decision making problem solving - university of wisconsin ... · problem solving i’m feeling...

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Decision Making

Problem Solving

Dona WarrenDepartment of Philosophy

The University of Wisconsin – Stevens Point

Decision Making

What major

Art? I know I’d enjoy studying that, but it might make my parents unhappy, and what if I can’t find a job?

Computer science? I find that a bit dull, but I think that I could get a job with it. I might even be able to retire early.

Education? I’d enjoy that more What major should I choose?

Education? I d enjoy that more than computer science, but my salary might be lower. I would be able to help children, however. That’s a plus.

When deciding what to do, we need to consider:

A

1) What our Options are

(Majoring in Art)

C

E

(Majoring in Computer Science)

(Majoring in Education)

A

2) The Possible Consequences of Each Option

E

U

P

(Enjoyment)

(Unhappy Parents)

(Unemployment)

C

EE

H

J

R

D

L

(Dull)

(Job)

(Early Retirement)

(Some Enjoyment)

(Lower Salary)

(Helping Children)

A

3) How Good or Bad Each Consequence Would Be.

E

U

P

(Enjoyment – Very Good)

(Unhappy Parents – Somewhat Bad)

(Unemployment – Very Bad)

C

EE

H

J

R

D

L

(Dull – Somewhat Bad)

(Job – Somewhat Good)

(Early Retirement – Very Good)

(Some Enjoyment – Somewhat Good)

(Lower Salary – Somewhat Bad)

(Helping Children – Very Good)

2

A

4) How Likely Each Consequence is.

E

U

ImpossibleCertain

P

C

EE

H

J

D

L

R

Yes, that’s all well and good. But I still don’t know what to do.

How can I compare a mildly bad but highly probable consequence to a consequence that’s very good but less likely?

Math can help us outMath can help us out.

Delightful! I enjoy mathematics.

When deciding whether or not to play a game of chance, we need to consider:

how much we stand to losethe probability of losinghow much we stand to winthe probability of winning

We need to compare a mildly bad but highly probable consequence (losing the game) to a consequence that’s very good but less likely (winning the game).

“W” is how much you’ll net, if you win. “L” is how much you’ll forfeit, if you lose. “PW%” is your probability of winning. “PL%” is your probability of losing. Suppose you play 100 games.

Since you have PW% chance of winning , and since you played 100 games, we can assume that you won PW times. Each time you won, you netted amount W. So, in all, you netted PW*W from your winning games.

Since you have PL% chance of losing, and since you played 100 games, we can assume that you lost PL times. Each time you lost, you forfeited amount L. So, in all, you forfeited PL*L from your losing games.

Your total winnings or losing, after you play 100 games, is your net winnings minus your net losses: PW*W – PL*L

If we wanted to see how much you won or lost onAssuming that gambling doesn’t

If we wanted to see how much you won or lost, on average, per game, we’d divide your total winnings or losings by the number of games you played:(PW*W - PL*L)/100. Now for a bit of math:(PW*W - PL*L)/100 =(PW*W) /100 - (PL*L)/100 =(PW/100)*W - (PL/100)*L =PW%*W - PL%*LW*PW% - L*PL%

violate your moral code:• If the expected utility is positive

then you can expect to earn money in the long run and you should play the game.

• If the expected utility is negative then you can expect to lose money in the long run and you shouldn’t play.

• If you’re faced with multiple games then you should play the one with the highest expected utility.

This is called your expected utility. If you play this game, you can expect to win or lose, on average, W*PW% - L*PL%

A raffle ticket costs $10. The prize is $50. The chance of winning is 25%.

If we win, we’d net $40. Our chance of winning is 25%. If we lose, we’d lose $10. Our chance of losing is 75%. Our expected utility, then, is (40)(25%)-(10)(75%) =10 – 7.5 = 2.5.


If we win, we’d net $20. Our chance of winning is 25%. If we lose, we’d lose $10. Our chance of losing is 75%. Our expected utility, then, is (20)(25%)-(10)(75%) = 5 – 7.5 = -2.5.


The rationality of betting is a function of:

1. How much we stand to win.

2 Ho m ch eIf we win, we’d net $26. Our chance of winning is 25%. If we lose, we’d lose $4. Our chance of losing is 75%.Our expected utility, then, is (26)(25%)-(4)(75%) = 6.5 – 3 = 3.5.

2. How much we stand to lose.

3. Our chances of winning and losing.

We should play the game that has the highest expected utility.

A raffle ticket costs $4. The prize is $30. The chance of winning is 12.5%.

If we win, we’d net $26. Our chance of winning is 12.5%.If we lose, we’d lose $4. Our chance of losing is 87.5%. Our expected utility, then, is (26)(12.5%)-(4)(87.5%) = 3.25 – 3.5 = -0.25.

That’s all very interesting, but how does it help

We’ll calculate the “expected utility” of each of your possible majors by identifying the possible consequences of each decision, assigning numbers to indicate how good or bad each consequence would be, and estimating the probability of each consequence. For each consequence, we’ll multiply its “goodness or badness” by its probability. We’ll then add these numbers up, and that will give us the expected utility of that major. The “right” major is the major with the highest expected utility.

But isn’t assigning numbers to indicate how good or bad a certain consequence would be, and estimating how does it help

me?consequence would be, and estimating the probability of each consequence, very subjective and artificial?

This mathematical calculation is a just a guide. It’s a way of considering both the nature and the probability of the consequences of our options, and allowing the more probable consequences to carry more weight. Even if we don’t assign numbers and carry out the calculation, we should still do that.

