Later-no-harm criterion

In the next election, Bob focuses on expanding his appeal with this group of voters, but does not manage to defeat Alice—Bob's rating increases from 6th-place to 3rd.

[1] Later-no-harm may be confused as implying center squeeze, since later-no-harm is a defining characteristic of first-preference plurality (FPP) and instant-runoff voting (IRV), and descending solid coalitions (DSC), systems that have similar mechanics that are based on first preference counting.

These systems pass later-no-harm compliance by making sure the results either do not depend on lower preferences at all (plurality) or only depend on them if all higher preferences have been eliminated (IRV and DSC), and thus exhibit a center squeeze effect.

Systems like instant runoff that pass later-no-harm but fail monotonicity still incentivize truncation or bullet voting in some situations.

Later-No-Harm can be considered not applicable to Anti-Plurality if the method is assumed to not accept truncated preference listings from the voter.

On the other hand, Later-No-Harm can be applied to Anti-Plurality if the method is assumed to apportion the last place vote among unlisted candidates equally, as shown in the example below.

Assume four voters (marked bold) submit a truncated preference listing A > B = C by apportioning the possible orderings for B and C equally.

The four voters supporting A decrease the probability of A winning by adding later preference C to their ballot, changing A from the winner to a loser.

Thus, Anti-plurality doesn't satisfy the Later-no-harm criterion when truncated ballots are considered to apportion the last place vote amongst unlisted candidates equally.

Assume now that the three voters supporting A (marked bold) would not express their later preferences on the ballots: The positions of the candidates and computation of the Borda points can be tabulated as follows: Result: A wins with 6 Borda points.

This example shows that the Schulze method doesn't satisfy the Later-no-harm criterion.

The pairwise preferences would be tabulated as follows: Result: B is Condorcet winner and thus, the Schulze method will elect B.