the probabilities.Maximin (Pessimist)The maximin person looks the worst that could happen under each action and then choose the action with
the largest payoff. They assume that the worst that can happen will, and then they take the action with the best worst case scenario. The maximum of the minimums or the “best of the worst”. This is the person who puts their money into a savings account because they could lose money the stock market.Minimax (Opportunist)Minimax decision making is based on opportunistic loss. They are the kind that look back after the state of
nature has occurred and say “Now that I know what happened, if I had only picked this other action instead of the one I actually did, I could have done better”. So, to make their decision (before the sự kiện occurs), they create an opportunistic loss (or regret) table. Then they take the minimum of the maximum. That sounds backwards, but remember, this is a loss table. This similar to the maximin principle in theory; they want the best of the worst
losses.

Example: A bicycle shop

Zed and Adrian and run a small bicycle shop called “Z to A Bicycles”. They must order bicycles for the coming season. Orders for the bicycles must be placed in quantities of twenty (20). The cost per bicycle is $70 if they order 20, $67 if they order 40, $65 if they order 60, and $64 if they order 80. The bicycles will be sold for $100 each. Any bicycles left over the end of the season can be sold (for certain) $45 each. If Zed
and Adrian run out of bicycles during the season, then they will suffer a loss of “goodwill” among their customers. They estimate this goodwill loss to be $5 per customer who was unable to buy a bicycle. Zed and Adrian estimate that the demand for bicycles this season will be 10, 30, 50, or 70 bicycles with probabilities of 0.2, 0.4, 0.3, and 0.1 respectively.

Actions

There are four actions available to Zed and Adrian. They have to decide which of the actions is the best
one under each criteria.

Buy 20 bicyclesBuy 40 bicyclesBuy 60 bicyclesBuy 80 bicycles

Zed and Adrian have control over which action they choose. That is the whole point of decision theory – deciding which action to take.

States of Nature

There are four possible states of nature. A state of nature is an outcome.

The demand is 10 bicyclesThe demand is 30 bicyclesThe demand is 50 bicyclesThe
demand is 70 bicycles

Zed and Adrian have no control over which state of nature will occur. They can only plan and make the best decision based on the appropriate decision criteria.

Payoff Table

After deciding on each action and state of nature, create a payoff table. The numbers in parentheses for each state of nature represent the probability of that state occurring.

Action

State of Nature
Buy 20
Buy 40
Buy 60
Buy 80
Demand 10
(0.2)
50
-330
-650
-970
Demand 30
(0.4)
550
770
450
130
Demand 50
(0.3)
450
1270
1550
1230
Demand 70
(0.1)
350
1170
2050
2330

Ok, the question on your mind is probably “How the [expletive deleted] did you come up with those numbers?”. Let’s take a look a couple of examples.

Demand is 50, buy 60:They bought 60 $65 each for $3900. That is -$3900 since that is money they spent. Now, they sell 50 bicycles $100 each for $5000. They had 10 bicycles left over the end of the season, and they sold those $45 each of $450. That makes $5000 + 450 – 3900 =
$1550.Demand is 70, buy 40:They bought 40 $67 each for $2680. That is a negative $2680 since that is money they spent. Now, they sell 40 bicycles (that’s all they had) $100 each for $4000. The other 30 customers that wanted a bicycle, but couldn’t get one, left mad and Zed and Adrian lost $5 in goodwill for each of them. That’s 30 customers -$5 each or -$150. That makes $4000 – 2680 – 150 = $1170.

Opportunistic Loss Table

The
opportunistic loss (regret) table is calculated from the payoff table. It is only needed for the minimax criteria, but let’s go ahead and calculate it now while we’re thinking about it.

The maximum payoffs under each state of nature are shown in bold in the payoff table above. For example, the best that Zed and Adrian could do if the demand was 30 bicycles is to make $770.

Each element in the opportunistic loss table is found taking each state of nature, one a
time, and subtracting each payoff from the largest payoff for that state of nature. In the way we have the table written above, we would subtract each number in the row from the largest number in the row.

