Actuarial Notes

Cognitive Bias

Study guide: Exam CP-311

A Cognitive Bias is a systematic, predictable departure of human judgment from what a rational analysis of the same information would conclude, usually caused by the mental shortcuts (heuristics) people use to decide quickly. Because the error has a direction rather than being random noise, it does not average out across decisions, and in organizations it compounds through groups, incentives and earlier commitments.

\hat{X} = A + \lambda (X - A)

v(x) = \begin{cases} x^{\alpha} & x \ge 0 \\ -\kappa(-x)^{\beta} & x < 0 \end{cases}

  • Symbols: In the anchoring formula, A is the anchor, X is the estimate the evidence supports, and \lambda, between 0 and 1, is how far the judge adjusts toward it. A value below 1 is insufficient adjustment, so \hat{X} stays biased toward A. In the prospect theory value function, outcomes are gains or losses from a reference point, \alpha, \beta < 1 make the curve concave for gains and convex for losses, and \kappa > 1 is loss aversion. Tversky and Kahneman's estimates were about \alpha = \beta = 0.88 and \kappa = 2.25.
  • Anchoring: Judgments start from a value, often an irrelevant or outdated one, and adjust too little. Last year's selected reserve, the plan's growth number or the first offer in a negotiation all act as anchors.
  • Overconfidence: People are too sure of their estimates. Ranges stated as 90% confidence intervals contain the true value far less than 90% of the time, so risk is understated.
  • Confirmation bias: People look for and weigh evidence that supports what they already believe, and discount evidence against it. An analyst who expects favourable development will notice the quarters that show it.
  • Availability: Events that are vivid, recent or easy to recall are judged more likely than they are. A recent large loss raises perceived frequency, and a long quiet period lowers it.
  • Framing: The same choice described as gains or as losses leads to different decisions, because people are risk averse for gains and risk seeking for losses relative to their reference point.
  • Escalation of commitment: Decision makers keep investing in a failing course of action to justify earlier choices, treating sunk costs as a reason to continue. Large IT projects and struggling acquisitions are the usual organizational examples.
  • Groupthink: A cohesive group seeking agreement suppresses dissent and stops testing alternatives, so the group is more confident and less accurate than its members. Strong leaders who state a view first make it worse.
  • Debiasing: Remedies include using outside views and base rates, asking someone to argue the opposite or run a pre-mortem, setting decision rules before seeing results, separating the person who made a commitment from the decision to continue it, and using formal decision analysis. Bazerman and Moore describe lasting change as unfreezing the old process, changing it and refreezing the new one.

An Anchored Reserve Estimate Last year the reserving team selected an ultimate loss of $50 million for an accident year. This year's data, analysed without reference to the prior selection, supports $58 million. The team reviews the new indications starting from last year's number and adjusts only 40% of the way. What does it select, and what is the bias?

Answer

\begin{align*}
\hat{X} &= 50 + 0.40(58 - 50) \\
&= 50 + 3.2 \\
&= \$53.2 \text{ million}
\end{align*}

The selection is $4.8 million below what the evidence supports, so the reserves are deficient by that amount. Each year repeats the partial adjustment, which is why anchored reserves tend to creep toward adequacy over several years rather than being corrected at once. A remedy is to form the indication before looking at the prior selection, and to document why any change from the indication is made, which the standards of practice expect in any case.

The Same Decision in Two Frames An insurer faces $600 million of exposure on a failing book. Under program A it saves $200 million for certain. Under program B it saves all $600 million with probability 1/3 and nothing with probability 2/3. Described as losses, A loses $400 million for certain, and B loses nothing with probability 1/3 and $600 million with probability 2/3. Using the prospect theory value function with \alpha = \beta = 0.88 and \kappa = 2.25, show which program each frame favours.

Answer Both programs have the same expected outcome, saving $200 million. In the gain frame:

\begin{align*}
v(A) &= 200^{0.88} \\
&= 105.9 \\
v(B) &= \tfrac{1}{3} \times 600^{0.88} \\
&= 92.8
\end{align*}

In the loss frame:

\begin{align*}
v(A) &= -2.25 \times 400^{0.88} \\
&= -438.5 \\
v(B) &= \tfrac{2}{3} \times (-2.25 \times 600^{0.88}) \\
&= -417.7
\end{align*}

The gain frame favours the sure program A, and the loss frame favours the gamble B, although the outcomes are identical. A management team told it can "save $200 million" and one told it will "lose $400 million" may choose differently. The defence is to present every option in the same frame, with the full distribution of outcomes.

How it appears on the exam

  • CP-311: The objective asks the candidate to explain the role of cognitive biases in suboptimal individual decisions. Questions describe a decision, such as an acquisition, a project overrun or a forecast, and ask the candidate to identify the biases at work, explain how they led to a poor outcome, and recommend debiasing measures. Name the bias, point to the evidence for it in the case, and match the remedy to the bias.
  • CP-311: The companion objective on organizational behaviour asks how group dynamics, incentives and decision processes affect decision quality, where groupthink, escalation of commitment and biased capital allocation are the usual examples.

Exam traps

  • Bias versus noise: A cognitive bias is systematic, so it shifts decisions in one direction and does not cancel out across many decisions. Random inconsistency between judges is a different problem with different remedies.
  • Sunk costs are not a reason: Escalation of commitment is recognized when past spending is cited as a reason to continue. The rational test looks only at future costs and benefits from today.
  • Framing changes nothing real: Two frames of the same decision have the same outcomes, so a change in choice between them is the bias. Do not argue that one frame is more accurate.
  • Naming is not explaining: A list of bias names earns little. Each should be tied to what happened in the case and to a specific remedy.
  • Statistical bias is different: The bias of an estimator is a property of a statistical method, while a cognitive bias is a property of human judgment. They can interact, as when an analyst picks the method that confirms the expected answer.