These are my notes taken during talk given by Dr McMillen, Mathematics department, California State University, Fullerton. On April 25, 2007. The subject of the talk was on Mathematical Problems of Decision Making
Dr McMillen started by asking the question: ”How to choose between different choices?”, examples given are: run or fight? and asked also: you might have to select between many choices, not just 2.
What are the choice-reaction model?
Need to vary signal to noise ratio and check how people can choose.
If some choices are close to each others, and one choice is distinct one, people tend to select the distinct one. For example, it is easier for people to choose between 2 bars that are drawn at 90 degree to each others, than 2 that are inclined such as they are very close to each others. The first case makes selecting easier since the choices are more distinct from each others.
There is a limit on how many choices people can handle at the same time. The limit seems to be around 7.
Now the talk went into discussing models of decision making:
This is a hard problem. Simplest types of models are only partially understood.
Statistical regularities
Reaction time (\(RT\)) effect:
Hick’s Law, where \(RT\sim \log (N)\) where \(N\) is the number of choices
Loss avoidance, this means people prefer choices that are far away from each others.
The magic number 7.
Stochastic differential equations are used to model decision making process. Mention of Fokker-Planck equation.
Now the talk presented a neural model of decisions making. Where 2 brain neurons are shown each accepting a separate input (with noise added), and there exist what is called an inhibition \(W\) factor between these 2 neurons. These neurons are subject also to a decay \(K\) factor. This is called Neural Model of perceptual choices.
The talk also discussed the effect on the amount of time a person has to make a decision on what decisions they make. When the time to make a decision is limited, it is called the interrogation model.
The talk now discussed what is an optimal method to decide between more than 2 random choices to select from.
Using the above neural model, the best decision is made when the inhibition between the 2 neurons and the decay factor is the same. A model by the name of SPRT (WALD): Wald’s Sequential Probability Ratios, was mentioned in relation to optimally theorem of decision making.
The conclusion of this talk was that a mathematical model of how the brain makes decisions is very complex problem and not well understood, and only a very simple model exist when it comes to making a decision between 2 choices. The optimal way to make a decision is an unsolved mathematical problem.
I found this talk a bit hard to follow. I could not make a clear distinction on how the neural model shown related to the stochastic differential equations presented earlier. I did not understand what does the inhibition factor between neuron mean, and what is the decay factor actually represent? I think the talk was a little advanced for me as I felt I did not completely follow all the points presented. But I did get from this talk that modeling a decision making in humans at the neural level is a very difficult problem, but it was not clear to me why and how this difficulty comes about. Never the less, I did find the talk interesting and informative.