Self-study
Whenever she considers voting in an election to select one candidate for a position and there is at least one issue important to her, Kay uses the following principle in choosing which course of action to take: 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; it is otherwise unacceptable to vote for that candidate. ██ ███ ████████ ███████ █████████ ███ █████ ██████████ ███ ████████ ███████ ███ ███████ █████ ██ ████ ███ █████ █████████ ██ ████ ███ ████ ██████ ██████ ███ ███████ ██ ████ ██████
Kay's Voting Principle
Kay's principle applies when she's voting in an election and there's at least one issue important to her. It has two parts:
Acceptable: If Kay disagrees with a candidate on at least one important issue, it's acceptable to vote for that candidate as long as she disagrees with each of the other candidates on an even greater number of important issues.
Unacceptable: The word "otherwise" here means "in any situation where the acceptable condition isn't met." So if Kay disagrees with a candidate on at least one important issue, but there's at least one other candidate she disagrees with on the same number or fewer important issues, it's unacceptable to vote for that candidate.
In simpler terms, Kay's principle is all about counting disagreements. It's acceptable to vote for a candidate only if she has a higher number of disagreements with each other candidate.
Here's an example. Suppose Kay has 5 important issues and three candidates are running:
Candidate A
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2 disagreements
Candidate B
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5 disagreements
Candidate C
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4 disagreements
Is it acceptable to vote for Candidate A? Yes, because Kay has more disagreements with each other candidate (5 and 4 are both greater than 2). Is it acceptable to vote for Candidate B? No, because Kay has only 2 disagreements with A and 4 disagreements with C, both of which are fewer than her 5 disagreements with B. Is it acceptable to vote for Candidate C? No, because Kay has only 2 disagreements with A, which is fewer than her 4 disagreements with C.
Anticipation
The question asks what "must be true" about Kay's course of action in any election. So the details about Legrand, Medina, and Norton aren't relevant here. We need to focus only on Kay's general principle and find an answer that is guaranteed by it.
23.
According to the principle stated ██ ███ ████████ ██ ███ ████████ ███████ ████████
a
it is acceptable ███ ███ ██ ████ ███ ██████ ██████ ██ ████████ ███ ██ ██ ████████████ ███ ███ ██ ████ ███ ██████
It's unacceptable for Kay to vote for Legrand. Kay disagrees with Legrand on 1 issue, but for it to be acceptable, she'd need to disagree with each other candidate on more than 1 issue. She doesn't, so voting for Legrand is unacceptable.
b
the only unacceptable ███████ ██ ██████ ███ ███ ███ ██ ████ ███ ██████ ███ ███ ███ ██ ████ ███ ███████
This is correct. The principle makes it unacceptable for Kay to vote for Legrand or Norton, because for each of them, Kay can't satisfy the requirement of disagreeing with every other candidate on a greater number of issues. (Since there's only 1 important issue, it's impossible to disagree with anyone on more than 1 issue.) And the principle doesn't make it unacceptable to vote for Medina, because Kay doesn't disagree with Medina on any important issue.
c
it is unacceptable ███ ███ ██ ████ ███ ███ ██ ███ ██████████
The principle doesn't make it unacceptable for Kay to vote for Medina. Remember, the principle kicks in only when Kay disagrees with a candidate on at least one important issue. Since Kay agrees with Medina on the one important issue, the principle is silent about voting for Medina. So voting for Medina might be acceptable.
d
the only unacceptable ██████ ██ ██████ ██ ███ ███ ██ ████ ███ ██████
This gets the result exactly backwards. The principle doesn't declare it unacceptable to vote for Medina. But the principle does declare it unacceptable to vote for Legrand and Norton.
e
it is acceptable ███ ███ ██ ████ ███ ███ ██ ███ ██████████
It's unacceptable for Kay to vote for Legrand or Norton. For each of them, Kay disagrees on 1 issue, but she can't meet the requirement of disagreeing with every other candidate on a greater number of issues.