united-states
Short Answer
They're a wealthy politician with a lot of influence, and they would
certainly do everything in their power to rather wind up in a
low-security prison.
The easiest way to do it would be to have a sentence of more than twenty but less than thirty years imposed because of a very large dollar amount fraud involving a great many victims (e.g. a large Ponzi scheme). Espionage is another plausible charge that could have the same sort of sentence length.
This would send them to a medium-security prison despite a lack of "points" from offense severity, a prior criminal record, or a history of violence, lack of gang involvement, or an absence of a prior escape attempt.
Long answer
Each U.S. state has its own system.
In the U.S. federal criminal justice system, a convicted felon's assignment to a particular prison is a decision made by the Federal Bureau of Prisons, after the defendant has been sentenced by a federal judge for a particular sentence length for a particular crime. The FBP states that:
The Bureau of Prisons shall designate the place of the prisoner's
imprisonment, and shall, subject to bed availability, the prisoner's
security designation, the prisoner's programmatic needs, the
prisoner's mental and medical health needs, any request made by the
prisoner related to faith- based needs, recommendations of the
sentencing court, and other security concerns of the Bureau of
Prisons, place the prisoner in a facility as close as practicable to
the prisoner's primary residence, and to the extent practicable, in a
facility within 500 driving miles of that residence.
It is quite an involved process and set of rules. And, there is necessarily flexibility in the system to reflect the availability of prison space at the time of assignment.
The overall context is as follows, according to a source writing as of November 2017 (the same source has at times had an online calculator helping people to predict an assignment):
The Federal Bureau of Prisons confines 184,855 people. About 83% of
those people, or 154,844 inmates, serve their time inside Bureau of
Prisons facilities. The other people serve their time in privately
managed prisons or other types of facilities. Males make up more than
93% of the federal prison population. Those people serve sentences in
the following types of security levels:
Minimum-security Federal Prison Camps: 32,189 people, or about 17% of
the population
Low-security Federal Correctional Institutions: 69,437 people, or
about 37% of the population
Medium-security Federal Correctional Institutions: 55,377 or about 30%
of the population
High-security United States Penitentiaries: 21,524 people, or about
12% of the population
Unclassified: 6,980 people, or about 4% of the population
The full federal BOP policy is here which notes that:
The review process to assign a custody level based on an inmate’s
criminal history, instant offense, and institutional adjustment. A
custody level (i.e., COMMUNITY, OUT, IN, and MAXIMUM) dictates the
degree of staff supervision required for an individual inmate.
The key table in the rules is below. It is somewhat hard to interpret without the larger context, but is the closest thing to an overall assignment key that exists in the rules. Basically, the left column lists a point score, which provides a default assignment, and each box has exceptions to the usual point score rules:

Medium security inmates either have 0-15 points with a prior serious escape attempt or a sentence of 20 years or more remaining, or 16-23 points. But they have less than 24 points, less than 30 years of their sentence remaining, are not part of a disruptive group (read hard core gang member) and have not been involved in a prison disturbance. The circumstances that gets someone to 16-23 points are not simple to describe succinctly.
Another source explains the factors involved (PSR is the pre-sentencing report presented to the judge before ruling on a sentence in the case):
Voluntary surrender to custody. Where a court permits a defendant to voluntarily surrender to BOP custody for service of an initial term
of confinement (not supervised release violation), three points are
subtracted from the security point total.
Severity of current offense. Appendix A to Program Statement 5100.08 contains a scale of various offense behaviors, and the Designation Manual provides a corresponding point assignment for
assessed severity. When evaluating offense severity, staff consider
the most severe documented behavior, as set forth in the PSR, not
necessarily the offense of conviction.
This ranges from 0-7. The key for assigning this score starts at page 97 of the pdf linked.
- Criminal history score. Points are assigned based on an offender’s criminal history points, taken from the judgment’s statement of
reasons or, if not found there, from the PSR. Scoring does not factor
in whether the court found a defendant’s points over – or
underrepresent criminal history.
This ranges from 0-10 based upon the criminal history score assigned at sentencing. If it is absent the BOP will (per the rule linked above):
(a)Add 3 points for each prior sentence of imprisonment exceeding one
year and one month;
(b)Add 2 points for each prior sentence of imprisonment of at least
sixty days not counted in (a);
(c)Add 1 point for each prior conviction not counted in (a) or (b), up
to a total of 4 points for this item; and,
(d)Add 2 points if the instant offense is a revocation accompanied by
a new state or federal conviction, or if the instant offense occurred
while under federal supervision including incarceration, probation,
parole or supervised release.
This together with the severity of the crime are major factors.
- History of violence. In assessing the violent nature of prior documented findings of guilt (convictions and supervised release
violations), policy distinguishes between “serious” and “minor”
incidents as well as time relative to when the case is being reviewed.
This category does not factor in the instant offense and can change
over time based on an offender’s institutional adjustment (i.e.,
violence in the BOP can result in assignment of points).
The rule provides with regard to this factor:

History of escape or attempts. Acts for which there are documented findings of guilt, including absconding from community supervision or
failing to appear for a criminal case, will be scored.
Detainers. Points are scored for detainers, including both those actually lodged and where law enforcement indicates a firm intent to
lodge one. Immigration and Customs Enforcement detainers are not
scored. Age. Given the correlation between age (youth) and negative
institutional adjustment, points are assigned, with inmates under 24
years old receiving eight points and inmates over 55 receiving none.
Education level. Where the PSR verifies a high school degree or GED, no points are assigned. Where neither is verified, two points are
assessed.
Drug/alcohol abuse. Where the PSR documents a defendant’s drug or alcohol abuse within the past five years, one point is assessed. If
there is no known abuse or abuse more than five years old, no points
are added.
An inmate’s security point total corresponds to a security level from
which staff determine facility placement. However, security point
total is not dispositive. The application of a public safety factor
(PSF) or a management variable can impact the placement decision. The
application of a PSF, which is not confined to evidence of
convictions, is intended to address information suggesting a need for
greater security precautions. Examples include sentence length,
removable alien status, sex offender status, and threat to a
government official. Management variables are grounded in the
“professional judgment of bureau staff” and are used to effectuate an
inmate’s placement at a facility inconsistent with the inmate’s scored
security level. This most commonly occurs when an inmate poses either
a greater or lesser security risk than his or her assigned security
level denotes or to facilitate program participation (e.g., permit
completion of residential drug treatment despite a drop in security
level).
It is also worth noting that the federal criminal justice system, generally speaking, deals disproportionately with lower risk felons committing white collar crimes and immigration offenses, while state criminal justice systems generally deals with higher risk felons who have mostly committed "blue collar" crimes, often violent ones.