Monday, May 11, 2009

STV Counting Explained

Members of the Citizens’ Assembly on Electoral
Reform have recommended BC adopt BC-STV for
future elections because it is a system in tune with
the values of a great many British Columbians.

BC-STV is fair because it produces
proportional results, it provides voters with
more choice and more control, and it
strengthens local representation. BC-STV is
designed to make every vote count.

BC-STV basics
· There are fewer ridings, each electing between
two and seven MLAs – depending on the
population of the riding. Because each riding
elects a number of MLAs, over-all results are
more proportional – that is, each party’s share
of seats in the riding reflects its share of votes.
· Generally, parties will put forward more than
one candidate in each riding – giving voters
more options.
· BC-STV does not change the number of
MLAs province-wide or the number of MLAs
representing each region.
· BC-STV ballots allow you to vote by ranking
candidates (1, 2, 3, etc).
· If your vote is not needed to elect your first
choice candidate, it can be transferred to the
candidate you marked on the ballot as your
second preference – and so on.
· BC-STV is designed to ensure vote counting
can be accurately checked and replicated.
· It is also designed to use ballot papers that can
be counted by hand or by machine.

Counting the ballots
Calculating the quota
To win a seat in the legislature, a candidate must
receive a minimum number of votes – called a
quota. This quota is calculated using the number
of valid ballots cast in the riding as well as the
number of MLAs to be elected in that riding.

Number of valid ballots in riding
Quota =
Number of MLAs in riding + 1 + 1

Counting first preferences
After the polls close, all valid ballots are sorted
and counted according to the first-preference
candidate marked on each.

Eliminating candidates
If no candidate has the minimum number of
votes (quota) needed to be elected, the candidate
with the fewest votes is eliminated.

All of the eliminated candidate’s votes are then
redistributed to the second-preference candidates
as marked on each ballot.

Transferring surpluses
It is rare for an elected candidate to gain exactly
the quota of votes required to be elected.
Successful candidates usually receive more
votes than needed to win a seat. Since these
surplus votes are not needed to elect the
candidate, they could be considered wasted.

But, because BC-STV is designed to make as
many votes as possible count fully and fairly,
these surplus votes are redistributed. But which
votes should be selected to redistribute?

To be fair and to ensure vote counting can be
precisely repeated, every ballot cast for the
newly elected candidate is redistributed to the
next-ranked candidate marked on each ballot.
But, not at full value, because a portion of each
vote has already been used to elect a candidate.

The portion of each vote used to give the elected
candidate a quota, stays with that candidate. The
unused portion is transferred. To determine
what fraction of the vote should move on to the
next preference, the transfer value is calculated.

Candidate’s surplus votes
Transfer Value =
Candidates’ total votes

So, if a winning candidate has twice as many
votes as needed to be elected, instead of
transferring half those votes at full value, all of
the votes are transferred at half value to the
candidates ranked next on each ballot. The
transfer value in this case is .5 – or ½.

Counting continues until all seats are filled
Counting continues as follows:
· The surpluses of elected candidates are
redistributed at the appropriate transfer value;
· If there are still unfilled seats and no surpluses
from elected candidates to redistribute, the
least popular candidate is eliminated and those
votes are redistributed at full value;
· This continues until all seats have been filled.

Exhausted ballots
If, in the course of counting, a ballot should be
transferred, but there are no more preferences
indicated on the ballot, it is considered
exhausted and is put aside.

This can happen when:
· The voter marks very few preferences, or
· All the preferred candidates have already been
elected and/or excluded.

If a seat becomes vacant between elections, a
by-election is held in that riding to elect a new
MLA. BC-STV specifies that by-elections will
use the same type of ballot used in regular BC-
STV elections – called a preferential ballot.

If only one MLA is to be elected, candidates
require a majority of votes (50% + 1) to be
elected. If more than one vacancy is to be filled
in a district, the normal BC-STV vote counting
procedures and quota calculation are used.

Elections BC
As today, Elections BC will supervise elections
and scrutineers will ensure accurate ballot counts.

Further information
For a wealth of information on the Citizens’
Assembly, BC-STV or other electoral systems,
see In particular,
for more detail on BC-STV ballot counting, see:
· the technical volume of the Final Report
· an animation of BC-STV ballot counting

1. Count voters’ first
preferences and allocate
these to each candidate
3. Does any
have enough
votes to be

4. Exclude last
placed candidate.
Redistribute those
votes to next
marked on ballots

5. Distribute
the surplus of
all newly
elected MLAs
to remaining

2. Quota determined

Step 1
All the votes are counted and sorted by the voters’
first preferences.

Step 2
The minimum number of votes required to win a
seat is determined. This number depends on how
many valid votes are cast and how many MLA
seats are available to be filled.

Step 3
Does any candidate have enough votes to win a
seat? If no, go to Step 4.
If yes, go to Step 5.

Step 4
Exclude the candidate with the fewest votes.
Redistribute these votes – at full value – to the next
preference shown on each ballot.

Add up new vote totals and return to Step 3.

Step 5
If the successful candidate has more votes than
needed to win a seat, these surplus votes are
redistributed to the remaining candidates – at a
calculated transfer value – based on the next
preference listed on each ballot.

Add up new vote totals and return to Step 3.

Counting Continues…
Repeat Steps 3 to 5 until all seats are filled.
Adapted from

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