# Difference between revisions of "Proposed Statutory Rules for DMC"

(Some rewording to answer questions from Dave Ketchum) |
(→Article 3: handle approval tie conditions more carefully) |
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== Article 3 == | == Article 3 == | ||

− | # A candidate X has a ''pairwise win'' over candidate Y, and Y suffers a ''pairwise defeat'' by X, when X defeats Y in the pairwise contest between X and Y. A qualified or write-in candidate X is called the ''Instant Round Robin winner'' X is not pairwise defeated by any other candidate. If there is an Instant Round Robin winner, then that candidate wins the election. A ''majority winner'' is a qualified or write-in candidate such that, on a majority of the valid ballots, this candidate is ranked above every other qualified or write-in candidate. The majority winner, if it exists, will always also be the Instant Round Robin winner. | + | # A candidate X has a ''pairwise win'' over candidate Y, and Y suffers a ''pairwise defeat'' by X, when X defeats Y in the pairwise contest between X and Y. A qualified or write-in candidate X is called the ''Instant Round Robin winner'' when X is not pairwise defeated by any other candidate. If there is an Instant Round Robin winner, then that candidate wins the election. A ''majority winner'' is a qualified or write-in candidate such that, on a majority of the valid ballots, this candidate is ranked above every other qualified or write-in candidate. The majority winner, if it exists, will always also be the Instant Round Robin winner. |

− | # Suppose there is no Instant Round Robin winner. A candidate is ''definitively defeated'' if that candidate suffers a pairwise defeat from any other higher-approved candidate. When no Instant Round Robin winner exists, each candidate suffers at least one pairwise defeat from another candidate, and the least-approved candidate must therefore be definitively defeated. A candidate is ''eliminated'' from the race when that candidate is removed from the set of candidates eligible to win the election. The ''Definitive Majority Choice winner'' is that candidate who, after elimination of the least-approved candidate, is the Instant Round Robin winner among all candidates remaining. | + | # Suppose there is no Instant Round Robin winner. A candidate is ''definitively defeated'' if that candidate suffers a pairwise defeat from any other higher-approved candidate. When no Instant Round Robin winner exists, each candidate suffers at least one pairwise defeat from another candidate, and the least-approved candidate must therefore be definitively defeated. A candidate is ''eliminated'' from the race when that candidate is removed from the set of candidates eligible to win the election. The ''Definitive Majority Choice winner'' is that candidate who, after elimination of the least-approved candidate, is the Instant Round Robin winner among all candidates remaining. While there is no Definitive Majority Choice winner, the least-approved remaining candidate is eliminated from the race. As soon as a Definitive Majority Choice winner is created, that candidate wins the election. The majority winner or the Instant Round Robin winner, if either exists, will also always be the Definitive Majority Choice winner. |

− | # Suppose that there is no Instant Round Robin winner | + | # Suppose that there is no Instant Round Robin winner; that an elimination stage of determining the Definitive Majority Choice winner cannot take place because two or more candidates are tied for lowest approval rating; and that the approval rating tie cannot be resolved using standard election recount procedures --- for example, some candidates may have received unanimous 100% approval or 0% approval. Then, |

− | ## total ballots ranking that candidate in first or second place. | + | ## If any of the tied least-approved candidates is pairwise defeated by another higher-approved candidate not tied for lowest approval rating, each such least-approved candidate shall be eliminated. |

− | ## If equal, total ballots ranking that candidate in first, second and third place. | + | ## Otherwise, if there are only two tied least-approved candidates, and one pairwise defeats the other, the pairwise loser shall be eliminated. |

− | ## If equal, total ballots ranking that candidate above last place. | + | ## Otherwise, eliminate the candidate with the lowest number of |

− | ## If equal, total ballots ranking that candidate in first place. | + | ### total ballots ranking that candidate in first or second place. |

+ | ### If equal, total ballots ranking that candidate in first, second and third place. | ||

+ | ### If equal, total ballots ranking that candidate above last place. | ||

+ | ### If equal, total ballots ranking that candidate in first place. | ||

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## Revision as of 08:56, 11 October 2005

This page is intended to specify the proposed statutory rules for Definite Majority Choice in a form suitable for use by legislatures or in referenda or initiatives. The properties, criteria satisfied and motivations for DMC should be discussed elsewhere.

