My Own Paradox of Choice

I thought I had the paradox of choice all figured out. The main reason why I thought choosing makes people suffer is that 1) they don't realize that there is a transaction cost to choosing, namely in the time and effort invested in gathering information to make the decision; and 2) they focus too much on opportunity costs and the differences in utility amongst the options as opposed to the total utility of the chosen option versus doing nothing.

What I didn't realize is that there is also another pitfall in making choices. Actually the problem is not with making choices per se, but with creating the choices themselves. Good oppportunities almost never come for free. One must almost always invest significant personal resources to gain the options before one can make a choice amongst them.

A problem arises however, if one faces uncertainty. Suppose a certain option is expected to generate a utility value of r and there's some estimation error around this expectation e. So the utility of this option is
u = r - k * e^2,
where k is the risk aversion parameter.

Now in order to gain this option, an individual must be willing to put in a certain amount of effort. In general the more effort one is willing to put in, the higher chance that he/she has of obtaining the option. So the probability distribution of gaining the option p is then a Bernoulli trial whose parameter p is a function of the effort expended:

f ( x | c ) = p ( c ) ^ k * ( 1 - p ( c ) ) ^ ( 1 - k )

There is also a relationship going the other way. Namely, an "appropriate" amount of effort an individual will put in to obtain this option must also be a function of the option's utility as well as the probability for obtaining that option:

c_app = g(f, u),

Now assuming some sense of rational behavior and fairly accurate estimation of utility, the maximum amount of effort that will actually be spent must not be greater than the present value of the option's utility:

c_max = min(u, c_app)

So far so good. But what if there is some uncertainty? What if there is a set of n mutually exclusive options that look attractive and each one takes some effort to obtain? The total utility one gains from the options is the maximum utility of the options, but the total cost of gaining the options is the sum of the costs:

sum(c_max_i) = min(u_max, sum(c_app_i))

This is problematic in two ways:

First, it reduces the surplus utility leftover after the choice is made. So lesson number 1 is to try and limit yourself to a small number of options before you set about trying to obtain these options to maximize your surplus utility.

Secondly, if the sum(c_app_i) > u_max, then it could easily result in an under-application of effort to each single option such that one spends a lot of total effort but obtains fewer options. So lesson number 2 here is to never bite off more than you can chew just to get more options.

Why did I formalize a bunch of these things in mathematical notation? I have no idea other than I'm a pedantic asshole. Hopefully there's some insight in here somewhere, but I don't have any more time today to do any derivations. Maybe tomorrow!