Kay's principle applies when there is at least one issue important to her. If there are no important issues, the principle is silent. We can't conclude that it's unacceptable for her to vote, because the principle simply doesn't address that situation.

Agreeing with each candidate on most important issues doesn't mean she can't vote for any of them. Imagine Kay has 10 important issues. She agrees with Candidate A on 8 issues and disagrees on 2. She agrees with Candidate B on 7 issues and disagrees on 3. She agrees with Candidate C on 6 issues and disagrees on 4. She disagrees with each candidate on at least one issue, but she disagrees with B and C on more issues than she disagrees with A. So it's acceptable to vote for A, even though she agrees with all three candidates on over half of the issues.

Agreeing with a candidate on only one important issue doesn't make it unacceptable to vote for that candidate. What matters is how the disagreement count compares to the other candidates. For example, suppose there are 10 important issues and Kay agrees with Candidate A on only 1 (disagrees on 9). That sounds bad, but if she disagrees with every other candidate on all 10 issues, then she disagrees with each other candidate on more issues than she disagrees with Candidate A. So it would be acceptable to vote for Candidate A.

If Kay disagrees with each candidate on exactly 3 important issues, then no candidate can satisfy the principle's requirement. For any given candidate, Kay would need to disagree with each other candidate on more than 3 issues. But every other candidate also has exactly 3 disagreements, which is not more than 3. Since no candidate passes the test, it's unacceptable for Kay to vote for any candidate. This must be true.

More generally, whenever Kay has the same number of disagreements with every candidate, she's stuck. The principle requires that she disagree with every other candidate on a greater number of issues. When everyone is tied, that's impossible.

Kay's principle compares her disagreements across candidates, not her agreements vs. disagreements within a single candidate. For example, suppose there are 10 important issues and Kay disagrees with Candidate A on 6 of them (and agrees on 4). If she disagrees with every other candidate on 8 or more issues, it's still acceptable to vote for Candidate A, because she has more disagreements with each other candidate.