Supplemental notes on the Cambridge PR elections
The Cincinnati Method for surplus distribution
The technique used by Cambridge for selecting ballots to transfer
from a candidate’s surplus to bring the candidate down to quota. The method is
as follows: the ballots of the candidate who has surplus are numbered
sequentially in the order in which they have been counted (that is, in the
sequence dictated by the random draw of precincts) and then every nth ballot
is drawn and transferred to a continuing candidate until the original candidate
is credited with ballots equaling no more than quota. The integer n is
the nearest whole number computed by the formula
A ballot selected by this method that does not show a preference for a continuing candidate is skipped and remains with the original candidate. If not enough ballots are removed when ballots n, 2n, 3n, .... have been transferred, the sequence starts again with n+1, 2n+1, 3n+1, ....
Comments:
It's important to stress that the #1 Choice of any voter is
overwhelmingly the most important choice. For most voters, that's exactly where
the ballot will end up without any need to consider any secondary or other
preferences. The basic idea is that the only ballots that might ever need to be
transferred are (a) those for which the #1 Choice has more than are needed to be
elected; and (b) those for which the #1 Choice is defeated at some point in the
vote tabulation. In the latter case, the intent is to ensure that the voter has
additional opportunity to have his or her ballot counted toward another
candidate who may still need that vote in order to gain election. In a typical
election, few candidates will have a surplus of ballots and the surplus is
usually relatively small, so the somewhat random aspect of surplus distribution
generally has only a minimal effect on the election outcome. In a very close
election, it could matter.
The Cincinnati Method is not the only method to transfer surplus ballots. There are, arguably, better ways available which do not depend upon which ballots are drawn or in which order they are counted. Cambridge is, however, in the position where we must abide by a 1938 law (Mass. General Laws, Chapter 54A) that restricts our methods for redistributing surplus ballots to systems that were in use somewhere in the United States at that time. Without a doubt, it is this issue of how surplus ballots are chosen for redistribution that is always the most difficult to explain and the hardest for people to accept.
Cambridge's choice of the "Cincinnati Method" is named after the place in the United States that was using this method in 1938. The basic idea is that you order all the ballots of the winning candidate in the order in which they were initially counted. You then determine what some people call "the integer" by dividing the total number of that candidate's ballots by the surplus and rounding up or down to the nearest whole number. Let's call this number n.
For example, let's say that there are 20,000 valid ballots cast in the election and Candidate A gets 2700 #1 votes. The election quota will be 10% of all valid ballots rounded up to the next integer (2001). This means that Candidate A will have a surplus of 699 ballots. Divide 2700 by 699 and you get about 3.86, so the "integer" is n = 4. This means that you pull ever 4th ballot starting from the beginning, i.e. in sequence, the 4th, 8th, 12th, etc. If you pull a ballot that has no available other ranked choices, you pass it by and continue. At some point you may reach the end of the 2700 ballots and still need to pull more ballots in order to reduce to quota. In that case, you go back to the start and keep pulling the ballots immediately following the original sequence, i.e. the 5th, 9th, 13th, etc. At some point you'll get down to quota.
It's quite possible that another candidate may reach quota as surplus ballots are being transferred. If so, the instant that candidate reaches quota, he is no longer eligible to receive ballots and any further surplus ballots will be transferred to the next candidate listed who is eligible to receive.
The Cincinnati Method (which I believe Cambridge adopted in 1973) is not my preferred choice. The method that is generally adopted these days is known as "fractional transfer" and is best characterized as transferring a fraction of ALL of a winning candidate's ballots to the next available ranked choices on those ballots. In the example above, the winning candidate would retain 2001/2700 of every one of his ballots giving him a total "weight" of 2001. Meanwhile 699/2700 of every one of his ballots would be transferred to candidates ranked next on each of those ballots. During the subsequent Rounds of the election process, each ballot is counted with its associated weight. The other difference is that when any candidate reaches quota during a Round, he will still be eligible to receive ballots through the end of the Round. This is necessary so that ballot order does not matter. At the end of the Round, any surplus would then be redistributed in the manner described above.
This method, although it does not involve "whole ballots", has the great advantage of being completely independent of the order of the ballots. In a system using fractional transfers, all of the ballots could be shuffled at the beginning of the Count and it would have no effect on the outcome. This method is actually the default option of the tabulation software we use in the Cambridge elections. We have to override that default option by instructing the software to use the "Cambridge Rules" instead. -- Robert Winters
Voting with the choice voting form of proportional representation - a system that makes sense for non-partisan elections - is simple.
