Instant Runoff Voting Variant With Majority Requirement
Traditional forms of instant runoff voting satisfy the later-no-harm criterion. But if a method permits incomplete ranking of candidates, and if a majority of initial round votes is required to win and avoid another election, that variant does not satisfy Later-no-harm. A lower preference vote cast may create a majority for that lower preference, whereas if the vote was not cast, the election could fail, proceed to a runoff, repeated ballot or other process, and the favored candidate could possibly win.
Assume, the votes are as follows:
|40: A||39: B>A||21: C|
In the Preferential voting method, described as an example in Robert's Rules of Order, elimination continues iteratively until "one pile contains more than half the ballots." Eliminating one of the two final candidate never changes who wins, but can change how many votes that final candidate receives. Thus, C would be eliminated, then B, and the B ballots would be counted for A, who would thereby obtain a majority and be elected.
Now, suppose the B voters would hide their second preference for A:
|40: A||39: B||21: C|
This failure to win a majority in the final round results in a runoff between A and B, which B could win.
By adding a second preference vote for A, the B voters eliminated the election possibility for B. Thus, this variant of instant runoff voting with majority requirement fails the later-no-harm criterion. In traditional IRV, A would have been elected by 40% of the voters, and the later-no-harm criterion would not have been violated.
Also, compliance of LNH can be reestablished by stopping the elimination process when there are two candidates left. Applying this to the example, the second preferences of B are ignored either case. Thus, the B voters would not violate later-no-harm by indicating A as a second choice.
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