[EM] draws in IRV

[I Like Irving]

- - - - - - - - - - - - - - - - - - - - - - - - - - - 02/21/01
Tie Solutions for all Ranked Choice Elections: by Donald Davison

There are two methods to solve ties - the Low Series method and the Next
Lower Choices method. It is best to try the Low Series method first because
if a Low Series does exist you will have a very quick solution for the tie.
If it is not possible to use the quick solution then you will need to use
the Next Lower Choice method. These two method will work on all elections
that use ranked choices.
We only need to deal with the ties that occur between the lowest two or
more candidates and only at the time when we are ready to drop one of them.
We are not to do anything with any ties that occur in some other place or
time. For example, in a Choice Voting(STV) election we would not be
concerned about any tie between the last two candidates until after all
surplus votes have been transferred, which may solve any tie before we need
to deal with it.
 Ties should be rare but when we do get one the first step is for us to
check and see if the tie is part of a Low Series of candidates. If so, then
we are allowed to drop the entire Low Series of candidates, that inturn
will solve the tie.

     We have a Low Series when we have two or more of the lowest candidates
with a total vote count that is less than the one candidate ahead of the
Low Series. If we do have a Low Series we are allowed to drop the entire
Low Series of candidates because none of those candidates have any
mathematical possibility of getting ahead of any candidate that is in front
of the Low Series. The tie becomes moot when the entire Low Series is
dropped.
Example please:

     150A   140B   140C   120D   40H   30I   20J   20K

   We have two ties in this group. Candidates B and C are tied, but we do
not need to do anything about that tie at this time. The transferring of
votes from eliminated candidates will most likely solve that tie.
   Also tied are candidates J and K, the two lowest. We need to do
something about this tie because we need to know which candidate to drop, J
or K, but please notice that we have a Low Series. The 110 sum of the votes
of H, I, J, and K is less than the 120 votes of D. These lowest four make
up a Low Series and we can drop all four at one time. This means that we do
not have to deal with the tie. So, the first thing to do when we are faced
with a tie between the two lowest is to check and see if we have a Low
Series. If so, we have a quick solution. Keep in mind that a Low Series
could be longer than the number of tied candidates.

The second solution to solve a ties is to use the Next Lower Choices of
only the tied candidates. The candidate with the lowest number of the next
lower choices is to be dropped.
    We do this by conducting a special tally of the next choices of the
current votes of only the two or more tied candidates.  We run this special
tally on the side because we are only trying to determine which candidate
to drop.  We deal only with the current votes of only these two candidates.
Whichever of the two tied candidates has the lowest number of next choices
is the candidate that is dropped. What we are doing is we are examining two
possible cases at once.  Case one: What would be the next vote tally for
these tied candidates if one of them is dropped?  Case two: What would be
the vote tally if instead the other candidate is dropped? Whichever one of
the tied candidates ends up the lowest that is the candidate that is
dropped. If they are still tied we must go to the second next choice on the
ballots of these tied candidates and seek a difference.  If they are still
tied after we exhaust all levels of choices then we go back to the next
choices of all the candidates and use them. I prefer to have the tie solved
in the choices of the votes of only the candidates that are tied but if
that does not break the tie then the next step is to use the next choices
of all the candidates. It is still a level playing field for the tied
candidates because each has the same mathematical chance of getting the
same number of choices in the next stage. If they are still tied we go to
the second next choices of all the candidates etc.

     I am trying to drop only one of these tied candidates at this place in
the tallying of the ballots. We have a number of stages in which to break a
tie - the tie most likely will be broken. Ties must be covered because if
there is a tie it will be important that it be handled correctly.

     This Next Lower Choices solution has a slight downside, which is, your
lower choice may help defeat one of your higher choices if and when it is
tied.
     I accept this downside because it will be small compared to the value
of making lower choices, it's a trade-off of values. Having your candidate
involved in a tie will be rare. Add to that the odds against your next
choice being the other candidate in the tie, it becomes something that may
never happen to you.
     Besides, this solution can also be used if the last two candidates are
tied, which is more democratic than random selection, that is, the Next
Lower Choices solution is better than tossing a coin.

  ------------ Orginial Letter ------------
Date: Sun, 18 Feb 2001 17:14:24 +0000
From: Martin Harper <mcnh2 at cam.ac.uk>
To: election-methods-list at eskimo.com
Subject: [EM] draws in IRV

What is the correct way to deal with draws in IRV - ie, in an election
between A,B,C,D, where C and D tie for lowest numbers of first place
votes. Should both C and D be eliminated? Or should one be chosen at
random for elimination? Or is there some other way to tie-break them?

Thanks,
Martin

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Speaking of tie breaking methods:
This is a true story - no names are used in order to hide the guilty.

        T I E   B R E A K E R  - American Style

On the radio one morning I heard the following story about an election for
mayor that ended in a tie. The city council decided to break the tie on the
toss of a coin. One of the tied candidates called "HEADS" when the coin was
in the air. When the coin hit the table it was a TAIL. This same candidate
yelled: "TAILS - I WIN" This caused some concern about what he said when
the coin was in the air -  but the council refused to listen to a tape of
the coin toss - but instead the council declared this same candidate the
winner - end of story.

               So much for that tie breaker method.