# ER-Bucklin

ER-Bucklin is an old name for Majority Choice Approval (MCA). Please see that article, which mostly supersedes the following.

## Contents

## Definition

It is a rated version of Bucklin voting that allows voters to give equal rankings to some candidates. There are at least two main versions of ER-Bucklin; these are **ER-Bucklin(whole)** and **ER-Bucklin(fractional)**.

## ER-Bucklin(whole)

*If a ballot lists n candidates as tied in kth place, count that ballot as a whole point for all n candidates beginning in the kth round.*

Note: A candidate is ranked in kth place on a given ballot if there are k-1 candidates who are ranked strictly higher. For exampe, a ballot marked A>B=C=D>E>F=G=H=I>J should be considered to rank A to in 1st place, B, C, and D in 2nd place, E in 5th place, F, G, H, and I in 6th place, and J in 10th place. Thus, the ballot would not count in favor of E until the 5th round, and it would not count in favor of J until the 10th round.

This rule is perhaps unique in that it satisfies both the "favorite betrayal" criterion and the Majority criterion for solid coalitions.

## ER-Bucklin(fractional)

*If a ballot lists n candidates as tied in kth place, count that ballot as 1/n point for all n candidates in the kth round, adding another 1/n point in each subsequent round until the ballot has contributed 1 point to all n candidates.*

## Example

- 36 voters: A>B1=B2>C
- 34 voters: B1=B2>C>A
- 30 voters: C>A>B1=B2

*or*:

# | 1st | 2nd | 3rd | 4th |
---|---|---|---|---|

36 | A | B1&B2 | C | |

34 | B1&B2 | C | A | |

30 | C | A | B1&B2 |

### ER-Bucklin(whole) tally

candidate | round 1 | round 2 |
---|---|---|

A | 36 | 66 |

B1 | 34 | 70 |

B2 | 34 | 70 |

C | 30 | 30 |

There is a tie between B1 and B2.

### ER-Bucklin(fractional) tally

candidate | round 1 | round 2 |
---|---|---|

A | 36 | 66 |

B1 | 17 | 52 |

B2 | 17 | 52 |

C | 30 | 30 |

A wins.

*work in progress*