Decision making

Making decisions is, usually, a process based on our experience, our judgement, the recognition of patterns, and our degree of aversion to risk. All in all, a process based essentially on our intuition. Decision diagrams or decision trees are tools that transform decision making into a structured process based on the analysis of the starting situation, the universe of all our possible and controllable actions, and an estimation of the probabilities of the different uncertain outcomes of our choices.





There are two structural elements in a decision tree:

1. Decision nodes: they show all possible choices under the control of the decision maker. Decision nodes are represented by squares, from which every choice we can make branches out. 
2. Chance nodes: they show every possible outcome of a choice, that is beyond the control of the decision  maker. Chance nodes are represented by circles, from which all potential uncertain outcomes branch out.

Let's use as a simplified example an individual considering two scenarios for investing his 100.000 € savings: investing in fixed income securities, or investing in a friend's start-up.  Figure 1 shows the corresponding decision nodes, and Figure 2 shows the uncertain outcomes for the choice "investing in a start-up".

 

Once the choices and the uncertain outcomes are identified, the decision tree is build by connecting the elements following a time line. Additionally, numeric values are assigned to every choice, and probabilities are estimated for the uncertain outcomes.

In our example, the only consequence of the choice "invest in fixed income securities" is that the capital is recovered after one year, plus a 3% AER. On the other hand, the choice "investing in a start-up" opens up three uncertain scenarios. Let's assume the investor gets a 50% ownership of the new company for his money, and that the the start-up will reward shareholders with dividends accounting for 50% of the net benefit. Additionally, the investor checks the success rate of the start ups in the sector he's investing and discovers that on average 25% go bankrupt during the first year. Finally, the business plan for the company expects a net benefit of 200.000 € during the first year.  Three big costumers accounting for 50% of sales, and representing the break-even point for the business, have already confirmed orders, while the rest of potential costumers have not yet decided whether they would purchase or not the new products. Under these circumstances, the investor estimates that the probability of the company reaching the target the first year is 50%. Since all branches in the chance node must up to probability = 1, the recalculated probabilities for every uncertain outcome are: start-up going broke = 0.25; start-up without benefit = 0.375; start-up reaches target = 0.375. And the resulting tree is:

At this point, people with an aversion to risk will probably just invest in fixed income securities, while risk seekers will probably consider that chances of getting a 50% return on capital during the first year still outruns the chances of loosing everything. A way of removing subjective thinking is to calculate the mathematical expected value of every end-point in a decision, using the numerical consequences associated with each branch, and the probabilities of the uncertain events. In our example:

At this point, our investor will conclude that with a one-year investing plan in mind, securities are a better deal than venturing in the start-up. Or, he could go back to his friend and negotiate better conditions for his capital, and help reworking a more ambitious business plan ...