Description
This article is from the soc.culture.australian FAQ, by Stephen Wales
with numerous contributions by others.
8.2.1 What is preferential voting?
The aim of a representative electoral system is to elect people who
represent their constituency. It is simple, intuitive almost, to see that
where you are trying to elect one person, that person should have the
support of over 50% of their constituents before they can claim to reflect
the views of their constituency.
There are two practical problems which this creates. Firstly, how do you
guarantee one person will end up with over 50% of the votes if more than
two people are standing? Secondly, is it fair, that in a worst case
scenario, with a close vote, that nearly 50% of constituents will be
unrepresented.
Answer 1 - Exhaustive Preferential Voting
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OK, we have one person to be elected, and more than two candidates.
The quota (the number of votes needed to be elected) is 1/2 plus 1, ie
50% plus one. This quota is commonly called a majority.
In exhaustive preferential voting, squares are placed next to the
names of each candidate. Constituents number these squares in order of
their choice. "1" goes against the person you most want, "2" against
the next person, and so on down the ballot paper.
After voting, all the ballot papers are sorted according to the number
"1" votes, and the papers are counted. If no-one has a majority (ie
has attained the quota) then the person who has the lowest number of
papers is removed from the ballot, and that person's papers a
distributed to the candidate of next choice (at this stage the number
"2" votes) and the results are tallied again. This process of
deleting the lowest, continues until a candidate finally gains a
majority. That candidate is then declared elected. In this way is is
ensured that there will always be one candidate with a majority.
Answer 2 - Proportional Representation
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There are different forms of proportional representation around. The
most rigorous (and therefore most accurate in terms of reflecting the
constituents) is Hare-Clark, which is used in Tasmania, ACT, (and, I
think Eire?). Another name for PR is Quota Preferential. The
differences between these forms are minor in procedure, but major in
effect.
First, let's look at this conceptually. Remember that what we are
trying to do is select people who can represent their constituents, ie
the chamber of parliament being elected should reflect the diversity
of views in the constituencies.
In a single member system, the worst case is that 1/2 - 1 voters did
not want the elected person. Remember, 1/2 + 1 to get elected. If two
people were to be elected we can't have a quota of 1/2 + 1 to get
elected, because there aren't enough votes; if there are two to be
elected then they should represent at least a third of the
constituents. That is, the quota becomes 1/3 + 1. Similarly, if three
are to be elected, the quota is 1/4 + 1. The interesting thing, and
this is why there are multi member constituencies, is that the more
members you have representing a constituency, the fewer people are un
represented. This is easier to see in a table. Remember this is a
worst case scenario
No elected quota total people electing total unrepresented
1 1/2 + 1 1/2 + 1 1/2 - 1
2 1/3 + 1 2/3 + 2 1/3 - 2
3 1/4 + 1 3/4 + 3 1/4 - 3
4 1/5 + 1 4/5 + 4 1/5 - 4
So that deals with the "why" of multi member constituencies. The next
thing to deal with is the "how".
Single user constituencies are easy. Enter your choices, and only one
person can get a quota. In a multi member constituency, what if one
candidate gets, for example, two quotas? If we had a "real time"
voting scenario, then people could simply punch in their choice, and
when that person got to the quota, they would be taken off the list of
available choices. For various reasons, including ensuring a secret
ballot, that is impractical, so the following algorithm is used.
1 Sort and count the papers according to first choice.
2a If one or more persons is elected, take the one with the highest
vote, distribute their surplus (see below). Go to 2a.
2b If no one is elected, cut up the papers for the lowest count
candidate at full value and distribute according to next available
choice. Go to 2a.
3 Finish.
What, I hear you cry, is a surplus? The surplus is the number of votes
in excess of a quota, so if the quota is 300, and a candidate has 500,
their surplus is 200. Now, it's here that Hare-Clark differs from the
senate. In the senate, they will select 200 of the 500 papers, at
random, and distribute them to the remaining candidates according to
the next available choice after the candidate being cut up.
In Hare-Clark, each paper is given a transfer value according to the
surplus - in our example we have 500 papers worth a surplus of 200,
therefore each paper is given a value of 200/500 or .4 of a vote and
all papers are distributed to the remaining candidates according to
the next available choice after the candidate being cut up.
It's just two different approaches to the distribution of the surplus.
They are both statistical manipulations, but I personally believe that
it only requires a moment's thought to see that Hare-Clark has more
reproducable results.
It is not an empty claim by Hare-Clark proponents, that Hare-Clark
changes "one person, one vote" into "one person, one effective vote".
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