413047-Underground-Commercial-Sex-Economy

1.2.1.2. Estimating the Relative Sizes of Pimp Populations
In our study, we interviewed UCSE participants in cities. For the sake of exposition, let
be the set of UCSE participants (both pimps and sex workers), and
be the set of cities. Whenever Kansas City is being excluded from consideration we
will specify this by reference to and .
As part of the interview protocol, each UCSE participant was asked to identify their “home” city
, that is, the city in which they were principally operating at the time when they were
apprehended. Each UCSE participant was also asked to identify the set
of all cities, excluding
, in which they had worked. The set of UCSE participants who call home is expressible as
. For each city , we shall denote the subset of UCSE participants who “visited” city —that
is, they spent time in for work, but did not make it their home—as
A naïve estimation method (which we shall not take, but describe here nonetheless) would be to use the
quantity
as a proxy for the attractiveness of city to UCSE participants. This quantity is simply the fraction of the
surveyed population that either called their home, or visited in the course of their work histories.
The flaw in this naïve formulation is that our sample of UCSE participants consisted of apprehended
subjects. Such a sampling frame necessarily implies that cities with strong (resp. weak) law
enforcement stance toward sex economy participants would witness larger (resp. smaller) cardinalities for
, which, in turn would produce a law-enforcement related bias into the above naïve proxy.
Clearly, a more careful construction is needed for the pimp population proxy. Two such constructions are
now provided.
A. Pimp Population Size Proxy : Direct Estimation Method
Let us denote the set of UCSE participants for whom city
is not home as
We may then estimate the attraction of UCSE participants toward city
as
This definition of considers the number of UCSE participants who visited for work, as a fraction of
the total number of “visits” made by UCSE participants whose home was not city
UCSE participants who considered
. By excluding all
as home (from both the numerator and denominator), this proxy for
pimp population size deftly sidesteps potential biases in the study sample stemming from possible nonuniformities
in law enforcement policies related to the sex economy. In other words, of all the travel
related to the sex market, some portion goes to city and this portion is denoted . The above
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