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Art How good or bad Probability

Enjoy it +70 90% +63

Parents unhappy -30 60% -18

Not find a job -70 50% -35

10

Computer Science How good or bad Probability

Find it dull -30 90% -27

Find a job +50 80% +40

Retire early +80 30% +24

37

Education How good or bad Probability

Enjoy it +50 90% +45

Lower salary -10 90% -9

Help children +70 80% +56

92

So, according to this way of thinking, education is the best choice for me.

But can’t this way of thinking go wrong? Mightn’t I realize in a few years that education was the wrong decision?

Decision making is vulnerable to error. Some of these errors aren’t avoidable, but others are.

By minimizing our avoidable errors, we can increase the chances that we’ll make the right decisions.

Element of Decision-Making Unavoidable Error Avoidable Error

Identifying our options. We can’t be expected to think of each and every option.

But we shouldn’t unduly narrow our options.

Think creatively.

Talk to other people.




Identifying the consequences of each option.

We can’t predict all of the consequences of our options.

But we shouldn’t ignore reasonably predictable consequences.

Consider how our actions might affect us and the world around us.

Reflect upon our own past experiences.

Avail ourselves of other people’s experience and research.

Recognize and counter our optimistic / pessimistic biases.






But we shouldn’t ignore reasonably predictable consequences.

Estimating how good or bad each consequence would be.

Sometimes a consequence might be better, or worse, than we expect.

But we shouldn’t allow ourselves to be irrationally optimistic or pessimistic.









But we shouldn’t ignore reasonably predictableconsequences.

Estimating how good or bad each consequence would be.

Sometimes a consequence might be better, or worse, than we expect.

But we shouldn’t allow ourselves to be irrationally optimistic or pessimistic.

Estimating how likely each consequence is.

Sometimes we might be legitimately mistaken about how likely a given consequence is.

But we shouldn’t ignore good evidence indicating the probability of each consequence.




Don’t equate intensity with probability.

Don’t equate proximity with probability.

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1) Consider our options.

2) Identify the possible consequences of each option.

3) Estimate how good or bad each consequence would be.

4) Estimate the probability of each consequence.

5) Evaluate each option in light of the nature and probability of its consequences.

- Think creatively.- Talk to other people.

- Consider how our actions might affect us and the world around us.

- Reflect upon our own past experiences.- Avail ourselves of other people’s experience and research.- Recognize and counter our optimistic / pessimistic biases.- Don’t equate intensity with probability.- Don’t equate proximity with probability.

When in doubt, utilize an expected utility formula:C1 *PC1% + C2 *PC2% + C3 *PC3% + … + Cn *PCn%Where “C” is a numerical representation of how good or bad

ld b d “PC%” i h lik l it i th t6) Select that option that’s best overall.

DecisionMaking

a consequence would be and “PC%” is how likely it is that this consequence will occur.

Caveats:

Use only for important decisions that we don’t need to make every day. Entrust other decisions to wisely cultivated habit. (We can use this method to help us decide what habits we want to cultivate.)

Use only for decisions that are appropriately made on the basis of probable consequences.

Problem Solving

I’m feeling unfulfilled in my current job.

I want greater job satisfaction.

End

Problem

I could ask for more challenging assignments in my current position.

Means

I l f

Options

Making Good Decisions:

1) Consider our options.

2) Identify the possible consequences of each option.

3) Estimate how good or bad each

I could find another job.

Means

Or, I could just continue this way and decide to live without the job satisfaction I want.

Abandoning the End

consequence would be.



6) Select that option that’s best overall.

More Challenging Assignments

How good or bad Probability

Greater Job Satisfaction

Alienate co-workers

Get a promotion

New Job How good or bad Probability

Greater Job Satisfaction

Lesser Job Satisfaction

Options that are means to the end will always have the attainment of the end as a consequence.

Reduction of Pay

Live without Job Satisfaction


Not Greater Job Satisfaction

Seek Satisfaction Elsewhere

The option that is the abandonment of the end will always have the non-attainment of the end as a consequence.

More Challenging Assignments


Greater Job Satisfaction +90 75% +67.5

Alienate co-workers -60 50% -30

Get a promotion +70 10% +7

+44.5

New Job How good or bad Probability

Greater Job Satisfaction +90 60% +54

Lesser Job Satisfaction -90 30% -27

Reduction of Pay -60 10% -6

+21

Live without Job Satisfaction


Not Greater Job Satisfaction

-90 100% -90

Seek Satisfaction Elsewhere

+40 100% +40

-50

Frankly, I’m disappointed that you even considered living without greater job satisfaction.

That’s defeatist thinking! You’ve got to fight for what you want! It’s always better to solve

a problem than to live with it!

That’s nonsense.

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“Pray, have you found a cure for my slightly

malformed, but neither particularly painful nor

incapacitating, left pinky toe?”

“Verily, my lord. We could cut it off.”

The Cure Worse than the Disease Fallacy:Any solution is better than no solution at all.

In fact, sometimes the all of the possible solutions to a problem are worse than the problem itself, in which case it’s best to let the problem be (at least until a better solution presents itself).

1) Decide upon the end that we want to achieve. (It’s generally more helpful to focus on the end that we want to achieve than it is to focus on the problem.)

2) Consider a variety of means to achieve that end.

3) Our options are all of those means plus the decision to not achieve the end. (Considering the option of not achieving the end allows us to avoid the Cure Worse than the Disease fallacy.)

4) Identify the possible consequences of each option. (Options that are means to the end will include

hi i h d Th i

ProblemSolving

achieving the end as a consequence. The option that is deciding to not achieve the end will have not achieving the end as a consequence.)

5) Estimate how good or bad each consequence would be.



8) Select the option that’s best overall.

decision making problem solving - university of wisconsin ... · problem solving i’m feeling...

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