Tuesday, September 6, 2011

Decision making: risk, utility and probability


For the completely rational human being the concept of the 'utility' of a thing (that is its 'usefulness') should be directly related to the amount of the thing that they receive. For example £10 should be twice as useful as £5. Two cabbages should be worth twice as much as one cabbage.

Actually the relationship between most items and utility is more like the following diagram which depicts the relationship between utility and money for a typical person:

To demonstrate this, how would you answer the following question:

Which would you prefer?

100% chance of winning £1,500

50% chance of winning £3,000

Most people will choose the $1,500 even though logically they both have the same value.

This is because, as you can see from the graph, twice the amount of money corresponds to less than twice the amount of utility.

This utility/money curve of course varies from person to person and how risk averse they are but similar curves exist for the majority of people.

The curve also implies some other things. The further the amount of the resource increases (in this case money) the less the relative difference. For instance your response to the question above will probably be even less logical (and more risk averse) if the amounts were £10 million and £20 million. The other side of the curve implies that £20 probably has more than 10 times the utility of £2. The exception being if you needed the £2 for a bus home, in which case you would be highly risk averse to any gamble.

risk and probability

This behaviour is also similar to our risk versus probability curve:

If we have a very low probability of something happening (the left hand side of the curve) then there is little perceived risk because it is very unlikely that we would make that choice. For instance if we could bet £1 at 1 in ten thousand odds of wining £10 we are highly unlikely to take the bet.

The right hand side of the curve also is perceived as low risk. It there is a very high probability of something happening we perceive it correctly as low risk.

The highest risk is at the 50/50 probability where it is totally uncertain if an event will happen or not.

From a purely logical perspective this curve does not make sense, it really should be a triangle with straight lines. It differs from this because humans do not easily perceive very low probabilities as being as low risk as they are (and vice versa for high probabilities.) For a probability of 99.9% that some event will happen there is a small doubt in our minds and this increases the perceived risk. consider the following scenario: your house insurance is normally £500 per year but your insurance company has a strange offer on, for £100 per year you can insure your house for all days starting with a T or an S (that is 4 out of 7 days), would you take out the insurance?

We do not react linearly to utility and resource, logically we should?

We do not estimate risk against probability well?

If we can incorporate an understanding of these behaviours into our decision making we will be able to improve it.

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