How a simple, but systematic mathematical approach in general (and causal mapping in particular) can help navigate common pitfalls in decision making. An introduction to the mathematical modelling of decisions

1. DECISION RISK ANALYTICS
confidence through insight
Decision decision decision
Releasing your inner mathematician to make better decisions

2. Carter racing
Carter racing team has had a run of engine failures,
8 failures in 24 races
There is a big race tomorrow. A good result will secure
sponsorship, but another failure will finish the team.
The team mechanic feels that the failures occur at
cold temperatures and it’s cold tomorrow.
Data show failures across all temperatures
Do you race?

3. The Monty Hall problem
Switch or stick?
You’re shown three doors. Behind one of the doors is
a car; behind the other two are goats.
You are asked to pick a door. The game show host
then opens one of the other two doors to reveal a goat
The game show host asks whether you want to stick
to the door your on or to switch to the other.

4. The Gambler
Which game should Alexei play?
Alexei Ivanovich has 1000 roubles. To win the hand of
the beautiful Polina, he needs 13,000 roubles
The immensely wealthy Marquis de Grieux offers him
two games, but he can only play one of them
Either
Alexei gives him all his money and rolls two dice.
If he gets a double 6, Le Comte will give him back his
stake plus 12,000 roubles
Or
Alexei gives him 1000 roubles and tosses a coin.
If he gets heads, Le Comte will give him back his stake
plus 2000 roubles and he may play again.
If he gets tails, the game stops.

5. Furnish complete, relevant and reliable information. Articulate
uncertainty. Surface bias. Know when to stop and when not to
Understand the levers. Distinguish between options and objectives.
Generate feasible and diverse alternatives. Understand relations.
Identify objectives and metrics. Determine decision criteria and
constraints. Define trade-offs. Articulate preferences.
Use the appropriate tools and ensure sound reasoning
Decision quality principles are entailed by modelling
Information
Framing
Options
Values
Logic
See, for example, Guidance for Decision Quality for Multicompany Upstream Projects (2016), SPE-181246 See, for example, Assessing the reliability of complex models (2012) National Research Council
Causal
Models decompose relationships between decisions and
objectives into causally related elements. Ensures coherence.
Actionable
Decisions and objectives are the poles of the axis on which all
uncertainty models are built.
Embrace virtuous simplicity that contains its complexity. Avoid
vicious simplicity that ignores complexity
Simple
Verifiable
Models are consistent with available data and make predictions
whose verification can refine or reject the model
Commitment
Decision quality principles Mathematical modelling principles

6. Carter racing
Carter racing team has had a run of engine failures,
8 failures in 24 races
There is a big race tomorrow. A good result will secure
sponsorship, but another failure will finish the team.
The team mechanic feels that the failures occur at
cold temperatures and it’s cold tomorrow.
Data show failures across all temperatures
Do you race?

7. Carter racing
Carter racing team has had a run of engine failures,
8 failures in 24 races
There is a big race tomorrow. A good result will secure
sponsorship, but another failure will finish the team.
The team mechanic feels that the failures occur at
cold temperatures and it’s cold tomorrow.
Data show failures across all temperatures
Decisions and objectives are the poles of the axis
on which all uncertainty models are built.
Models decompose relationships between decisions
and objectives into causally related elements.
Race?
Race / Don’t
Fame &
Glory

8. Carter racing
Race?
Race / Don’t
Engine fail
Fail / Doesn’t
Other factors
affecting race
outcome
Other factors
affecting engine
outcome
Temperature
Hot / Cold
Fame &
Glory
Carter racing team has had a run of engine failures,
8 failures in 24 races
There is a big race tomorrow. A good result will secure
sponsorship, but another failure will finish the team.
The team mechanic feels that the failures occur at
cold temperatures and it’s cold tomorrow.
Data show failures across all temperatures

9. Carter racing
Race?
Race / Don’t
Engine fail
Fail / Doesn’t
Other factors
affecting race
outcome
Other factors
affecting engine
outcome
Temperature
Hot / Cold
Fame &
Glory

10. The Monty Hall problem
Switch or stick?
You’re shown three doors. Behind one of the doors is
a car; behind the other two are goats.
You are asked to pick a door. The game show host
then opens one of the other two doors to reveal a goat
The game show host asks whether you want to stick
to the door your on or to switch to the other.

11. The Monty Hall problem
Switch?
Switch / Stick
Car or
Goat
Decisions and objectives are the poles of the axis
on which all uncertainty models are built.
Models decompose relationships between decisions
and objectives into causally related elements.
Door?
1 / 2 / 3
You’re shown three doors. Behind one of the doors is
a car; behind the other two are goats.
You are asked to pick a door. The game show host
then opens one of the other two doors to reveal a goat
The game show host asks whether you want to stick
to the door your on or to switch to the other.

