The Encyclopedia of Economic Principals

Chapter 19

Attention, Information Avoidance, and Bounded Rationality

Scarce attention decides what gets weighed, how long search runs and which signals are read.

Four of the chapter's worked examples, made interactive: a vivid demo against verified breadth, a satisficing hire, a retirement alert left unopened, and a contest that concentrates attention. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

Demo salience versus verified breadth

How much weight on verified breadth does it take before the broad project beats the vivid demo?

Each project's score is a straight line in w. The demo project starts high because of its salience and falls as breadth gets more weight; the broad project rises. Where the lines cross, the ranking reverses without any change in the underlying scores.

Equation, written in LaTeX: Q_A=0.6(55)+0.4(95)=71

Equation, written in LaTeX: Q_B=0.6(68)+0.4(55)=62.8.

Equation, written in LaTeX: Q_A'=0.9(55)+0.1(95)=59,

Equation, written in LaTeX: Q_B'=0.9(68)+0.1(55)=66.7.

Scroll sideways for the whole equation

Q_j = w E_j + (1 - w) S_j is the committee's score for project j, with E_j its verified breadth and S_j its presentation salience on a 100 point scale. Project A has breadth 55; project B has breadth 68 and salience 55. w rises as credible evaluation becomes cheaper to digest.

Predict first. At breadth weight w = 0.75 with the book's scores, which project wins?

Your prediction

Choose an example

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Figure: Demo salience versus verified breadth. Two straight score lines against the breadth weight w. At w = 0.6 project A scores 71 and project B 62.8; the lines cross at w = 0.755.
Breadth weight w: 0.6, Project A salience: 95
Constructed example: the chapter's hypothetical projects A (breadth 55, salience 95) and B (68, 55) at the book's weights 0.6 and 0.9; weights 0.3 and 0.75 and A salience values 75 and 100 are added for comparison.

Calculated values

Q_A
71
Q_B
62.8
Winner
Project A
Tie weight w*
0.755

Q_A = 0.6(55) + 0.4(95) = 33 + 38 = 71, and Q_B = 0.6(68) + 0.4(55) = 40.8 + 22 = 62.8. Project A receives the budget despite its lower verified breadth. The scores tie at w = (95 - 55) / ((95 - 55) + 13) = 0.755; above that weight the broad project wins.

Worked steps

  1. Q_A = 0.6 x 55 + 0.4 x 95 = 33 + 38 = 71
  2. Q_B = 0.6 x 68 + 0.4 x 55 = 40.8 + 22 = 62.8
  3. Winner: Project A
  4. Tie: 55w + 95(1 - w) = 68w + 55(1 - w) gives w = 40 / 53 = 0.755

Use the idea

Before a review, write down the weight your committee actually puts on verified breadth and compute the weight at which the ranking would flip.

Where the conclusion applies

A linear score with fixed attribute values. Salience may itself proxy for usability, so a high weight on it is not automatically an error.

Check your understanding: With the book's scores, at what breadth weight do the two projects tie?
55w + 95(1 - w) = 68w + 55(1 - w) gives 95 - 40w = 55 + 13w, so w = 40/53 = 0.755.

Chapter 19 source: section "Attention economics and the demo effect".

Demonstration 2 of 4

Hiring the first good-enough applicant

When is stopping at the first applicant who clears the bar cheaper than seeing everyone?

The satisficer compares each score with the aspiration, not with the unseen applicants. Raising the bar lengthens the search; raising the interview cost makes the extra interviews needed for an exhaustive comparison less worthwhile.

Equation, written in LaTeX: \tau=2

Equation, written in LaTeX: (91-77)(\$100)=\$1{,}400.

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Applicants arrive in the order Lina 68, Omar 77, Priya 91, Chen 82. A is the aspiration level and tau is the first applicant whose score reaches A. Each interview costs the amount shown, and each score point is worth $100 of contribution in a one-month job.

Predict first. With aspiration 85 and $300 interviews, who is hired and at what tau?

Your prediction

Choose an example

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Figure: Hiring the first good-enough applicant. Bars for four applicants in interview order with an aspiration line at 75. The manager stops at applicant 2, Omar, scoring 77; later applicants are unseen. Exhaustive review would net $800.
Aspiration level: 75, Cost per interview ($): $300
Constructed example: the chapter's hypothetical repair shop (scores 68, 77, 91, 82; aspiration 75 or 85; interviews $300 or $900); aspiration 65 and interview cost $600 are added for comparison.

Calculated values

Stopping point tau
2
Hired
Omar (77)
Screening cost
$600
Extra cost of exhaustive review
$600
Gain from exhaustive review
$1,400
Net of exhaustive review
$800

Interviewing in order (Lina 68, Omar 77), the first score at or above 75 is Omar's 77, so tau = 2 and screening costs 2 x $300 = $600. Exhaustive review needs 2 more interviews costing 2 x $300 = $600 and gains (91 - 77) x $100 = $1,400. Net $1,400 - $600 = $800, so exhaustive review would pay. In plain numbers: 2 x 300 = 600 and 1,400 - 600 = 800 dollars.

Worked steps

  1. First score at or above 75: Omar (77), so tau = 2
  2. Screening cost = 2 x $300 = $600
  3. Extra interviews = 2 x $300 = $600
  4. Gain = (91 - 77) x $100 = $1,400
  5. Net = $1,400 - $600 = $800

Use the idea

For any sequential search, compare the cost of the remaining inspections with the most you could gain by seeing them before deciding whether to keep looking.

Where the conclusion applies

Scores are observed exactly at each interview, the order is fixed, and the exhaustive gain uses the hindsight best score. A real searcher does not know the unseen scores in advance.

