This question is a flaw question, and they're my favorite type to answer. I mean, LSAT questions are FULL of flaws, so why not have fun doing them! I digress...
So in this question, right off the bat I noticed that there was a conditional statement:
"as there cannot be a good legal system where the police are not well paid"
Logically, this can be interpreted as "If the police are not well-paid, then you cannot have a good legal system". Don't be afraid to rethink the conditional statement; the LSAT loves to try and hide the conditionals, for that person who was not paying very much attention during the conditional logic chapter in their book.
You can diagram this as:
~WP --> ~GLS
WP= Well paid and GLS= Good legal system
(the ~ symbol denotes a negation)
The contrapositive of this statement would be:
GLS --> WP
Okay, so where is the flaw exactly, you might ask?
Well, in the last sentence of the stimulus, the conclusion, the political theorist states "it follows that where the police are well paid there will be a good legal system".
AHA! Right off the bat, I see that the political theorist is saying that if the police are well paid (WP), then the good legal system (GLS) must follow. But as you'll see, by looking at our contrapositive statement, well paid (WP) police officers is a necessary condition to the good legal system (GLS). This type of fallacy is known as affirming the consequent (the necessary condition), which if logically done, will never logically lead to affirming the antecedent (sufficient condition).This is sometimes known as the converse error. (click link to see this explained in more detail)
Question: The reasoning in the argument is not sound because it fails to establish that:
Answer choices:
(A) is incorrect because the political theorist does not fail to establish that many governments with bad legal systems have poorly paid officers. Heck, we don't need to know anything about other governments in order to analyze the logic of this stimulus. Therefore, this answer choice is out of scope.
(B) is incorrect because if you diagram it, you get:
GLS --> ~WP, which is logically inconsistent with our diagrammed analysis of the premises or conclusion; so get rid of it.
(C) is incorrect because this is talking about the effectiveness of a well paid police force, which the argument in the stimulus never discussed; therefore, this answer choice is out of scope.
(E) is incorrect for the same reason that (A) was incorrect; the argument does not need to establish that some bad governments have good legal systems because frankly, this has nothing to do with the logic of the argument.
Lastly, answer choice (D) is correct because the argument fails to establish that a well paid police force is sufficient go guarantee a good legal system, because as far as we can tell, being well-paid (WP) is necessary to establishing a good legal system (GLS), but not sufficient. Therefore, the argument fails to show us that its sufficient as well.
Eeek, I guess I exaggerated when I said that this was fun! lol