12. The Monty Hall problem
You’re shown three doors. Behind one of the doors is
a car; behind the other two are goats.
You are asked to pick a door. The game show host
then opens one of the other two doors to reveal a goat
The game show host asks whether you want to stick
to the door your on or to switch to the other.
Car or
Goat
Car
1 / 2 / 3
Monty’s move
2 / 3
Switch?
Switch / Stick
Door?
1 / 2 / 3
Final door
1 / 2 / 3

13. The Monty Hall problem
You have a 1 in 3 chance of picking the car.
Monty can open either door. If you switch you’ll get a goat. If you
stick you’ll get the car.
You’ve twice as good a chance of picking a goat.
Then Monty has to choose the other goat. Now if you switch, you’ll
get the car. If you stick, you’ll get a goat.
If your strategy is to switch, you’re twice as likely to get the car.
Car or
Goat
Car
1 / 2 / 3
Monty’s move
2 / 3
Switch?
Switch / Stick
Door?
1 / 2 / 3
Final door
1 / 2 / 3

14. The Gambler
Which game should Alexei play?
Alexei Ivanovich has 1000 roubles. To win the hand of
the beautiful Polina, he needs 13,000 roubles
The immensely wealthy Marquis de Grieux offers him
two games, but he can only play one of them
Either
Alexei gives him all his money and rolls two dice.
If he gets a double 6, Le Comte will give him back his
stake plus 12,000 roubles
Or
Alexei gives him 1000 roubles and tosses a coin.
If he gets heads, Le Comte will give him back his stake
plus 2000 roubles and he may play again.
If he gets tails, the game stops.

15. The Gambler
Which game should Alexei play?
Decisions and objectives are the poles of the axis
on which all uncertainty models are built.
Models decompose relationships between decisions
and objectives into causally related elements.
Alexei Ivanovich has 1000 roubles. To win the hand of
the beautiful Polina, he needs 13,000 roubles
The immensely wealthy Marquis de Grieux offers him
two games, but he can only play one of them
Either
Alexei gives him all his money and rolls two dice.
If he gets a double 6, Le Comte will give him back his
stake plus 12,000 roubles
Or
Alexei gives him 1000 roubles and tosses a coin.
If he gets heads, Le Comte will give him back his stake
plus 2000 roubles and he may play again.
If he gets tails, the game stops.
Love
Loss
Fortune
Ruin
Game?
Dice / Coin

16. The Gambler
Which game should Alexei play?
Dice Coin
Winnings
Alexei Ivanovich has 1000 roubles. To win the hand of
the beautiful Polina, he needs 13,000 roubles
The immensely wealthy Marquis de Grieux offers him
two games, but he can only play one of them
Either
Alexei gives him all his money and rolls two dice.
If he gets a double 6, Le Comte will give him back his
stake plus 12,000 roubles
Or
Alexei gives him 1000 roubles and tosses a coin.
If he gets heads, Le Comte will give him back his stake
plus 2000 roubles and he may play again.
If he gets tails, the game stops.
Love
Loss
Fortune
Ruin
Game?
Dice / Coin

17. The Gambler
Alexei Ivanovich has 1000 roubles. To win the hand of
the beautiful Polina, he needs 13,000 roubles
The immensely wealthy Marquis de Grieux offers him
two games, but he can only play one of them
Either
Alexei gives him all his money and rolls two dice.
If he gets a double 6, Le Comte will give him back his
stake plus 12,000 roubles
Or
Alexei gives him 1000 roubles and tosses a coin.
If he gets heads, Le Comte will give him back his stake
plus 2000 roubles and he may play again.
If he gets tails, the game stops.
Dice
Coin
12,000
-1,000
2,000
-1,000
Coin
4,000
1,000
W
L
W
L
W
L1
2
... Coin
12,000
9,000
W
L
6
Probability weighted winnings = -640 Roubles
Probability weighted winnings = 4500 Roubles
Probability of winning the hand of Polina = 2.7%
Probability of winning the hand of Polina = 1.5%
Love
Loss
Fortune
Ruin
Game?
Dice / Coin

18. Take aways
Decide or be damned
Decisions and objectives are the poles of the axis
on which all uncertainty models are built.
Causes are key
Models decompose relationships between decisions
and objectives into causally related elements.
Cause to effect
To investigate causal relations, control or condition
causes and investigate effects
Release your inner mathematician
Uncertainty is not intuitive. Take a step back.
Use what you have learned.
Inevitable probabilistic goals
Articulate risks, rewards and how you trade between
the two

19. Carter Racing:
Brittain and Sitkin (1989). Facts, figures and
organisational decisions: Carter Racing and quantitative
analysis in the organisational behaviour classroom
Organisational Behaviour Teaching Review, 14 (1) 62-81
The Monty Hall Problem
Selvin (1975). A problem in probability (letter to the
editor). American Statistician, 29 (1): 67
The Gambler
Very very loosely based on an example from
Körner (2008). Naive decision making CUP
Acknowledgements

20. Probabilistic intuition (or lack of same)
Kahnemann (2013). Thinking fast and slow.
Farrar, Straus and Giroux
Causal analysis
Pearl & Mackenzie (2018). The book of why.
Allen Lane
Decision theory
Körner (2008). Naive decision making. CUP
Probability theory
Hacking (2001). An introduction to
probability and inductive logic. CUP
Kahnemann, Slovic and Tversky (1982).
Judgement under uncertainty: Heuristics
and biases. CUP
Hacking (1983). Representing and
Intervening. CUP
Berger (1985). Statistical decision theory
and Bayesian analysis. Springer.
Jaynes (2003). Probability Theory: The logic
of science. CUP