In a Beckerian world, a higher price for committing crimes includes making prison itself unpleasant (and prospects thereafter).  This higher price, if the demand curve slopes downward for criminals, should lower the quantity of crime.

In short, society tolerates prison rapes because society doesn't like crime.

One problem with this analysis is pointed out by commenter "dan":

[T]he trouble with the theory of prison-rape-as-punishment...is that only the victims of prison rape are "punished".  ... For the "alpha prisoners", those doing the raping, prison starts to look like something of a playground, a reward for crime.

To this I would add:  Prisoners don't choose the worst from among them to be raped; they choose the physically weakest.  Physical weakness is little correlated with the severity of one's crimes, and this is a problem.  If a physically weak person perceives that the punishment for minor crimes is not only jail time but also a high probability of being raped, this person's incentive to use violence to avoid conviction goes up.  For example:  when punishment for drug use is severe (i.e., including a high perceived likelihood of being raped), a person with a mild drug habit confronted with the possibility of arrest may be more tempted to harm witnesses or forcibly to resist that arrest.

If anyone has the video or finds a link, please provide.

UPDATE:  Saw it again!  Seems I forgot that one of the prisoners offers a wolf whistle for the viewer.

I skimmed the larger report, and here are a few selections I found interesting:

"What This Research Did Not Do
First, this research did not gather rape prevalence or incidence data."  (p. 59)

30% of male inmates that have served at least five years know "for sure" of rape that has happened in their facility, and 71% have heard about rape in their facility.  (pp. 116-119)

"A Cautionary Note to Readers
Prison culture’s sexual worldview conceptualizes homosexuality, sexual affairs, and sexual violence as a symbolically complex interplay of unconscious forces emerging in a social reality.  Prison worldview uses symbols of sexual violence contrary to and radically different from concepts of sexual violence in free society.  Prison culture’s worldview assumptions are predicated on physical and mental weakness, a 'blame the victim' sexual victimization philosophy, and antipathy toward victims’ pain and suffering.  Paradoxically, however, as noted above, prison culture worldview also abhors prison rapists and prison rape."  (p. 144)

"Prison culture interprets sexual violence by its context.  An act of sexual violence in one context may be interpreted as rape, but in another context, the same act may be interpreted as a turn-out, and in still another it may be an act of coming out of the closet.  Inmates see sexual violence.  However, their subjective perception of sexual violence dominates their interpretation of the violent act.  When inmates identified contexts of sexual violence, some said an act was rape; others said the same act was not rape."  (p. 154)

WASHINGTON, D.C. - State and federal correctional authorities substantiated nearly 2,100 incidents of sexual violence in adult prisons, local jails and juvenile facilities during 2004, according to a Department of Justice report released today.  The Department's Bureau of Justice Statistics (BJS) said this represented one-third of all completed investigations into alleged sexual violence behind bars.

During 2004, an estimated 8,210 allegations of sexual violence were reported by correctional authorities -- the equivalent of 3.2 allegations per 1,000 inmates and youths incarcerated in 2004.

Forgetting for the moment what happens to a snitch, and forgetting that there is little point in making allegations when nothing will be done, do keep in mind that these data are collected and submitted by correctional authorities; that is, these are collated responses to a questionnaire from their bosses on an issue related to their own job performance.  By way of contrast, we can expect non-prison crime data to be pretty good because there isn't such a severe conflict of interest; police departments don't (and shouldn't) take a large share of blame when murders or burglaries in their jurisdictions go up.

Now, contrast the DOJ data with the claims of Stephen Donaldson, a leading activist -- from 1995:

The precise number of sexually assaulted prisoners is unknown, but rough estimates can be derived by extrapolating previous studies of a jail system (by Philadelphia District Attorney Alan J. Davis) and medium-security prison (by sociologists Wayne S. Wooden and Jay Parker, their data confirmed by a 1994 survey of an entire state prison system) to estimate conservatively that more than 300,000 males are sexually assaulted behind bars every year.  This compares with a 1992 Bureau of Justice Statistics estimate of 135,000 female rapes a year outside confinement.  By all accounts, the situation is even worse in juvenile detention centers.  Once victimized, a prisoner is marked as a continual target for sexual exploitation and repeatedly is subjected to gang rapes, or must trade sexual use by one or a few men for protection from the remainder.  An estimated 60,000 prisoners are subjected to involuntary sex each day.  Very few of these rapes ever are reported to administrators, much less prosecuted.

Donaldson's version of the numbers gets support from the respected Prison Journal, cited by Human Rights Watch in 2001:

No conclusive national data exist regarding the prevalence of prisoner-on-prisoner rape in the United States.  But the most recent statistical survey, published in the Prison Journal, showed that 21 percent of inmates in seven Midwestern prisons had experienced at least one episode of pressured or forced sex since being incarcerated, and at least 7 percent had been raped in their facility.  And an internal departmental survey of corrections officers in one southern state found that line officers - those charged with the direct supervision of inmates -- estimated that roughly one-fifth of all prisoners were being coerced into participation in inmate-on-inmate sex.

Accepting Donaldson's "conservative" figure and taking into account the 40% increase in the prison/jail population since 1995, we would be looking at over 400,000 male rape victims annually; with 2.2 million Americans in prisons or jails, this figure is in line with the one-in-five estimates offered by that more recent academic research.  Given that NOW estimates 1.2 million female rape victims annually, I have to ask:  Could it be true that, today, in the United States of America, one of every four rape victims suffers his fate right under the nose of government law-enforcement agents?