Later-no-harm criterion

Later-no-harm methods

The plurality vote, two-round system, instant-runoff voting, and descending solid coalitions satisfy the later-no-harm criterion. First-preference plurality satisfies later-no-harm trivially, by ignoring every preference after the first.

Non-LNH methods

Nearly all voting methods not discussed above fail LNH, including score voting, highest medians, Borda count, and all Condorcet methods. The Condorcet criterion is incompatible with later-no-harm (assuming the resolvability criterion, i.e. any tie can be removed by a single voter changing their rating).

Bloc voting, which allows a voter to select multiple candidates, does not satisfy later-no-harm when used to fill two or more seats in a single district, although the single non-transferable vote does.

Examples

Anti-plurality

Main article: Anti-plurality voting

Anti-plurality elects the candidate the fewest voters rank last when submitting a complete ranking of the candidates.

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.

Result: A is listed last on 2 ballots; B is listed last on 3 ballots; C is listed last on 3 ballots. A is listed last on the least ballots. A wins.

; Adding Later Preferences Now assume that the four voters supporting A (marked bold) add later preference C, as follows:

Result: A is listed last on 2 ballots; B is listed last on 5 ballots; C is listed last on 1 ballot. C is listed last on the least ballots. C wins. A loses.

;Conclusion 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. |}

Borda count

Main article: Borda count

; Express later preferences Assume that all preferences are expressed on the ballots.

The positions of the candidates and computation of the Borda points can be tabulated as follows:

Result: B wins with 7 Borda points.

;Hide later preferences 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.

;Conclusion By hiding their later preferences about B, the three voters could change their first preference A from loser to winner. Thus, the Borda count doesn't satisfy the Later-no-harm criterion. |}

Copeland

Main article: Copeland's method

;Express later preferences Assume that all preferences are expressed on the ballots.

The results would be tabulated as follows:

Result: B has two wins and no defeat, A has only one win and no defeat. Thus, B is elected Copeland winner.

;Hide later preferences Assume now, that the two voters supporting A (marked bold) would not express their later preferences on the ballots:

The results would be tabulated as follows:

Result: A has one win and no defeat, B has no win and no defeat. Thus, A is elected Copeland winner.

;Conclusion By hiding their later preferences, the two voters could change their first preference A from loser to winner. Thus, Copeland's method doesn't satisfy the Later-no-harm criterion. |}

Schulze method

Main article: Schulze method

; Express later preferences Assume that all preferences are expressed on the ballots.

The pairwise preferences would be tabulated as follows:

Result: B is Condorcet winner and thus, the Schulze method will elect B.

Hide later preferences

Assume now that the three voters supporting A (marked bold) would not express their later preferences on the ballots:

The pairwise preferences would be tabulated as follows:

Now, the strongest paths have to be identified, e.g. the path A C B is stronger than the direct path A B (which is nullified, since it is a loss for A).

Result: The full ranking is A C B. Thus, A is elected Schulze winner.

; Conclusion By hiding their later preferences about B and C, the three voters could change their first preference A from loser to winner. Thus, the Schulze method doesn't satisfy the Later-no-harm criterion. |}

Criticism

Douglas Woodall writes:

Notes

Bibliography

• D R Woodall, "Properties of Preferential Election Rules", Voting matters, Issue 3, December 1994 http://www.votingmatters.org.uk/ISSUE3/P5.HTM
• Tony Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002. https://web.archive.org/web/20090204174848/http://www2.mnbar.org/benchandbar/2002/oct02/voting.htm
• John Brown, Jr. v. W. H. Smallwood, 130 Minn. 492, 153 N.W. 953 (July 30, 1915)

References

References

1. Lewyn, Michael. (2012). "Two Cheers for Instant Runoff Voting". 6 Phoenix L. Rev..
2. Stensholt, Eivind. (2015-10-07). "What Happened in Burlington?". Discussion Papers.
3. (July 29, 2011). "Why Approval Voting is Unworkable in Contested Elections - FairVote".
4. (2023-06-12). "An Examination of Ranked-Choice Voting in the United States, 2004–2022". Representation.
5. Brams, Steven. (1982). "The AMS nomination procedure is vulnerable to 'truncation of preferences'". American Mathematical Society.
6. (1984-01-01). "Manipulability of voting by sincere truncation of preferences". Public Choice.
7. Douglas Woodall (1997): [http://scorevoting.net/Woodall97.pdf Monotonicity of Single-Seat Election Rules], Theorem 2 (b)
8. Woodall, Douglas, Properties of Preferential Election Rules, [http://www.votingmatters.org.uk/ISSUE3/P5.HTM Voting matters - Issue 3, December 1994]