# [EM] Vacancy and Ballot Recount:

Donald Davison donald at mich.com
Thu Nov 13 17:19:04 PST 2003

```Recounting the original ballots when seeking a replacement:
by Donald on 11/13/03

There are jurisdictions in the world that when filling a STV vacancy, will
only use the ballots that elected the now vacant member.  Because this
policy has been used for many years does not mean that it is correct.  We
must be willing to use a sharp eye and examine the policy.  The two methods
of recounting the ballots will usually elect two different candidates,
Both these candidates cannot be the correct replacement.  This tells us
that one of these two methods must be wrong.  We must determine which is
wrong.

In the original election, the elected members were all elected by a quota
or near quota of votes.  This is considered to be proportional results for
an election, but if the replacement is to be elected from only the ballots
of one of these members then the replacement will receive far less than the
original quota, even less than a majority of a quota.  This fact should
tell everyone that something is wrong with the policy of only using the
votes of the vacant member.  If all the members of the new body have not
been elected by a quota or near quota of votes then the body is not
proportional.

We get proportionality when we elect all the member at once via the math of
STV.  When we select a replacement separate and then insert him into the
body, the body will not be proportional.  The next preferences of only the
votes of one member is not proportional.  That vacant member was once part
of the proportionality of the original election, but he is now gone.  It is
not proper to select the replacement separate from the entire body of
sitting members.  Only having all the members elected together can the
results be proportional.

In a STV election the votes are sorted out, that is, the votes are
collected into sums, then the surpluses are transferred in fractional
parts, then votes of eliminated candidates are transferred around until we
have enough candidates with enough votes so that we can declare the
election of a proportional body of members, but if we lose one of those
members, that proportionality is lost.  We must accept that lost and
proceed to find the proportionality of the ballots with the vacant member
out of the mix, we must sort out all the ballots again in order to again
have a proportional body of members.

In other words, we work the ballots as if the vacant member never was a
candidate in the original election, only this time we do it with a rule to
protect the sitting members.  There are two good reasons why it is
necessary to have the rule that no siting member can be eliminated.

One: We want all sitting members to be part of the current
proportionality, therefore they must all be elected in the recount.  The
rule will elect all the sitting members plus one replacement, which gives
us a proportional body of members.

Two: We don't want any of the lower preferences of any of the sitting
members to be used in the election of the replacement.  This would distort
the results.  The votes that elected the sitting members are already spoken
for, those votes cannot be used to help elect the replacement candidate.
If we were to allow one of the sitting members to be eliminated before the
replacement was determined, then the transferred votes of this sitting
member would influence the choice of the replacement.  This is not proper
because those votes already have elected a member, they cannot be allowed
to elect two members.

----------- Forwarded Letter ------------
From: Jim Riley <jimrtex at pipeline.com>
Date: Tue, 11 Nov 2003 20:54:29 -0600
Subject: Re: Let's fill the vacancy with the runner-up:

What are our choices?

1. Recount the ballots eliminating the preference for the vacant
member (treating him as having withdrawn before the election).

Advantages: If the members collectively represent the constituents,
then the set elected by such a recount would best represent the
constituents.  This recognizes the results of STV as being unordered.

Disadvantages: A sitting member could be displaced by a vacancy caused
by the death or resignation of another member.  This could even lead
to mischievous resignations.  Ballots would need to be securely
stored.  Voters and parties might use different strategies.

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.

Advantages: To a slightly less extent than (1), the collective set of
members should be fairly representative of the constituents views.
Votes that had elected the now vacant member, will tend to be
distributed to like-minded candidates.  And unlike (1), no sitting
members could be displaced.

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.
Ballots would need to be securely stored.  Voters and parties might
use different strategies, but perhaps not the extent of (1).

3. By-election for all members elected from constituency.

Advantages: Would get fair representation for constituents.

Disadvantages: Expense, possibly lower turnout, possibly increased
voter alienation.  Results would be influenced by more recent events
than were issues in the other constituencies.  Could cause larger
shifts in the composition of the entire body.  Could encourage
deliberately disruptive resignations.

