Adjusted Condorcet Plurality

Adjusted Condorcet Plurality (ACP) is a single-winner election method devised by Kevin Venzke in January 2023. It passes both later-no-harm and later-no-help and thus has no burial incentive.

Method

1. Determine the candidate with the most first preferences - the first preference winner - based on the submitted rankings.
2. Edit the ballots so that all preferences below the first preference winner are removed/truncated.
3. Check if the revised ballot set has a Condorcet winner. If so, elect that candidate.
4. Otherwise elect the first preference winner.

Examples

25: A>B>D
20: B>C>D
20: C>D>A>B>E
18: D>C
17: E>D

The Condorcet winner is D, and is elected by instant-runoff voting. However, the adjusted CW is C, and is elected by Adjusted Condorcet Plurality.

25: A>E>B>C>D
21: B>D>C
20: C
19: D>C>A
15: E>C

The Condorcet winner is C, which IRV elects. But there is no adjusted Condorcet winner, so ACP defaults to the first preference winner, which is A.

Criterion compliances and implications

Besides later-no-harm and later-no-help, Adjusted Condorcet Plurality passes the Plurality criterion. It fails the Condorcet loser criterion, mono-add-top, and mono-raise.

It is third-order summable: the summary contains the truncated Condorcet matrix for each candidate, as well as a count of first preferences for each candidate.

Like some other methods that are invulnerable to burial, it can be combined with a Condorcet stage to create strategy-resistant Condorcet methods by analogy to Condorcet-IRV hybrid methods. In contrast to the Smith-IRV methods, some of these, like Smith,ACP, would be summable.

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