Saturday, November 14, 2009

Consider a simple two dimensional choice dilemma

Suppose you have two choices, option A and option B, A ≠ B. The constraints are such that you cannot choose both. Each one of these options is equally appealing, yet choosing each will lead to a drastically different outcome. Each outcome, in its turn, is just as appealing as the other, i.e. you know that you can be happy with either outcome. An economist, then, would say that you are indifferent towards either one of these choices, since each choice gives you the same utility (fancy word for satisfaction). Except that in real life you’re not “indifferent” in the true meaning of the word, because (i) you can’t compare these choices, since outcomes are so different that we’re talking apples and oranges at this point; (ii) when you choose A, you will never know what it’s like to have chosen B and vice versa. Therefore by choosing A you have eliminated the possibility that you could ever have B (and vice versa). That does not leave a lot of room for indifference now, does it?
Q: How would you make your choice?

12 comments:

Richard said...

Flip a coin.

Anonymous said...

Slightly offtopic, but I had to share this ;)

A Psycological Tip

Whenever you're called on to make up your mind,
and you're hampered by not having any,
the best way to solve the dilemma, you'll find,
is simply by spinning a penny.
No -- not so that chance shall decide the affair
while you're passively standing there moping;
but the moment the penny is up in the air,
you suddenly know what you're hoping.

- Piet Hein

T.

T.S.T. said...

I like the "psychological tip" comment almost as much as I like the original post . . . which says quite a lot.

Nika said...
This comment has been removed by the author.
Nika said...

But of course! The coin! Thank you, T., for the tip. I think I may be on the verge of some kind of epiphany. Seriously.

margarita said...

shushanika jan, uremn im economist ynkernric meky, tvela hetevyal patasxany:
I will chose option C !!! cose I like C, I am comfortable with C :))

margarita said...

chto ti skajesh na eto?

Anonymous said...
This comment has been removed by the author.
Anonymous said...

act as an intelligent agent might do when its performance measure is not affected by the time factor and the environment is dynamic. wait untill the environment changes. thus your initial state changes yet the performance measure unaffected. there might emerge a utility difference between the outcomes (eventual environment states, when an action is done), understand? then there you go, you choose the one with higher utility.
is your performance measure affected by time factor?

Anonymous said...

exercise (quite a simple one): point out one obvious drawback of the abovementioned method.

Nika said...

I am not sure what you mean by performance measure, but lets look at this a bit closely. Suppose that the environment is dynamic. Then it does make sense to wait until circumstances change in such a way that a difference in utilities emerges and you can choose an option with higher utility. BUT, since in this case utility becomes a function of time, the difference in utilities can no longer be constant and is subject to change at any point in time. If the environment were static, all you had to do is seek global optima with respect to your choice option and you’d have your solution fall into your lap. But because you’re dealing with the time dimension as well, it makes a whole lot more sense to seek a fixed point or an equilibrium (depending whether you’re treating time as discrete or continuous). In each case you’re either at a point where the rate of change of your solution with respect to time is zero (if time is continuous) or your next iterate ends up at exactly the same point as the previous one (if time is discrete). Furthermore, you not only want to end up at equilibrium, but a stable one at that too or at least an asymptotically stable one. Highly preferred if the stability is global for all time t. How’s that?

Anonymous said...

the performance measure is simply the criteria that determine how successful an agent is.
in general case you are very right! now let me introduce some new requirements. now the time is considered in the performance measure, i. e. the longer it takes for an agent to solve the problem the worse its performance measure is. still, consider, there is no need to rush the things up, i. e. there is some time constraint but the time is vast enough. in this case it is unlikely that the utility of the outcomes will make it to interchange twice or more (if this is not your case and the utility of your outcomes oscillate at speed of a ferrari, then throw a coin).
i would like to make a real example from a real life, but i have never been good at making analogies. wish you got my point.