Well, it depends (and here's some info for the rest of you)...

If the GP is based off the Japanese police system [at least in Fukuoka,
Kyoto, and Tokyo, so I'll assume this near standard, then there are
different classes/categories of police officers (I'll get to the US in a
moment)].  

I'd also venture a guess that Japan has based it's modern police off the
US, so most likely, the US ranks are pretty applicable as well.

There are the community safety police, the general run of the mill cop
on the street.

Then there are the criminal police, the detectives, who investigate
crimes.

The traffic police work the meters and enforce traffic laws, and may
also deal with the "hot-rod gangs" of Japanese boys among other things.

The Regional police are the folks in the "koban" (police boxes), they
maintain the police presence throughout the city and stay very close to
the public, even visiting each home once a year to give advice on crime
prevention, get to know everyone in the neighborhood, and check out the
suspicious characters.

The final kind are the Security Police, who are pretty scary and, I
quote from the Fukuoka police guide, "Security police are to crack down
terrorists and guerrillas who are seeking to disturb the peace of Japan
with violence." They're combination Secret Service/SWAT/Search &
Rescue/etc.

*****

In the US, the general ranking is this, from the TOP DOWN:

Superintendent of Police
First Deputy Superintendent
Deputy Superintendent
Chief
Ass't Deputy Superintendent
Deputy Chief
Commander
Captain
Lieutenant -or- inspector
Sergeant
Police Officer assigned as: Detective, Technician, Patrol Specialist,
Investigator, Gang Crime Specialist, Police Agent, Traffic Specialist
Police Officer

A) A complete ditz whose lack of competence indicate that she 
must surely have gotten into the GP on the strength of her 
looks or due to nepotism or somesuch, or 

In the TV series, Mihoshi is 1st-class Galaxy Police, without a relative
in the upper ranks.  She's also quite dumb.  

B) A complete ditz whose great memory, great observation 
skills, and great luck *just barely* make up for her 
clumsyness and airheadedness to produce someone who's 
simultaneously a competent police officer (good enough to get 
into GP on her own) and walking disaster area.

 
In the OVA, Mihoshi is smart, just...spacey.  Like you described.
However, she's not in the GP still of her own accord - it's hinted that
she wouldn't be there if she wasn't the Commissioner's grand-daughter.




... Jerry Levine .................       www.patchmonkey.net [personal]
... jerry@onimedia.net ...........       www.onimedia.net [media]
... jlevine@umd.edu ..............       www.drunkenlargo.com
[local-offline]
... patchmonkey@patchmonkey.net ..       www.gaijeans.com [high fashion]
........."He who knows he has enough is rich." - Tao Te Ching..........



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