# [EM] Equal Ranking of some Candidates in a STV election

Donald E Davison donald at mich.com
Fri Apr 21 13:49:06 PDT 2000

```  ------------ Forwarded Letter -----------
From: Alejandro Solá
To:  <donald at mich.com>
Subject: Ties in ranked voting systems
Date: Thu, 20 Apr 2000 09:28:52 -0400

Dear Sirs:

I would like suggestions for ranked voting systems (such as the single
transferable vote) which allow tied preferences. By allowing the ranking of
individual candidates and of groups of candidates defined by the voters
(which may or may not conform to party lines), this would make such systems
more "voter friendly" for most citizens.

For example, let's suppose a STV legislative election for a four-member
district contested by two parties, A and B, with four candidates per party:
A1,..., A4, B1,..., B4. I could rank my pet candidate, A1, first. My second
preference could be a tie for the remaining candidates of my political
party (A), excepting its candidate I like least (A4), whom I would rank
third, along with all of the other party's candidates. So my preferences
would be:

1) A1, my preferred candidate.

2) Double tie between A2 and A3.

3) Quintuple tie between A4, B1, B2, B3 and B4.

How do I count the votes? If A1 is eliminated or elected in the course of
the election, my vote (or fraction thereof) is distributed equally between
A2 and A3. If then A2 is eliminated or elected, the fraction of my vote
that went to her (or the subfraction thereof) goes to A3. If in turn A3 is
eliminated or elected, what remains of my vote is distributed equally
between A4, B1, B2, B3 and B4. And so on.

However, the actual processing of the ballots in this case is
mathematically very complicated. Any suggestions of how it could be done
(both manually and in computerized form)?

Thanks.

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Greetings Alejandro,

Thank you for writing, I welcome your letter.
I am in favor of giving the voter as many options as possible, and it
is possible to give him the option of ranking candidates equally, but how
many is a question.

Earlier this year I gave this policy some study, and that is why I
would like to open my comments by suggesting two rules.

Rule One is that the voter can only give two candidates the same
choice, and that he can only do this once.
While I stated that I favor giving the voter as many options as
possible, this rule should keep the math of our discussions well within the
limits of the possible, until we learn what are the limits.
The next step can be to allow three candidates to have the same choice.

The second rule is that if the last choice includes the final
remaining candidate on the ballot, then that choice is to be disregarded.
This rule will not change the results of the election, but this rule
will reduce the math. For example, your third choice includes the final
remaining candidate on the ballot, therefore your third choice would be
disregarded.
Your third choice does not make any distiction between any of the
candidates.
We don't need to know your third choice in order to determine the
correct elected candidates. No matter what part of your vote gets to the
third choice, it will be divided equally between five candidates and then
between four, etc. That part of your vote will have no influence in the
election.
You are in effect saying that any one of the final five is acceptable.
You are merely giving a vote of confidence to one or more candidates, which
is nice, but it is best we avoid the extra math.

So, under my rules, your example is merely:
Choice One:  (A1)
Choice Two:  (A2) and (A3)

My suggested solution is that this ballot be divided into two half
vote ballots, as follows:

Half Vote Ballot One         Half Vote Ballot Two
Choice One    (A1)           Choice One    (A1)
Choice Two    (A2)           Choice Two    (A3)
Choice Three  (A3)           Choice Three  (A2)

Nothing more needs to be done, The intent of the voter will be carried
out as these ballots are worked along with the other ballots in the
election.
If you agree, then we can consider three candidates with the same
ranking, but the big question is: How many candidates should be allowed to
have the same ranking?
(The More is not The Merrier)

Regards, Donald Davison

+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+
|                         Q U O T A T I O N                         |
|  "Democracy is a beautiful thing,                                 |
|       except that part about letting just any old yokel vote."    |
|                            - Age 10                               |
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A Few Words about What I Am Doing

* I examine every feature of initiative and candidate election methods.
* I keep the good, correct that which can be corrected, create some new, and
discard the extraneous, the erroneous, and the corrupt features.
* My quest is to reveal the best possible election methods to be used in each
government jurisdiction.
* I engage in debates and I email updates and digests of this ongoing work.
* The cumulative results of my efforts are posted to my web site which
I call New Democracy and can be seen at:  http://www.mich.com/~donald
* All this action has resulted in an exchange of email, from which I feel
I have learned the most.
* I look forward to learning more.   Regards, Donald Davison

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