A loop to learn to go in the right direction

What a journey from the blackboard to dark chocolate!

From a young age, we learn on the blackboard in math class that if A is greater than B and B is greater than C, then A is greater than C. But very early on, sometimes as soon as the next recess, the game rock-paper-scissors casts doubt on these obvious truths: indeed, the player who shows a hand symbolizing rock beats the one representing scissors, scissors beat paper, but paper beats rock by covering it! Thus, the hierarchy of choices is not so obvious and is so complex that this basic game has given rise to abundant literature on how to win.

The problem of transitivity of preferences becomes more complex when the choice is no longer based on one criterion (in our example, rock wins or loses) but on three criteria to rank options. Imagine Céline hesitating between three boxes of dark chocolates to offer her guests at the New Year's Eve party:
- the "artisan box" costs €15 for 12 chocolates with 3 fillings,
- the "gourmet box" costs €20 for 20 chocolates with 2 fillings,
- the "luxury box" costs €25 for 24 chocolates but with only one filling.

Obviously, on the price criterion, the artisan box is preferred over the gourmet box, which in turn is preferred over the luxury box. For the number of fillings, the gourmet box is preferred over the luxury box; but the luxury box, overlooked in the previous criteria, is preferred over the artisan box for the number of chocolates it contains!

The landmark study² on intransitivity of preferences in multicriteria choices dates back to 1969. Amos Tversky asked participants to rank 45 candidate profiles by successive pairs according to three criteria (intelligence, emotion and sociability), the first indicated as essential and each quantified by scores. The author highlights the use of the semi-lexicographic order³, which is a decision rule where options are compared according to a hierarchy of criteria, taking into account thresholds to judge whether a difference is relevant. The existence of a sensitivity threshold below which small differences are ignored leads to intransitive preferences and ultimately to contradictions between choices that participants do not perceive at all.

One can easily imagine the complexity of choosing the box of dark chocolates to offer when, moreover, one must choose not according to one’s own (incoherent) preferences but on behalf of someone else!

Not everything is so black!

Thus, even in the presence of clear criteria, choice can be complex. Enough to discourage any desire to make relevant financial decisions. In personal finance, it is already complicated to rank choices based solely on the risk/return pair. Indeed, to be meaningful, one must properly understand the desired level of return and the acceptance of risk (which vary between individuals) but also correctly assess the probabilities of realizing that return and that risk.

The question of transitivity of preferences arises as soon as different criteria are mixed. Yet, the risk/return pair constitutes a criterion to be evaluated just like liquidity (the ability to sell a financial asset without time constraints), volatility (a linear increase in the value of an asset or erratic evolution that can cause the discomfort of a latent loss), or the time dimension (short, medium, or long term). It is easy to understand that few investments perfectly meet these four criteria, making it complex to rank the options considered.

Returning to the reference study on the subject, Tversky compares the results proposed by participants with those given by the Weighted Scoring Technique method, which precisely respects transitivity and coherence. This method ranks options by adding the scores obtained for each of the different criteria, previously weighted.

In this methodology, we find the principle known to students: that of the weighted average of different scores… including that of the math class at the beginning of the article! Like rock-paper-scissors… the circle is closed once again.

Now it’s your turn to link this article to your personal financial management !