#22 - Whenever she considers voting in an election to select

[gkp]

Hi,

I'm slightly lost for why D is the right answer. I eliminated it thinking that because it mentioned exactly three issues important to her, the question was out of scope, however I am unsure where I went wrong.

[Eric Ockert]

Bear in mind that all of the answers in this question begin with the "If....." construction. So the first clause of each answer is essentially adding an additional piece of information to what is already in the stimulus. It's almost like saying "If all of the information in the stimulus is true, AND we add this extra piece of information, then is what follows necessarily true?"

In answer (D) we accept the truth of this "if" clause: that she disagrees with each of the candidates on exactly three issues important to her. So, if that is true and the stimulus is true, is it unacceptable for her to vote for any candidate?

Since we know there is at least one issue important to Kay here, the principle in the stimulus applies. That principle can be diagrammed as:

Principle:
Acceptable to support candidate with at least one disagreement Disagree with all other candidates on more issues

Once this principle kicks in, the only way it is acceptable for her to support any candidate that differs from her on at least one issue is that she must disagree with the other candidates on more issues than the candidate she supports.But answer (D) says she disagrees with all of the candidates on exactly three issues. So since she can't disagree with any of the candidates more or less than the others, then it is not acceptable for her to support any of the candidates. Thus, (D) must be true.

Hope that helps!

[MikeJones]

In answer (D) we accept the truth of this "if" clause: that she disagrees with each of the candidates on exactly three issues important to her. So, if that is true and the stimulus is true, is it unacceptable for her to vote for any candidate?

Since we know there is at least one issue important to Kay here, the principle in the stimulus applies. That principle can be diagrammed as:

Principle:
Acceptable to support candidate with at least one disagreement Disagree with all other candidates on more issues

Once this principle kicks in, the only way it is acceptable for her to support any candidate that differs from her on at least one issue is that she must disagree with the other candidates on more issues than the candidate she supports.But answer (D) says she disagrees with all of the candidates on exactly three issues. So since she can't disagree with any of the candidates more or less than the others, then it is not acceptable for her to support any of the candidates. Thus, (D) must be true.

Hope that helps!

Hi Eric,

I might be wrong here, but I took the conditional statement as a biconditional due to the word "otherwise." If that isn't the case, I think you may have your elements reversed, as the word "whenever" seems to modify "disagree with other candidates..." as a sufficient condition.

Can someone please clarify? Thanks.

[nicholaspavic]

Hi Mike,

Thanks for the great question and I am just going to jump in here, even though I am not Eric. After looking at the question, I think that Eric has diagrammed it correctly. I also think that you may be referring to instances where the phrase "otherwise not" is converted into a biconditional, but that is not the case here, as the stimulus only mentions "otherwise." Remember that negation is crucial when you are trying to determine whether or not a statement can be expressed as a biconditional.

I hope I didn't misunderstand your question though, so please let us know if that helps!

[silent7706]

Hi,

I thought I had a good grasp on conditional logic, but I guess not so much... I'm confused how (D) can be correct.

The stimuli says “It is acceptable for me to vote for a candidate whose opinions differ from mine on at least one issue important to me whenever I disagree with each of the other candidates on even more such issues”

Let A =: "whenever I disagree with each of the other candidates on even more such issues"
Let B =: "It is acceptable for me to vote for a candidate whose opinions differ from mine on at least one issue important to me"

Wouldn't you diagram this conditional statement as A B, since whenever introduced a sufficient condition? Hence, via contrapositive, we know that -B -A.

Doesn't "If" in (D) introduce a sufficient condition, hence (D) can be diagrammed as -A -B. Isn't this a case of Mistaken Negation? As you can tell, I'm a little bit lost here. Really appreciate if someone can help me clear up my confusion.

Thanks in advance.

[Adam Tyson]

I do believe that the "otherwise" in the stimulus sets up a biconditional, as suggested by a student earlier in this thread (and I don't disagree with Eric or Nick lightly, ever). I believe you have the original diagram correct, and that what Eric diagrammed was based on the "otherwise", which I interpreted to mean "if I do not disagree with the other candidates on more important issues, then it is not acceptable for me to vote for someone with whom I disagree on an important issue." His diagram is the contrapositive of that relationship, so it means the same thing.

So, it's both or neither here - either it is acceptable and they do have more disagreements with all other candidates, or it is not acceptable and they do not have more disagreements with all the other candidates. Using A and B here to mean exactly what meanings you assigned them, that's:

A B

That's why D works. If she has the same number of disagreements with every candidate (not more), then it would not be acceptable to vote for any of them. Both, or else neither.

I think you grasp is still good here, silent7706! Just ask yourself what that "otherwise" means to you, and I think you'll be there.