## Article 1

Each ballot shall list all qualified candidates for the office, and the voter shall be allowed to write in one additional candidate. On the ballot, the voter shall be allowed to rank candidates in order of preference. A voter may also rank two or more candidates equally or leave some candidates unranked. The number of ranks shall be sufficient for a voter to express separate rank for each qualified and write-in candidate. Leaving a candidate unranked will be considered equivalent to giving that candidate the lowest possible rank. A ballot ranking one candidate higher than another shall be counted as a vote cast for the higher-ranked candidate in the *pairwise*, or one-on-one, contest between those two candidates. A ballot ranking two candidates equally casts no vote for either candidate in their pairwise contest.

## Article 2

The ballot shall allow a voter to specify an *approval cut-off*, either by ranking candidates above a predetermined rank or as a separate *Disapproved* option on the ballot, in order to indicate that all candidates above the approval cut-off are to be considered approved, and all candidates at or below the approval cut-off are to be considered disapproved. The number of separate ranks shall be sufficient to rank all qualified and write-in candidates at separate rank entirely above or entirely below the approval cut-off. If a voter ranks no candidates at or below the approval cut-off, all ranked candidates shall be considered approved. Ranking a candidate higher than the approval cut-off shall be considered equivalent to casting an *approval* vote for the candidate. The *approval rating* of a candidate is the total number of valid ballots on which that candidate is ranked above the approval cut-off. A candidate X is *higher-approved* than another candidate Y when X's approval rating is larger than Y's. The *least-approved* candidate is that candidate with the lowest approval rating.

## Article 3

- A candidate X has a
*pairwise win*over candidate Y, and Y suffers a*pairwise defeat*by X, when X defeats Y in the pairwise contest between X and Y. A qualified or write-in candidate X is called the*Instant Round Robin winner*when X is not pairwise defeated by any other candidate. If there is an Instant Round Robin winner, then that candidate wins the election. A*majority winner*is a qualified or write-in candidate such that, on a majority of the valid ballots, this candidate is ranked above every other qualified or write-in candidate. The majority winner, if it exists, will always also be the Instant Round Robin winner. - Suppose there is no Instant Round Robin winner. A candidate is
*definitively defeated*if that candidate suffers a pairwise defeat from any other higher-approved candidate. When no Instant Round Robin winner exists, each candidate suffers at least one pairwise defeat from another candidate, and the least-approved candidate must therefore be definitively defeated. A candidate is*eliminated*from the race when that candidate is removed from the set of candidates eligible to win the election. The*Definitive Majority Choice winner*is that candidate who, after elimination of the least-approved candidate, is the Instant Round Robin winner among all candidates remaining. While there is no Definitive Majority Choice winner, the least-approved remaining candidate is eliminated from the race. As soon as a Definitive Majority Choice winner is created, that candidate wins the election. The majority winner or the Instant Round Robin winner, if either exists, will also always be the Definitive Majority Choice winner. - Suppose that there is no Instant Round Robin winner; that an elimination stage of determining the Definitive Majority Choice winner cannot take place because two or more candidates are tied for lowest approval rating; and that the approval rating tie cannot be resolved using standard election recount procedures --- for example, some candidates may have received unanimous 100% approval or 0% approval. Then,
- If any of the tied least-approved candidates is pairwise defeated by another higher-approved candidate not tied for lowest approval rating, each such least-approved candidate shall be eliminated.
- Otherwise, if there are only two tied least-approved candidates, and one pairwise defeats the other, the pairwise loser shall be eliminated.
- Otherwise, eliminate the candidate with the lowest number of
- total ballots ranking that candidate in first or second place.
- If equal, total ballots ranking that candidate in first, second and third place.
- If equal, total ballots ranking that candidate above last place.
- If equal, total ballots ranking that candidate in first place.