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Something is really bothering me about this question, but it's not integral to getting it correct. If deceit is a quality of rottenness, that means that rottenness implies deceit, not the other way around. Which means that the first part of the argument isn't valid at all.
effective politicians must be deceitful, but that doesn't mean that they must be rotten. The conditional chain only sets off if deceit --> rottenness. For example, if sweetness is a quality of fruit, that means fruit --> sweet. If something is sweet, you can't say for sure that it's fruit.
Anyway... the question stem makes it kind of seem like it's valid which I think is why this is bugging me.
Admin Note: https://7sage.com/lsat_explanations/lsat-19-section-4-question-13/
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Although... it's now occurring to me that they messed it up on purpose to waste your time when it has no bearing on the correct answer. They succeeded.
An often employed trap is to hint toward conditional logic diagramming when it's not necessary or even detrimental. This is why its important in my opinion to read the whole stimulus and evaluate it as a whole before just jumping into diagramming.
In this question the last sentence is all you need. Someone who is honest will never be an effective politician. Therefore it must be false that some honest politicians are effective.