Part of a series exploring how economic thought leads to cognition and cognitive behaviour
There is a dirty little secret that all clever people harbour; they think they’re cleverer than everybody else. They hate finding another clever person as though another individual’s learning somehow diminishes them. *
They would have hated meeting John von Neumann.
Looking at von Neumann’s work shatters any illusions that we’re smart or a bit brainy.
In comparison to von Neumann we all look like amateurs. He possessed the sort of intellect where the rest of us might as well pack up our suit case and go home and leave him to it.
Amongst many subjects he investigated – along with Oskar Morgenstern – he turned his attention to how we seek to maximise our benefit from an event.
When uncertainty has been reduced around a decision this is a straight forward choice. Would you for instance prefer me to give you a gift of $5, $10 or $15?
The rational answer is obvious – $15.
Von Neumann and Morgenstern (VNM) laid out their reasonings or axioms that if we were rational we would satisfy in making this decision.
Completeness – We know what we are choosing between and can always make a choice between alternatives. I’m quite happy choosing between a $10 note and a $5 note.
Transitivity – From your original decision if you have decided that $10 is better than $5 and that $15 is better than $10 then $15 must be better than $5.
Independence – If you have chosen a gift of $15 and then I offer you the choice to switch to a gift of five $1 notes you would rationally dismiss this, just as you would have done if it was presented along with the original offer.
Continuity – There exists a point of equilibrium between the most and least favoured options (I’d argue where completeness disappears although others would disagree pointing out than indifference should be included in that axiom) leaving a combination which leads to indifference on the choosers behalf. There would be no difference in choice for you between receiving $15 and having to give $5 back or receiving $10 and being able to keep all of it.
It would be quite right to point out that VNM axioms are often applied under risk. In the examples above we have completely reduced uncertainty. You are sure that the $10 I have shown you is a $10 bill and that you would receive it – i.e. my offer is truthful.
If uncertainty has not been reduced we have to incorporate it into our decision making and in simple lotteries we still follow the four axioms when we maximise our profit, preference or utility depending on your term of choice.
You can follow through the list for these three choices:
- 80% chance of receiving $10
- 90% chance of receiving $4
- 40% chance of receiving $12
If we were VNM rational we would choose option a) as over the long term, if we repeated these choices we’d expect to receive a) $8 versus b) $3.6 or c) $4.8.
We’d expect a benefit of $8 to be available from the environment so in the case of a simple lottery it makes no sense for us to pursue a lesser benefit.
In our environment we naturally and automatically seek the greatest benefit from the options available to us.
For us, the function enacted as a response to the environment in pursuit of the greatest perceived available benefit we can call U.
* As a rule of thumb if I don’t go to bed realising I’m stupider than when I woke up I have generally wasted the day.
Photo credit: © Wilfred Stanley Sussenbach