4. By-election for single member elected from constituency.

Advantages: Simple.  Uses STV (albeit degenerate form).  Voters get to
choose replacement.  Could discourage resignations by members of minor
parties.  Could serve as referendum on the government, in same manner
as happens in by-elections under single member FPTP elections.

Disadvantages: Expense, probably lower turnout.  Would likely increase
influence of major party.  Results would be influenced by more recent
events than were issues in the other constituencies.  Would tend to
cause a shift towards the major parties in the composition of the
entire body.  Could discourage resignations by members of minor
parties, causing them to forgo opportunities elsewhere.  Could serve
as referendum on government, in same manner as happens in by-elections
under single member FPTP elections.

5. Leave seat vacant.

Advantages: Simple.  Inexpensive.  Small effect on composition of
overall body.  Discourages resignations for light cause.

Disdvantages: Leaves constituency underrepresented, though
arrangements could be made to provide a continued channel for
constituent matters.

6. Leave seat vacant, but distribute political power of vacant member
among the other members elected from the constituency.  For example,
in a 5-seater, the 4 remaining members would have 1.25 votes.
Arrangements could be made to increase staffing to handle constituent
matters.

Advantages: Simple.  Inexpensive.  Maintains influence of those most
interested in the constituency.  Small effect on composition of
overall body.  Discourages resignations for light cause.

Disdvantages: Leaves some constituents' views less well represented.

7. Elect best runner-up.  This is almost equivalent to (6) (e.g. in a
4 seater, the power is shared among the 4 members: 3 of the 4 that
were originaly elected, and the runner-up).

Advantages: Simple.  Inexpensive.  Maintains influence of those most
interested in the constituency.  Small effect on composition of
overall body.  Discourages resignations for light cause.  Avoids
perception of unfairness of (2).

Disadvantages: Likely will shift representation of constituency, but
this could be in direction of those left unrepresented by STV (e.g.
the candidate who ended up with .99 quotas).  To avoid a delayed
recount, many multiple exclusions could not be done during the
original count.

8. Successively count the ballots to generate lists of n elected; n+1
elected; n+2 elected; etc.  Vacancies would be filled from ordered
lists.  If 4 are elected, then the fist replacement would be from the
list of 5, etc.  If the successor counts would produce more than one
additional replacement, back up a count to determine their order:

4 members: A B C D win.
5 members: A B C E F win. (D excluded).

Then A,B,C,D are elected; E and F would be the first replacements,
with their order being determined by their level of support when
excluded from the count for 4 members.

Advantages: If the members collectively represent the constituents,
then the set elected by such would best represent the constituents,
less the vacant member.  This recognizes the results of STV as being
unordered.  Avoids displacement problem of (1), or perception of
unfairness of (2).

Disadvantages: Shifts the influence toward the electorate at large,
rather than those who particularly supported the vacant member.
Mitigating this is that the shift may be small, and may give an

9. Replacement selected by members of his party.

Advantages: Simple.  Tends to preserve overall balance of total body.
Replacement probably has similar views to now vacant member.

Disadvantages: Replacement was not elected by voters.  Does not handle
replacement of independents.  Uncertainty of who should select
replacement if vacant member had left his original party - did the
voters support him, or did they support his party.

10. Replacement designated by candidate at time of election (system
used in Northern Ireland for Assembly vacancies).

Advantages: Simple.  Tends to preserve overall balance of total body.
Replacement probably has similar views to now vacant member - though
in Northern Ireland, of the 3 seconds who were replacements and are
now seeking election in their own right, two were not selected by
their original party.  Unlike (9), handles independents, and members

Disadvantages: Replacement was not elected by voters.

11. Replacement designated by candidate at time of election from among
all other candidates.

Advantages: Simple.  Tends to preserve overall balance of total body.
Replacement probably has similar views to those espoused by vacant
member.  Unlike (9), handles independents, and members who had
switched parties.

Disadvantages: Replacement was not elected by voters.  May encourage
additional candidates with little hope of election, but who could
provide a replacement opportunity.  These effects could be mitigated
by requiring a minimum level of support be reached before being
elected (e.g. if a candidate reaches a support level to save his
deposit, he could be considered non frivolous and worthy of serving as
a replacement).

--
Jim Riley

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