Book seminar 1

Ullrika Sahlin

2023-08-30

Risk aversion - lottery

  • The probability of winning is \(p\).
  • A lottery ticket costs \(1\) SEK.
  • If you win you get \(100\) SEK.

The expected utility is: \[ EU = p \cdot 100 - 1 \]

Would you buy a ticket in this lottery?

  • If no, why? If yes, why?

Two doors

In this case you are to choose one out of two doors. Behind every door there is a chance of winning \(X\) with probability \(p\). Thus, each door is a lottery with the expected utility \(X\cdot p\).

  • Which lottery do you prefer in the three situations A, B and C?

Expected utilities

  • A: \(0.25\cdot 100 = 25\) vs \(0.25\cdot 10 = 2.5\)

  • B: \(0.05\cdot 100 = 5\) vs \(0.75\cdot 10 = 7.5\)

  • C: \(0.05\cdot 100 = 5\) vs \(0.5\cdot 10 = 5\)

Linquistic uncertainty

Impact on biodiversity is high

There is a 30% probability of rain tomorrow

  • Prominent in qualitative risk assessment due to the use of qualitative expressions

  • Can be avoided by using well defined questions, quantities and outcomes and meaningful scales

Subjective Risk Assessment

A tool from Mark and his colleagues to reduce linguistic uncertainty

SRA tool manual

Likelihood and impact scales

Subjective Risk Assessment

Rain - Rain tomorrow

Rocket - Next moon rocket crash on earth

Trump - Trump becomes the next president of USA

Use these likelihood and impact scales

Make judgements with single scores e.g. 3 or ranges, e.g. 2-4

Delphi process to aggregate judgements from a group of experts

  • Make individual judgements
  • Compare where there are large differences in judgements. - Discuss and resolve the reason for differences. Here is where linguistic uncertainties can be reduced.
  • Redo individual judgements
  • Aggregate the judgements

Interpretation of probability

Tutorial on uncertainty where Ullrika explains probability distribution

the frequency with which sampled values arise within a specified range or for a specified category

a quantification of a judgement on the likelihood of a particular range or category

Note

The mathematical theory for probability is the same for both interpretations!

Probability distributions

Visualising probability distributions

Uncertainty and variability