1. You decide which candidates you would like to see elected.
2. You rank those candidates in order of preference - knowing that a
lower-ranked choice will never hurt the chances of a higher-ranked choice.
Your vote will be counted toward the highest candidate on your ranked list who can be helped by your vote. As many people as mathematically possible will elect one person - most voters will help elect one of their top two choices.
Coalitions of candidates can run as a team (or what we call a "slate" here in Cambridge) and try to win a proportional share of seats. In general, this is an important consideration. It's not just about individual candidates reaching out to get their quota of votes. For example, if there was one issue of great importance to all voters and if a majority of voters favored one position on that all-important issue, there may be some incentive for candidates on either side of that issue to run as a coalition in order to try to win a majority of seats.
Cambridge's proportional representation elections require that the candidates’ names be rotated in alphabetical order on the ballot so that each candidate appears in the desirable top-of-the-ballot position on an approximately equal number ballots.
Instructions to Voters
Mark your choices by completely filling in the numbered ovals using a black pen
(provided).
Fill in the number 1 oval next to your first choice.
Fill in the number 2 oval next to your second choice.
Fill in the number 3 oval next to your third choice, and so on.
You may fill in as many choices as you please.
Fill in no more than one oval per candidate.
Fill in no more than one oval per column (ranking).
To vote for a write-in candidate:
Fill in a numbered oval next to the name you have written (or the sticker you
have affixed to the ballot), showing your choice as a number for a candidate.
Record write-ins from the top line down.
If you spoil your ballot, return it for cancellation to the election officer in charge of the ballots and get another from such officer. (Under Massachusetts law, a voter is permitted up to two spoiled ballots after which the third ballot must be cast.)
Cambridge's optical scan voting machines will reject any ballot with an overvote (for example, #1 votes given to two different candidates). The scanners are also programmed to set aside any ballots with write-in candidates or any apparently blank ballots for inspection by the election commissioners the following day. These "auxiliary ballots" will then the tabulated when voter intent has been determined. Only after all ballots have been recorded will the final ballot tabulation take place (usually the afternoon or evening of the day after Election Day).
How the PR quota system works
Under PR a candidate needs to win a certain proportion of the the votes to be
elected. This winning fraction of the votes is referred to as the “quota”.
The quota is determined by dividing the total number of valid ballots cast by one more than the number of positions to be elected, then rounding up or adding one to the resulting dividend.
Thus, to elect 9 City Councillors, the total number of valid ballots cast is divided by 10.
For example, if 25,000 valid ballots are cast for City Councillors, the quota will be 2,501 (25,000 divided by ten, plus 1).
How the ballots are counted
The count begins with the sorting of ballots by the first preference shown. This
is known as the “First Count.”
Any candidates who reach the necessary quota with Number 1 votes are declared elected. Any extra ballots they receive beyond the quota, referred to as the “surplus,” are redistributed to the candidates marked next in preference on those surplus ballots according to the “Cincinatti Method.”
After the surplus is redistributed, the count continues with the elimination of those candidates who received fewer than fifty votes in the first count. Their ballots are redistributed to the remaining unelected candidates according to the next preference marked.
[The simultaneous elimination of candidates with less than 50 votes is a Cambridge-specific rule. The New York City School Boards used a different rule and there would be virtually no difference if this rule were eliminated altogether. In the early days of Cambridge's use of this system, the intent was to eliminate all of the very fringe candidates at once, but there is a lot of flexibility in how you may choose to do this.]
After each distribution, the candidate having the lowest number of votes is eliminated and his/her ballots are redistributed to the next indicated preference among the remaining unelected candidates. In the event of a tie, the relative position of the candidates in the previous Round determines which candidate will be next eliminated.
As candidates “reach quota” through the addition of redistributed ballots to their totals, they are declared elected and no further ballots are transferred to them.
This process continues until all candidates have been eliminated except the nine winners.
The School Committee election is governed by the same rules except that the election quota is one-seventh of all valid ballots and there will be six candidates elected.
Robert Winters
Cambridge, MA
Robert@rwinters.com
617-661-9230
Cambridge Civic Journal: http://rwinters.com