Lately in my life, (maybe it's the side of me trying to budget) I've really done my best to get the best possible deal when I buy something. It doesn't matter if it is contact lens solution or a new cell phone, I do my research and try to find the best solution at the best possible price. I'll wait for weeks or even months depending on what it is to get the best deal I can. (Black Friday anyone?) The problem is that in the end, I'm not sure that it makes me any happier doing it that way. I spend hours pouring over reviews, read pages and pages of user comments, and check at least half a dozen websites trying to find the best product for as cheap as possible. And what usually ends up happening? A couple days after I buy it, it goes on sale cheaper somewhere else. Or a new model comes out with more features than what I just bought. Funny thing is what I purchased was good enough when I got it.
I guess what I'm getting at is that while I think that doing research and making sure you're getting a good product, it's OK if it's a non-optimal solution. As an engineer, that's hard to deal with. If an optimal solution exists I should achieve it, right?
10 comments:
Of course you should look for an optimal solution. You just need to look for an optimal solution to the right problem.
For example, in searching for a camera you've been trying this:
x => the utility of the camera
y => the price of the camera fully landed
maximize(x/y) subject to a constraint about the minimum value of x and the maximum value of y.
But in searching for a camera you might instead try this.
x,y as given
z the cost of time spent researching. (measured as cost/time times time to acquire y, so really z(y) similarly, time plays in as a but it's getting hard to express in plaintext)
a the time value of having the camera now versus later
maximize (x+a)/(y+z) subject to a constraint on x,y as given and with appropriate values for a and z
With an appropriate value for a the optimal solution occurs at a point where you don't care much what comes out tomorrow. z should similarly factor in whether you actually enjoy hunting for the bargain or not.
I like Ben's approach, and he's right the issue here is all about the specific problem that we're trying to optimize. However, in proposing his formula, he changed the problem at hand. Ben's solution is for purchasing the optimal product based on current knowledge. Brett's problem is disappointment when future events show that a better choice could have been made.
Regardless of how many parameters Ben adds, the release of a new camera that has double the features and costs 3 dollars the day after Brett makes his purchase is going to continue to cause the same feeling of disappointment. Brett's problem is can not be optimized unless he can somehow get vastly more information than is realistically available to him. (Future product features, release dates, prices, upcoming sales, etc.)
Oh all of you nerds! What we would do without you?
Clark,
I think it's not difficult to add terms for the risk of future events. The problem is assigning appropriate waits to those events.
I agree that as you characterize Brett's problem it is unsolvable. The correct course is to wait forever since there is a non-zero that disaster will obviate the need to make a choice. This is however untenable.
Brett,
If you look at this the way Clark characterizes it, then perhaps serenity is just a resignation to the uncertainty of the future you need. As an engineer you may know that buying a lottery ticket does not significantly affect your chances of winning the lottery. However, consider what might happen if you engaged the lottery thusly: for each drawing, select a set of numbers but do not purchase a ticket. If those numbers don't win, congratulate yourself for not making a bad purchase. If the numbers do win, be really disappointed that you didn't buy a ticket.
That should of course read non-zero chance.
First, amen Sabrina!
Second, Maybe you should try not doing ANY research on items AFTER you buy them. If you don't know that it was 10% more off the very next day could you be happy just assuming you got the optimal thing at the optimal price? =)
So, if you're disappointed with the camera, I'll buy it from you second hand, because I know you did the research. Now that's optimal!
Ben makes some good points. (Look at this. An exchange on the internet where two people are progressively agreeing with each other, while adding additional points.) Gauging the likelihood of future sales being lower than the current sale price is not too difficult to do, as well as adding factors for the likelihood of new product releases in the near future. Thus, the problem could be optimized in general. However, those parameters about the future will necessarily be statistical, and thereby wrong from time to time*. In that sense, the problem can't be optimized for every purchase. The problem could be optimized with respect to all information publicly available at the time of purchase, however.
* Of course, we'd need an in depth study of the regularity and magnitude of sales. Perhaps they are well behaved and quite predictable, in which case in a large majority of purchases you would be correctly accounting for future sales. If, however, they are very random in both frequency and magnitude, you would be able to predict the future with very little certainly and be open to high rates of disappointment.
This optimization problem has been thought through quite thoroughly. I must agree with the derivations and explanations given and feel that I might be able to add a little bit to the problem. Given Clark's most recent comment, if we assume that the magnitude and frequency of such occurrences are random, then by all of our time and research we can compile a database of such said frequencies and magnitudes. Then we may perform the necessary statistical analysis. By determining the mean and standard deviations of these parameters, we could allow for additional factors to account for the probability of a better deal coming within a given timeframe. While this would not guarantee the best price (because of the aforementioned randomness) it could be determined to within an agreeable confidence level that such a price would not be available again for a particular amount of time and research put into the system.
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