Confusing inferences Forum

[gg2]

Most voters prefer Candidate A to Candidate B. Of those who prefer Candidate A, some feel that budgeting for schools is the most important issue. All voters who prefer Candidate B feel that budgeting for schools is the most important issue.

Is this a valid inference?:
At least some voters who prefer Candidate B do not share at least one common concern with at least one voter who prefers Candidate A.

I understand that the above statement is not inferable, but why is it FALSE (according to MLSAT)?

This is my understanding of the statement:
Let's say there are 10 voters total: 9 prefer A. 1 prefers B.
1 of the 9 who prefer A thinks budgeting is the most important issue. The rest think safety is the most important issue.
Thus, it is possible that at least some of the voters who prefer B do NOT share at least one common concern (safety =/= budgeting) with at least one voter who prefers Candidate A.

I think if it read "at least some voters who prefer Candidate B do not share at least one common concern with even one voter who prefers Candidate A. It would be false indeed but the statement reads "at least."

What am I not getting here?

[Daily_Double]

Here's what we have:

People who prefer B ---> budgeting is the most important issue <--(S)--> Voters who prefer A < --(M)-- voters

So, going from right to left, because we should focus on the presence of relative negativity, we have most voters are voters who prefer candidate A. And some voters who prefer candidate A feel that budgeting is the most important issue. Lastly, if you prefer B, then you think budgeting is the most important issue.

Now what we can infer here is that all people who prefer B share at least one concern with one or more (some) people who prefer A. That's really all we can infer. What concern do they share? That budgeting is the most important issue.

This is my understanding of the statement:
Let's say there are 10 voters total: 9 prefer A. 1 prefers B.
1 of the 9 who prefer A thinks budgeting is the most important issue. The rest think safety is the most important issue.
Thus, it is possible that at least some of the voters who prefer B do NOT share at least one common concern (safety =/= budgeting) with at least one voter who prefers Candidate A.

Nope. They must share at least one common concern. In your example, the 1 person who prefers B would think that budgeting is the most important issue, and some, in your example one, thinks that budgeting is the most important issue. Thus, even in your example we have a person preferring B sharing one concern with a person who prefers A.

Do you follow?

[sighsigh]

As far as I can tell, everything the OP said is correct.

At least some voters who prefer Candidate B do not share at least one common concern with at least one voter who prefers Candidate A.

This statement has the potential to be true. It is not necessarily true, and it is not necessarily false.

The problem is that we don't know whether all of those who prefer candidate A feel that budgeting for schools is the most important issue, or whether only less than all of those who prefer candidate A feel that budgeting for schools is the most important issue. If it is the former, than the statement becomes necessarily false, while if it is the latter, the statement becomes necessarily true.

Unfortunately, all we know is that some of those who prefer candidate A feel that budgeting for schools is the most important issue, which isn't all that helpful to us.

[Daily_Double]

Unfortunately, all we know is that some of those who prefer candidate A feel that budgeting for schools is the most important issue, which isn't all that helpful to us.

I disagree sighsigh, respectfully, but we know that at least one voter who prefers candidate A feels that budgeting for schools is the most important issue, and all voters who prefer candidate B feel the same way. Thus, there must exist at least at least one issue, budgeting for schools and it's importance, that all voters who prefer candidate B share with at least one (some) of the voters who prefer candidate A.

[Micdiddy]

I think the confusion here is with the phrase "do not share at least one common concern." If it's true that someone in B does not share at least one common concern, that means they have NOTHING IN COMMON with anyone in A. Since all members of B have at least one thing in common with some members of A, the statement is false.

[sighsigh]

Nevermind, I read it wrong. Yeah, the statement is false.

[gg2]

I think the confusion here is with the phrase "do not share at least one common concern." If it's true that someone in B does not share at least one common concern, that means they have NOTHING IN COMMON with anyone in A. Since all members of B have at least one thing in common with some members of A, the statement is false.

I think this was my misinterpretation. Thanks for the clarification.
Also, thanks Daily_Double. I just reasoned this without diagramming but the method that you used (I'm guessing from Powerscore?) makes it less prone to confusion.