This is horribly wrong on so many levels.

False reports/accusations of crime in general tend to be low, in the 2-8% range reported here. By this logic, we can dispense with this whole silly and expensive criminal justice system and just convict everyone based on simple accusation. We used to call this sort of thing "lynching", and it is generally considered a good thing that it's become rare.

"It is better that ten guilty persons escape than that one innocent suffer"[1]

Also note that the "low rate" for false accusations is for cases were the false accusation is proven:

"The determination that a report of sexual assault is false can be made only if the evidence establishes that no crime was committed or attempted. This determination can be made only after a thorough investigation. This should not be confused with an investigation that fails to prove a sexual assault occurred.
In that case the investigation would be labeled unsubstantiated. The determination that a report is false must be supported by evidence that the assault did not happen."[2][3]

By this standard, cases of rape that are actually proven are also low, depending on where you look in the 7% range of reported[3]. So the "we just don't know" figure is very, very high, we simply do not have strong evidence either way[4]. Other studies have found false report rates much higher [5][6].

The Air Force study[6]
is interesting in that admissions of false accusations increased dramatically when it became known that
a Polygraph would be administered (though AFAIK, the Polygraph information itself was not used as indication of a false report, only an actual admission). The raw data of admitted false cases was then combined with other characteristics of those cases to develop a model for "likely" false accusations (things like "does the rape cause problems or solve problems for the accuser", "does the report follow widely assumed patterns of rape vs. real patterns", "do the injuries show patterns that are typical of self-infliction" etc.) With that model, applied conservatively, the false report rate was above 50%.

There is
also an interesting investigation showing that the 2% figure that pops up in many "studies" books and
papers on the subject can all be traced to a single off-the-cuff, non-researched remark.[7]

So the reference figures are at best flawed and way too uncertain to base a model on.

Additionally, the statistics are incorrectly applied to a single event ("How likely is someone ..."). The statistics only work for a sufficiently large population.

Finally, as many others have pointed out, the events are not uncorrelated, and the assumption that they are and that "lots of reports must mean there is something there" is a well-documented fallacy of human cognition. The McMartin case is an obvious one, but there is also the famous case of the French city of Orleans, where an entire city was convinced that girls were being drugged and abducted in fashion stores, which turned out to be completely unfounded.[8][9][10]

So please pack up this model, or let's all just abandon our legal system, due process and meet for a happy lynching.

[1] http://en.wikipedia.org/wiki/Blackstone's_formulation

[2] http://yesmeansyesblog.wordpress.com/2010/09/09/false-rape-a...

[3] https://rainn.org/get-information/statistics/reporting-rates

[4] http://lawprofessors.typepad.com/crimprof_blog/2004/12/2_fal...

[5] http://www.informationisbeautiful.net/visualizations/rape-a-...

[6] http://www.fathersmanifesto.net/mcdowell.htm

[7] http://digitalcommons.lmu.edu/cgi/viewcontent.cgi?article=22...

[8] https://www.kirkusreviews.com/book-reviews/edgar-morin/the-r...

[9] http://de.wikipedia.org/wiki/Gerücht_von_Orléans

[10] http://fr.wikipedia.org/wiki/Rumeur_d'Orléans