Action

State of Nature
Buy 20
Buy 40
Buy 60
Buy 80
Demand 10
0
380
700
1020
Demand 30
220
0
320
640
Demand 50
1100
280
0
320
Demand 70
1980
1160
280
0

Remember that the numbers in this table are losses and so the smaller the number, the better.

Expected Value Criterion

Compute the expected value for each action.

For each action, do the following: Multiply the payoff by the probability of that payoff occurring. Then add those values together. Matrix multiplication works really well for this as it multiplied pairs of numbers together and adds them. If you place the probabilities into a
1×4 matrix and use the 4×4 matrix shown above, then you can multiply the matrices to get a 1×4 matrix with the expected value for each action.

Here is an example of the “Buy 60” action if you wish to do it by hand.0.2(-650) + 0.4(450) + 0.3(1550) + 0.1(2050) = 720

The expected values for buying 20, 40, 60, and 80 bicycles are $400, 740, 720, and 460 respectively. Since the best that you could expect to do is $740, you would buy 40 bicycles.

Maximax
Criterion

The maximax criterion is much easier to do than the expected value. You simply look the best you could do under each action (the largest number in each column). You then take the best (largest) of these.

The largest payoff if you buy 20, 40, 60, and 80 bicycles are $550, 1270, 2050, and 2330 respectively. Since the largest of those is $2330, you would buy 80 bicycles.

Maximin Criterion

The maximin criterion is as easy to do as the maximax. Except instead
of taking the largest number under each action, you take the smallest payoff under each action (smallest number in each column). You then take the best (largest of these).

The smallest payoff if you buy 20, 40, 60, and 80 bicycles are $50, -330, -650, and -970 respectively. Since the largest of those is $50, you would buy 20 bicycles.

Minimax Criterion

Be sure to use the opportunistic loss (regret) table for the minimax criterion. You take the largest loss under each action
(largest number in each column). You then take the smallest of these (it is loss, afterall).

The largest losses if you buy 20, 40, 60, and 80 bicycles are $1980, 1160, 700, and 1020 respectively. Since the smallest of those is $700, you would buy 60 bicycles.

Putting it all together.

Here is a table that summarizes each criteria and the best decision.

Action

Criterion
Buy 20
Buy 40
Buy 60
Buy 80
Best Action
Expected Value
400
740
720
460
Buy 40
Maximax
550
1270
2050
2330
Buy 80
Maximin
50
-330
-650
-970
Buy 20
Minimax
1980
1160
700
1020
Buy 60

Practice Problem

Since there aren’t any problems of this kind in the text, work this problem out, and then you can check your answer with the instructor.

Finicky’s Jewelers sells watches for $50 each. During the next month, they estimate that they will sell 15, 25, 35, or 45 watches with respective probabilities of 0.35, 0.25, 0.20, and … (figure it out). They can only buy watches in lots of ten from their dealer. 10, 20, 30, 40, and 50 watches cost
$40, 39, 37, 36, and 34 per watch respectively. Every month, Finicky’s has a clearance sale and will get rid of any unsold watches for $24 (watches are only in style for a month and so they have to buy the latest model each month). Any customer that comes in during the month to buy a watch, but is unable to, costs Finicky’s $6 in lost goodwill.

Find the best action under each of the four decision criteria.

Which criterion is known as the criterion of pessimism?

The Maximin criterion is a pessimistic approach. It suggests that the decision maker examines only the minimum payoffs of alternatives and chooses the alternative whose outcome is the least bad.

Which method is to be used for pessimistic decision maker?

Answer and Explanation: We know that in statistics, the maximin criterion is used by the pessimistic decision-makers. In general, when we maximize the minimum payoff, then the criterion used is the maximin criterion. Hence, the correct option will be: Answer: B.

Which of the following decision criterion would likely be employed by an optimistic decision maker?

The maximax decision criterion is the one used by the optimistic decision maker.

Which of the following is a pessimistic decision criterion Mcq?

Thus, the correct answer is option C) maximin.
The Maximin criteria takes a pessimistic view of the world. It implies that the decision maker considers only the minimum payoffs of options and chooses the one with the least negative outcome.
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Hurwicz criterion
Pessimistic criterion Calculator
Criterion of pessimism
Hurwicz criterion formula

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