Check your understanding: With $600 per interview and aspiration 75, is exhaustive review worth it relative to stopping at Omar?
Two more interviews cost 2 x $600 = $1,200 against a gain of $1,400, so the net is $200 > 0: yes, barely.

Chapter 19 source: section "Bounded rationality and satisficing".

Demonstration 3 of 4

Not opening the alert

When does a free and useful signal go unread?

Useful information never has negative instrumental value, because it can be ignored after receipt. Avoidance needs another cost of knowing. The decision flips when that cost crosses the instrumental value.

Equation, written in LaTeX: 0.5(\$120)=\$60.

Equation, written in LaTeX: \$60-\$80=-\$20,

Equation, written in LaTeX: \$60-\$30=\$30,

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p is the chance the retirement alert reveals a correctable shortfall, and fixing it is worth $120. The instrumental value of opening is p x 120. The anxiety cost is the expected immediate cost of knowing and acting.

Predict first. With shortfall probability 0.75 and anxiety $80, does she open the alert?

Your prediction

Choose an example

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Figure: Not opening the alert. Bars for instrumental value $60, anxiety cost $80 shown below zero, and net value -$20. Decision: Avoid the alert.
Expected anxiety cost ($): $80, Shortfall probability: 0.5
Constructed example: the chapter's hypothetical retirement alert (probability 0.5, $120 correction, anxiety $0, $80 or $30); probabilities 0.25 and 0.75 are added for comparison. At probability 0.25 with anxiety $30 the net value is exactly zero.

Calculated values

Instrumental value
$60
Anxiety cost
$80
Net value
-$20
Decision
Avoid the alert
Break-even probability
0.667

Instrumental value = 0.5 x $120 = $60. Net value = $60 - $80 = -$20. In plain numbers: 0.5 x 120 = 60 and 60 - 80 = -20 dollars. She avoids it, even though the signal is useful. Opening pays only when 120p exceeds 80, that is p above 0.667.

Worked steps

  1. Instrumental value = 0.5 x $120 = $60
  2. Net value = $60 - $80 = -$20
  3. Decision: Avoid the alert
  4. Break-even p = 80 / 120 = 0.667

Use the idea

Before calling a refusal to look irrational, price both the instrumental value of the signal and the cost of learning it; lowering the second (for example a preselected correction) may be cheaper than raising the first.

Where the conclusion applies

A one-shot choice, a free and accurate signal, and a feasible correction. Distrust, privacy or an inability to act would also reduce demand for the signal.

Check your understanding: With anxiety $80, what shortfall probability makes opening worthwhile?
120p > 80 gives p > 2/3; at p = 0.75 the net is $90 - $80 = $10, so she opens it.

Chapter 19 source: section "Information avoidance".

Demonstration 4 of 4

Winner takes the attention

How does a ranking concentrate attention, and when does entering the contest signal capability?

The left panel shows amplification: a small score gap becomes a large attention gap once ranks carry unequal weight. The right panel shows credibility: entry signals capability only when the weak type loses by imitating. Visibility and credibility are separate questions.

Equation, written in LaTeX: \alpha_A=\frac{5}{6.5}\approx0.7692,

Equation, written in LaTeX: \$5-\$2=\$3>0

Equation, written in LaTeX: \$5-\$8=-\$3<0

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Vendors A, B and C have reliability scores 95, 92 and 88. After the contest, ranks receive weights (first-rank weight, 1, 0.5) and 1,000 buyers divide inquiries in proportion, alpha_j = weight / total. The badge is worth $5 million; preparing costs a high-capability vendor $2 million and a weak imitator the amount shown.

Predict first. With the weak type's cost at $5 million, does entry still separate the types?

Your prediction

Choose an example

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Figure: Winner takes the attention. Left: expected inquiries of about 769, 154 and 77 for vendors A, B and C with first-rank weight 5. Right: net entry benefit 3 for the high type and -3 for the weak type. Separating.
First-rank weight: 5, Weak type entry cost ($ million): $8 million
Constructed example: the chapter's hypothetical vendor contest (weights 5, 1, 0.5; 1,000 buyers; badge $5 million; costs $2 million and $8 million or $3 million); first-rank weights 1 and 2 and a weak-type cost of $5 million (exact indifference) are added for comparison.

Calculated values

Inquiries A, B, C
769, 154, 77
Share of A
0.7692
High-type net ($ million)
3
Weak-type net ($ million)
-3
Outcome
Separating

Total weight is 5 + 1 + 0.5 = 6.5, so A's share is 5 / 6.5 = 0.7692 and A expects about 769 of 1,000 inquiries (B 154, C 77). Entry nets are $5 - $2 = $3 million for the high type and $5 - $8 = -$3 million for the weak type. Only the high type gains from entry, so entry separates the types.

Worked steps

  1. Total weight = 5 + 1 + 0.5 = 6.5
  2. A: 5 / 6.5 x 1,000 = 769.2
  3. B: 1 / 6.5 x 1,000 = 153.8; C: 0.5 / 6.5 x 1,000 = 76.9
  4. High type: 5 - 2 = 3
  5. Weak type: 5 - 8 = -3
  6. Outcome: Separating

Use the idea

Check the separation inequalities for any badge or certification before treating it as evidence of quality, and measure the attention it brings separately.

Where the conclusion applies

Fixed rank weights, proportional inquiries, and a known badge benefit that is the same for both types. Concentrated attention can also reflect real quality or scale.

Check your understanding: With first-rank weight 2, how many inquiries does A get?
2 / (2 + 1 + 0.5) x 1,000 = 571.4, about 571.

Chapter 19 source: section "Signaling and winner-take-attention markets".