Maarten Maartensz:    Philosophical Dictionary | Filosofisch Woordenboek                      

 E - Expectation

Expectation: What a person believes will happen in certain conditions; or, in probability-theoretical based reasoning: the product of probability and value.

1. In the first sense, expectation is the basis of habit and of much of what one believes. Normally, expectations are expectations of probabilities, which is to say that many though not all expectations are not confident certainties.

It should be noted that expectations are personal and normally based on learning, including false learning: What one expects may be in part based on illusion, and indeed much of what people expect is not based on their own experience, but on what they believe based on what they were told by others ('hear-say evidence').

2. In the second sense, expectation as the product of probability and value, one has a useful if also sometimes misleading idea to guide one's actions in so far as these are guided by probabilities and seek to maximize one's pleasure or make the most of one's ends.

Note that in the last sense, and in general, it is useful to explicitly make probabilities and values personal: If a is the name of a person, one accordingly has

'p(a,q)' = 'the probability a attributes to the event that q'
'v(a,q)' = 'the value a attributes to the event that q'
'e(a,q)' = 'the expectation of a for q' = 'p(a,q)*v(a,q)'

Here it is also supposed - as a matter of useful convenience - that values may be rendered as positive or negative numbers, the higher and more positive for the more valued, and the lower and more negative for the events one does not like to happen, in proportion to one's dislike for them.

This also makes it sensible to put v(a,q)=0 for those things q that person a is indifferent to.

Three problems with the notion of expectation as defined in the second sense is that it gives rise to some paradoxes (St. Petersburg Paradox); that it is a statistical and 'on average' notion; and that it does not include reference to what one can afford.

That the expectation of person a is defined as p(a,q)*v(a,q) makes its application in guiding one's life and choices a statistical affair, where one in fact tries to judge whether the doing of a specific act q is sensible according to one's own appraisals of the probability and value of q by referring this particular q to similar cases of q, and one compares this possible act also with alternative expectations for r, s, t etc.

The criterion of maximizing one's expectation then counsels one to choose that expectation from all one's expectations that one considers that is highest, on the theory that this will give one, according to one's own estimates of probability and value, the highest expected outcome.

This may be useful and sensible where one has many similar cases to go by, and especially so if these indeed are very similar, but it may be less helpful when one's choice concerns something rather unique and important, like the choice of a wife.

Also, part of the problem here is that one judges in terms of probabilities, which makes one's expectations fractions of values, whereas what one gets is either the full value or nothing, depending on whether one succeeds or fails.

A related problem with expectations is that it is wise when considering one's expectations to also consider what happens if one fails i.e. p(a,~q)*v(a,~q), and indeed if one can afford to fail. You may be willing to gamble a dollar with a chance of 1 in 10 to gain 10 dollars, but it may be unwise if it is your last dollar. In that case it may make more sense to spend it on the certainty of having a one dollar meal, even if this is less satisfactory than winning ten dollars, if one does.


See also: Habit, Probability



 Original: Mar 31, 2005                                                Last edited: 12 December 2011.   Top