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Decision decision decision

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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

Published in: Leadership & Management
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Decision decision decision

  1. 1. DECISION RISK ANALYTICS confidence through insight Decision decision decision Releasing your inner mathematician to make better decisions
  2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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