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Civil Systems Planning Benefit/Cost Analysis. Scott Matthews Courses: 12-706 / 19-702/ 73-359 Lecture 16. Admin. Project 1 - avg 85 (high 100) Mid sem grades today - how done?. Recall: Choosing a Car Example. Car Fuel Eff (mpg) Comfort

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civil systems planning benefit cost analysis

Civil Systems PlanningBenefit/Cost Analysis

Scott Matthews

Courses: 12-706 / 19-702/ 73-359

Lecture 16

admin
Admin
  • Project 1 - avg 85 (high 100)
  • Mid sem grades today - how done?

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recall choosing a car example
Recall: Choosing a Car Example
  • Car Fuel Eff (mpg) Comfort
  • Index
  • Mercedes 25 10
  • Chevrolet 28 3
  • Toyota 35 6
  • Volvo 30 9

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pricing out
“Pricing out”
  • Book uses $ / unit tradeoff
  • Our example has no $ - but same idea
  • “Pricing out” simply means knowing your willingness to make tradeoffs
  • Assume you’ve thought hard about the car tradeoff and would trade 2 units of C for a unit of F (maybe because you’re a student and need to save money)

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with these weights
With these weights..
  • U(M) = 0.26*1 + 0.74*0 = 0.26
  • U(V) = 0.26*(6/7) + 0.74*0.5 = 0.593
  • U(T) = 0.26*(3/7) + 0.74*1 = 0.851
  • U(H) = 0.26*(4/7) + 0.74*0.6 = 0.593
    • Note H isnt really an option - just “checking” that we get same U as for Volvo (as expected)

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mcdm swing weights
MCDM - Swing Weights
  • Use hypothetical combinations to determine weights
  • Base option = worst on all attributes
  • Other options - “swings” one of the attributes from worst to best
  • Determine your rank preference, find weights

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add 1 attribute to car cost
Add 1 attribute to car (cost)
  • M = $50,000 V = $40,000 T = $20,000 C=$15,000
  • Swing weight table:
  • Benchmark 25mpg, $50k, 3 Comf

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stochastic dominance defined
Stochastic Dominance “Defined”
  • A is better than B if:
  • Pr(Profit > $z |A) ≥ Pr(Profit > $z |B), for all possible values of $z.
  • Or (complementarity..)
  • Pr(Profit ≤ $z |A) ≤ Pr(Profit ≤ $z |B), for all possible values of $z.
  • A FOSD B iff FA(z) ≤ FB(z) for all z

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stochastic dominance example 1
Stochastic Dominance:Example #1
  • CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.

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stochastic dominance again
Stochastic Dominance (again)
  • Chapter 4 (Risk Profiles) introduced deterministic and stochastic dominance
    • We looked at discrete, but similar for continuous
    • How do we compare payoff distributions?
    • Two concepts:
    • A is better than B because A provides unambiguously higher returns than B
    • A is better than B because A is unambiguously less risky than B
    • If an option Stochastically dominates another, it must have a higher expected value

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first order stochastic dominance fosd
First-Order Stochastic Dominance (FOSD)
  • Case 1: A is better than B because A provides unambiguously higher returns than B
    • Every expected utility maximizer prefers A to B
    • (prefers more to less)
    • For every x, the probability of getting at least x is higher under A than under B.
  • Say A “first order stochastic dominates B” if:
      • Notation: FA(x) is cdf of A, FB(x) is cdf of B.
      • FB(x) ≥ FA(x) for all x, with one strict inequality
      • or .. for any non-decr. U(x), ∫U(x)dFA(x) ≥ ∫U(x)dFB(x)
      • Expected value of A is higher than B

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slide12
FOSD

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Source: http://www.nes.ru/~agoriaev/IT05notes.pdf

fosd example
Option A

Option B

FOSD Example

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second order stochastic dominance sosd
Second-Order Stochastic Dominance (SOSD)
  • How to compare 2 lotteries based on risk
    • Given lotteries/distributions w/ same mean
  • So we’re looking for a rule by which we can say “B is riskier than A because every risk averse person prefers A to B”
  • A ‘SOSD’ B if
    • For every non-decreasing (concave) U(x)..

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sosd example
Option A

Option B

SOSD Example

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slide17

Area 2

Area 1

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slide18
SOSD

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sd and mcdm
SD and MCDM
  • As long as criteria are independent (e.g., fun and salary) then
    • Then if one alternative SD another on each individual attribute, then it will SD the other when weights/attribute scores combined
    • (e.g., marginal and joint prob distributions)

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reading pdf cdf graphs
Reading pdf/cdf graphs
  • What information can we see from just looking at a randomly selected pdf or cdf?

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