# [EM] Recount and Party Proportionality:

Donald Davison donald at mich.com
Mon Nov 17 15:07:04 PST 2003

```Greetings list,                                 November 17, 2003

Jim Riley wrote: "Arguably, the first runners-up method serves as a
correction for a source of disproportionality under STV - the extra quota."

Donald:  Yes, it could be argued that the entire proportionality of the
original election includes the one first runner-up who holds `the extra
quota', the quota that did not elect a member.

When the time comes to fill a vacancy it can also be argued that because
the first runner-up is part of the total proportionality of the original
election, it is proper to fill the vacancy with the first runner-up, in
that we lose a near quota of proportionality when we have the vacancy then
what is wrong if we replace the lost with another near quota of
proportionality from the same original election.

What's wrong with that thinking is that it has been determined that largest
party proportionality comes first.  That is why every STV election uses the
Droop Quota.  The first runner-up may not be from one of the largest
parties, but the leading next preference of the vacant member most likely
will be from the same party as the vacant member.  This is why some favor
only using the ballots of the vacant member.

I argue in a different vein, as follows:
Recounting only the ballots of the vacant member most likely will keep the
same original party proportionality, but it is not the correct
proportionality, because now the vacant member is not available as a
candidate.  The original proportionality was determined when the vacant
member was a candidate.
Because both the original election and the recount use the Droop quota,
both will produce the correct party proportionality for the candidates
available.  If the voters give the same party proportionality to the
recount it will be because the voters put that in their next preferences in
the original election, it's up to the voters.  But, when a recount does
produces a different proportionality, we must accept it because it was the
voters' choice.  STV is not Party List, in STV party proportionality can
shift because of different party candidates and this shift can take place
between original election and the recount.  There is nothing wrong when
there is this shift, on the contrary, this is why STV is a better method
than Party List.  The difference between candidates is important and STV
will show this importance by shifting the party proportionality.
And, that is why I support using all the ballots in any recount.

Jim: "John Smith (the losing candidate) said, "All I know is that more
people voted for me than voted for Bill Bloggs, and I'm out and he's in.
How can you explain that?"

Donald:  First let me say that it will be very rare for this to happen,
there just is not enough votes floating around to give the second
replacement more votes than one of the original sitting members, each of
which won with a full quota or near full quota, but if this should happen,
John Smith and the rest of the unelected candidates from the original
election need to be told and realize that they are not running against the
sitting members, the sitting members are not candidates to fill the
vacancy, they have already been elected in the original election.  Their
names and ballots are in the recount because we need to work all the
candidates and ballots together in order to get the correct proportionality
of the sitting members and the replacement together in one routine of STV
math.  John Smith lost to the first replacement, not to one of the sitting
members.

Jim:  "STV is like the old shell game, where you have 3 shells and 2 peas.
If you get the empty shell, you lose."  If the paper attempts to explain
the analogy, (i.e. shells are like quotas, peas are like candidates), they
in effect support its validity."  Jim R.

Donald:  The empty shell is the flaw of using the Droop Quota to gain party
proportionality.  The answer is to use something else in place of the Droop
Quota to assure party proportionality.

One something else is a new elimination rule for partisan STV elections
that goes as follows:
"Eliminate the lowest candidate of the party
with the lowest average votes per candidate."
(until the number of candidates equals the number of seats.)

This rule will give party proportionality to every party, not just the
largest, and without any `empty shell' nor `extra quota'.

And, there should be no `disproportionality' because all the votes will be
on all the elected members, meaning that all the voters are represented,
none are excluded as is the case when the Droop Quota is used.

I first created this rule for some other purpose, but then I quickly seen
that it could replace the Droop Quota and do a much better job of
protecting party proportionality.

The rule's major value is that it will make the math easier if we wish to
design a STV method in which the voters are allowed to rank candidates
and/or parties in any mix.

Anyway, for now, my elimination rule should replace Droop and its empty
shell in all partisan STV elections.

Donald,

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Full text of Jim's letter is below:

------------ Forwarded Letter ------------
From: Jim Riley <jimrtex at pipeline.com>
Date: Sat, 15 Nov 2003 19:52:10 -0600
Subject: Re: Let's fill the vacancy by Bjarke's words:

On Sat, 15 Nov 2003 05:45:38 -0500, donald at mich.com wrote:

> * * * *
>
>Bjarke wrote: "I think the best method, if the replacement must be
>determined from the original STV election result, is to eliminate the
>leaving candidate from all ballots, then repeat the STV count with the
>constraint that the n-1 remaining seats must be kept (cannot be eliminated)."
>
>Donald here:  I agree with these words of Bjarke, this is the best method.
>
>Having said that, I would also like to say that when the replacement is
>determined (by Bjarke words), we will find that he is the same person as
>the first runner-up in the original election, it's in the math.

Looking at the results from the 1998 election for the Northern Ireland
Assembly, this doesn't appear to be the case.

The 18 runners-up were distributed this way:
SDLP  7
DUP   3
UUP   2
APNI  2
SF    2
UKUP  1
UDP   1

This is largely due to SDLP having an unfortunate distribution of
votes, where they were midway between a full number of quotas (e.g.
0.5, 1.5, or 2.5 quotas, and unable to accumulate enough transfers to
secure a 1st, 2nd or 3rd seat).  Arguably, the first runners-up method
serves as a correction for a source of disproportionality under STV -
the extra quota.

If we look at the NI results on a 3-faction basis (unionist,
nationalist, and other), and consider which faction the runners-ups
supported, in many cases they were underrepresented in the original
vote:

4 seats: 8
3 seats: 1
2 seats: 2
1 seat:  5
0 seats: 2

In 8 cases, the runners-up faction had won 4 (of 6) seats.  There is a
reasonable chance that they would be replacing someone of their
faction.  But in 7 cases, there was zero or one of their faction
elected, and the runners-ups would most likely replace someone from
another faction.

A full recount, with the vacant members eliminated, would likely
produce the same factional distribution as the original election.

> * * * *
>
>Jim Riley wrote:
>"2. Recount the ballots eliminating the preference for the vacant
>member (treating him as having withdrawn before the election), but
>adding a constraint that the originally elected members could not be
>excluded.

>Disadvantages: A possibility that some candidates could end up with
>more votes than one of the previously elected, non-excludable
>candidates, and still not be elected.  Though not necessarily unfair,
>it could have the appearance of being so, delegitimizing STV."
>[end of Jim's quote]
>
>Donald here:  While it is true that it is possible for a losing candidate
>to receive in the recount a few votes more than one of the sitting members,
>if the public is well informed that the sitting members are to be retained
>because they did win in the original election and this current count is not
>a recall effort, then the public should accept the results.

Would the public be well-informed?  If there were a recount with
ordinary results (the new member represents the same party as the old
party), a newspaper would report the replacement, and perhaps mention
the recount in passing.

But if there were an upset, the paper would add to their report:

John Smith (the losing candidate) said, "All I know is that more
people voted for me than voted for Bill Bloggs, and I'm out and he's
in.  How can you explain that?"

Single Transferable Voting (STV) is a complex scheme which attempts
to represent the interests of all voters.  Don ___ at the University
of Michigan said that results like this "happen sometimes".

Here you have 'scheme', 'complex', and 'attempt' desribing the
process, and your explanation trimmed to in effect to suggest that STV
doesn't always work.

"STV is like the old shell game, where you have 3 shells and 2
peas.  If you get the empty shell, you lose."

If the paper attempts to explain the analogy, (i.e. shells are like
quotas, peas are like candidates), they in effect support its
validity.

--
Jim Riley

```