The following preference table summarizes the outcome of an election.
 
Rankings
1st	Vincent	Aaron	Leah	Leah
2nd	Leah	Vincent	Aaron	Ricardo
3rd	Aaron	Leah	Vincent	Aaron
4th	Ricardo	Ricardo	Ricardo	Vincent
Total Votes	73
67
25
52

Vincent is the winner using the plurality with elimination method. Assume the 25
 voters in the third column change their votes in such a way that Vincent increases his ranking while the order of the other candidates stays the same.
 
Rankings
1st	Vincent	Aaron	Vincent	Leah
2nd	Leah	Vincent	Leah	Ricardo
3rd	Aaron	Leah	Aaron	Aaron
4th	Ricardo	Ricardo	Ricardo	Vincent
Total Votes	73
67
25
52

Would this violate the monotonicity criterion?
Answer
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The **monotonicity criterion** in voting systems states that if a candidate wins an election, then they should not lose the election if their ranking improves on some voters' ballots, provided that the relative rankings of other candidates remain the same.

### Initial Situation:
In the initial ranking, Vincent wins using the plurality with elimination method.

- Column 3 has Vincent ranked 3rd with 25 votes.

### New Situation:
After the change, the voters in column 3 rank Vincent 1st instead of 3rd, and the rankings of other candidates remain unchanged.

### Effect on the Election:
Since Vincent's ranking improves in the 25 votes of column 3 (from 3rd to 1st), this increases his overall support. Given that Vincent already won the election, improving his ranking should not result in a loss, and thus this change should not lead to a violation of the **monotonicity criterion**.

### Conclusion:
This change **does not violate** the monotonicity criterion because improving Vincent’s position on some ballots will not cause him to lose, which is consistent with the principle of the criterion.

Would you like further clarification on how the plurality with elimination method works or details on any aspect?

Here are 5 related questions you might find helpful:
1. How does the plurality with elimination method work?
2. What other voting criteria are relevant in evaluating voting systems?
3. What are the conditions under which the monotonicity criterion can be violated?
4. Can you give an example where the monotonicity criterion is violated?
5. How does the Borda count method differ from plurality with elimination?

**Tip**: The monotonicity criterion ensures that helping a candidate by ranking them higher should never harm their chances in a fair election system.

The following preference table summarizes the outcome of an election.
Rankings
1st Vincent Aaron Leah Leah
2nd Leah Vincent Aaron Ricardo
3rd Aaron Leah Vincent Aaron
4th Ricardo Ricardo Ricardo Vincent
Total Votes 73 67 25 52

Vincent is the winner using the plurality with elimination method. Assume the 25 voters in the third column change their votes in such a way that Vincent increases his ranking while the order of the other candidates stays the same.

Rankings
1st Vincent Aaron Vincent Leah
2nd Leah Vincent Leah Ricardo
3rd Aaron Leah Aaron Aaron
4th Ricardo Ricardo Ricardo Vincent
Total Votes 73 67 25 52

Would this violate the monotonicity criterion?

Explore how the monotonicity criterion applies to a voting scenario using the plurality with elimination method. Learn why Vincent's improved ranking does not violate the monotonicity criterion, with detailed explanations on voting theory concepts suitable for Grades 11-12.

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