Choosing Among Alternatives
© Copyright 2009 Herbert J. Bernstein

The essence of decision-making is to choose among alternatives. The essential steps in the process are:

• Organize the alternatives to be considered
  • Identify dependencies
  • Identify mutual exclusions
  • Identify uncertainties
  • Identify stakeholders
  • Idenfity which parameters are controlled by which parties
• Assign values to choices and groups of choices
  • Value to one stakeholder may be different from or opposed to from value to other stakeholders
  • Common value systems are needed in comparing values of alternatives
  • Both costs and benefits need to be considered to try to get a net payoff
  • Indirect costs need to be considered (space, power, administrative costs, fringe benefits)
  • Values need to be brought to common time-frames (future values versus present values, life-cycle costs)
  • Utility functions may be used to assign values to intangibles
  • Values may be uncertain: discrete or continous probability distributions, or just bounds.
• Decide on your objectives.
  • Payoff versus risk
  • Intangible goals (e.g. satisfaction of "winning")
  • Skin in the game (real risks versus emotional risks)
• Apply a strategy to decide among alteratives in light of the assigned values and objectives
  • Minimax Strategy (Game Theory)
    • organize alternatives over which stakeholder has control versus conditions not controlled by the stakeholder or controlled by other staekholders
    • for each alternative controled by the stakeholder look for the outcome that might produce the maximal loss or the minimal payoff
    • select the alternative controled by the stakeholder that minimizes the maximal losses
    • or maximizes minimum payoff (maximin)
    • first priority -- limit downside risks
  • Maximal Gain Strategy or Maximax Strategy (Greed is Good)
    • maximize maximal payoff
    • first priority -- highest payoff
    • ignores risk -- can lead to gambler's ruin
  • Maximal Mean Gain (maximean) Strategy
    • organize alternatives over which stakeholder has control versus conditions not controlled by the stakeholder or controlled by other stakeholders
    • for each alternative controled by the stakeholder form an appropriately weighted mean of the possible payoffs
    • select the alternative controled by the stakeholder that maximizes the mean payoff
    • attempts to balance risk against payoff
  • Minimal Regret Strategy
    • organize alternatives over which stakeholder has control versus conditions not controlled by the stakeholder or controlled by other stakeholders
    • for each alternative controled by the stakeholder assign a "regret" (least expected return - payoff)
    • for each alternative controled by the stakeholder look for the maximal possible regret
    • select the alternative controled by the stakeholder that minimized the maximal regret
    • similar to minimax, but emphasises the range of losses stakeholder-controlled alterative by alternative rather than globally
  • Uncertainty
    • Important to distinguish parameters that are random variables from parameters that may be adversely controlled by other stakeholders
    • Payoff based on truly random variables may be represented by the expected payoff, by the 5% value at risk, by the 1% value ot risk, ..., or by an interval, say, from the 5% value at risk to the 95% value at risk.
    • Minimax, maximean, and minimax regret may all be applied with random varaibles.
    • Expected payoff strategy: maximean with probability weighted means.
    • Expected regret strategy: minimax regret with probability weighted mean regret instead of the maximal regret
    • Risk-constrained expected payoff strategy. Apply a selection strategy considering only alternatives for which the standard deviation is within some acceptable limit. This strategy can produce very strange results, causing rejection of alternatives with high standard deviations even if the 5% value at risk is much higher than that for any other alterntives or even grater than their means.
    • Payoff-constrained minimum risk strategy. Apply a selection strategy considering only alternatives for which the expected payoff is greater than some acceptable level, and selecting the alternative with the smallest standard deviation. As with the prior strategy, this can produce very strange results.
    • Payoff at risk strategy. Apply a selection strategy considering only alternatives for which, say, the 5% value at risk payoff is over some acceptable level.
    • Percentile criteria. Apply a selection criterion to, say, the 5% value at risk (or other suitable percentile) instead of to the means.
• Dependent decisions -- decision trees, fault trees
  • Decision Tree -- connect each decision to the decisions on which it depends
  • Fault Tree -- Connect each event to the events that may arise from it
  • Decisions with Prior information
    • Bayes' theorem
    • More on Bayes' theorem
    • Expected Value of Perfect Information
    • Value of Information