IIAOPSW
Page 1 (the very first words): "We found corruption to be widespread".
Page 10: "Commissioner Murphy in his early statements about corruption regularly included a pointed statement indicating that the corruption in the Department was limited to a few officers. On one occasion he went so far as to imply that there were no more than about 300 corrupt police officers in the entire Department. After Patrolman Phillips had completed two of his three days of testimony at our public hearings, Commissioner Murphy found it necessary to discount his testimony of widespread corruption, referring to him as a 'rogue cop.'"
"Smith defined it [the rotten apple doctrine] as standing for the proposition that 'police departments are essentially free of corruption except for the presence of a few corrupt officers who have managed to slip into police service and also into key assignments such as gambling investigations, despite rigorously applied screening procedures designed to keep them out.'"
"the Department now rejected this approach 'not just on principle, but because as a way of controlling corruption it had utterly failed.'"
Page 7: "The Commission examined and rejected the premises upon which the rotten-apple doctrine rested"
Page 11: ". . . they [the public] are sick of ‘bobbing for rotten apples"
Page 5: "investigations have occurred on the average of once in twenty years since before the turn of the century, and yet conditions exposed by one investigation seem substantially unchanged when the next one makes its report. This doesn’t mean that the police have a monopoly on corruption. On the contrary, in every area where police corruption exists it is paralleled by corruption in other agencies of government, in industry and labor, and in the professions."
Page 61: "The Commission’s findings were hardly new. As long ago as 1844, when the state legislature created the New York police force as the first municipal police department in the country, historians record an immediate problem"
(This was followed by a brief summary of every previous scandal and Commission dating back to 1844).
For example, journalists. There's enormous investigative journalism value in the documents that have been filed in court. People say all sorts of shit in affidavits which turns out to be relevant outside the context they intended it for. PACER should be free, if nothing else than for the public interest value of its content (outside as well as inside the court).
If you haven't read it already, I strongly recommend the Knapp Commission Report. Its about police corruption in New York City in 1972, but its lessons on systemic and institutionalized corruption are highly transferable to other contexts.
Probably the most common naive mistake I see is people thinking their subfield is special and they are the first to really notice / understand fraud within it. I've certainly seen people in the "sleuth community" (scientific fraud whistle blowers) reinvent the wheel a few times.
All fraud is basically the same. Financial, scientific, police corruption...it almost doesn't matter. I'm not even the first to say this. A really good summary can be found in Ashforth 2003 ("The Normalization of Corruption in Organizations").
So, with the caveat that I haven't read your work yet and maybe you already know, I'd say look at past corruption far outside your area of interest / expertise. There's a lot you can learn there. Police corruption reports are usually great because of how accessible they are in several senses (more numerous, usually simple to understand), but I have no police related agenda to push here and it really doesn't matter where you decide to look. Just pick any Commission and read their findings.
In the opening words of the Knapp Commission "We found corruption to be widespread".
It is both obvious and profound, the more information you already have, the more information you already have.
So we all know addition swap. One generalization that comes to mind is doing some other in-place transform on the two input variables. Lets keep it simple and suppose that its a linear transform. Thus the problem is to apply some matrix [[a,b],[c,d]] to two input variables [x,y] using entirely in-place operations.
We can do this by realizing that our basic operands can be expressed as matrices. x += ky is the same as the matrix [1, k] [0, 1]
likewise y += kx is equiv to the lower triangular matrix [1, 0] [k, 1]
and lastly, the = operator is equiv to a matrix with an element on the diag. x = k [k ,0] [0, 1]
y *= k [1, 0] [0, k]
From this point on it becomes a challenge of if you can construct any desired matrix into some combination of these available ones (spoiler, yes you can).
The next generalization one could contemplates is doing operations in place on more than 2 variables. Well, if one has already solved arbitrary 2x2 matrix operations, then that can be rigged to implement larger matrices one submatrix at a time.
The final generalization that comes to mind is what can we do with non-arithmetic operators? We've already seen an example of this with using xor-swap rather than addition-swap. But is there anything out there vaguely like xor-2x2-matrix-multiply?
I legit don't know. I have some thought, but I won't meander out loud if its not going to lead anywhere.
>It is clear that the risks of severe punishment for corrupt behavior are slight. A dishonest policeman knows that, even if he is caught and convicted, he will probably receive a court reprimand or, at most, a fairly short jail sentence. Considering the vast sums to be made in some plainclothes squads or in narcotics enforcement, the gains from corruption seem far to outweigh the risks. Both William Phillips and Edward Droge said that they assessed the risk of meaningful punishment and determined that they had little to fear.
I've read enough reports of this nature and experienced enough regulators to be really convinced that where you see apparent stupidity you are also likely to see a table like the one on page 250 showing virtually no prosecutions prior to the Commission.
Neither Drodge nor Phillips were wrong in their calculation. I hate to say, your estimate of a 10% chance of getting caught was way too optimistic. Going by the data, it was much much lower than that.
(My axe to grind is not with the police in particular, reports on police corruption just happen to be the most available and easily understandable).
This broadly goes for non-criminal acts too. Sometimes powerful people do seemingly dumb things because they are only dumb in the context of the incentive structures if one of us tried to do it. In their context, it would be stupid not to egregiously take advantage.
(this is an unsolved problem that exists in many domains from long before AI)