(version 1.0, Chris M. Dickson, 14/4/99)
When somebody casts a vote in a simple yes/no vote, such as whether or not to create a newsgroup, they have three choices as to how to cast their vote. If they prefer "yes" to "no", they vote for "yes". If they prefer "no" to "yes", they vote for "no". If they have no preference between the two, they vote "abstain". When someone votes in a Condorcet-counted vote, they are doing essentially the same task, expressing preference for some options over other options.
I think it is likely that most uk.* Condorcet-counted votes will come when there is one newsgroup to be created with one of two possible names, or two alternative suggestions to change an existent charter or guideline. In either circumstance, we must also provide an option to preserve the Status Quo; also, we must provide an option to Re-Open the Discussion, but in only the first two votes on any one proposal. Condorcet, Status Quo and two Discussion Re-Openings were all mandated by Paul Bolchover's voting procedures guideline change CFV of April '98. Thus it is usual that a Condorcet-counted ballot paper will look like this.
======================= Start of Ballot XXX01 ====================== Your real name: [ Fill in your name between the brackets ] Your e-mail address: [ Fill.in@your.address.between.the.brackets ] *PLEASE COMPLETE THE ABOVE SECTIONS FOR VOTE TO BE VALID.* Please rank your preferences below: Option A : [ ] Option B : [ ] Status Quo (create neither group): [ ] Re-Open Discussion: [ ] ======================== End of Ballot XXX01 =======================
Should there be more options to choose from, they would go between Option B and Status Quo.
Immediately before the ballot paper, you should include this text, which seems to have been accepted as the usual description of "how to vote".
---start quote---
This vote is being counted under the Condorcet system. Voters are required to mark a 1 by their favourite option, a 2 by their second favourite option and so forth. Voters are permitted to mark the same number by more than one option when they are indifferent between them. Voters are permitted to leave options unmarked, but are requested not to; the voter is assumed to show indifference between unmarked options, but to prefer all the marked options to all the unmarked options. To abstain from the vote, fill in your name and e-mail address only, leaving all four options unmarked.
---end quote---
As a result, you will get people filling the four (or more) boxes with digits. If they fill in the boxes like this:
Option A : [2] Option B : [1] Status Quo (create neither group): [4] Re-Open Discussion: [3]
then they are expressing six preferences:
A Condorcet count is little more than six simultaneous yes/no votes on those six issues. An alternative way to fill the boxes might be:
Option A : [ ] Option B : [ ] Status Quo (create neither group): [1] Re-Open Discussion: [1]
which expresses the following six statements:
Incidentally, there's no difference between
Option A : [ ] Option B : [ ] Status Quo (create neither group): [1] Re-Open Discussion: [1]
and
Option A : [2] Option B : [2] Status Quo (create neither group): [1] Re-Open Discussion: [1]
or
Option A : [3] Option B : [3] Status Quo (create neither group): [1] Re-Open Discussion: [1]
or even
Option A : [4] Option B : [4] Status Quo (create neither group): [1] Re-Open Discussion: [1]
which all express the same six statements. Boxes left blank are equivalent to boxes filled in with the number of boxes there are to fill in; that is, boxes left blank are all equal last place.
Once all the votes have come in, you can draw up a chart of voters and votes which might look like this:
| Name | A | B | S | R |
|---|---|---|---|---|
| Voter Jones | 1 | 2 | 3 | 4 |
| Voter Smith | 2 | 1 | 3 | |
| Voter Brown | 1 | 1 | 2 | |
| Voter Green | 3 | 4 | 2 | 1 |
| Voter White | X | |||
| Voter Black | 1 | 3 | 1 | 2 |
| Voter Robinson | - | - | 1 | 1 |
...and so on...
The counting is done in two stages: the first compares each of the options to the Status Quo and determines which options go on to the second stage.
The general counting technique that you need to master is how to convert a chart like the one above into a set of statements that one option beats another option by a number of votes.
Concentrate on one pair of options at a time; in the first stage, you will compare each of the options, apart from Status Quo, against Status Quo. In this case, you will compare Option A against Status Quo, then Option B against Status Quo and finally Re-Open Discussion against Status Quo. We shall deal with the first of these only.
What you need to do is ignore the rest of the chart apart from the columns containing the options you're comparing. In this case, your chart would look like
| Name | A | S |
|---|---|---|
| Voter Jones | 1 | 3 |
| Voter Smith | 2 | 3 |
| Voter Brown | 1 | |
| Voter Green | 3 | 2 |
| Voter White | X | |
| Voter Black | 1 | 1 |
| Voter Robinson | - | 1 |
...and so on...
In Jones' case, he's expressing a higher preference for A than for the Status Quo, so this is a vote for A and against Status Quo. Ditto Smith and Brown. Green and Robinson express a higher preference for the Status Quo than for Option A, so this is a vote for Status Quo and against Option A. White just put a cross against one option and left all the others blank; this is clearly a vote for Status Quo and a vote against the rest. Black expressed no preference between Option A and Status Quo, so this is an abstention between the two.
Once you've gone down the list, you'll have a statement that some number of people (say 38) prefer Option A to the Status Quo, and some other number of people (say 21) prefer the Status Quo to Option A. Do check the list going up from the bottom to the top as well as down from the top to the bottom. (I tend to split the list into groups of ten and fifteen then add the numbers of preferences in each group up to come to a final total, simply because it is easy to get confused.) This result can be treated just like the result of a simple yes/no newsgroup creation vote: if an option beats the Status Quo by at least 12 votes, it succeeds; if it doesn't beat the Status Quo by 12 or more votes, it fails.
Work this out for each of the options apart from Status Quo, because comparing Status Quo against Status Quo makes no sense.
If no options beat Status Quo by 12 or more votes, then the Status Quo prevails and Stage Two is not necessary.
If exactly one option beats Status Quo by 12 or more votes, then it is the winner and Stage Two is not necessary.
If two or more options beat Status Quo by 12 or more votes, they both survive to Stage Two, which does become necessary to declare a winner.
Again, we concentrate on one pair of options at a time. In Stage Two, we compare each surviving option against each other surviving option. Any options that failed to beat Status Quo by 12 or more votes in Stage One are ignored in Stage Two. I would imagine that the two most common situations at this point will be:
1) all the options (apart from Status Quo) reaching Stage Two
2) all the options apart from Re-Open Discussion (and Status Quo) reaching Stage Two.
The technique for comparing options against each other in Stage Two is exactly the same as in Stage One. Pick the possible pairs of competing options out one at a time and compare only the preferences awarded in those two columns.
In our example, let us suppose Option A and Option B make it through to Stage Two from the case above. Isolating those columns only,
| Name | A | B |
|---|---|---|
| Voter Jones | 1 | 2 |
| Voter Smith | 2 | 1 |
| Voter Brown | 1 | 1 |
| Voter Green | 3 | 4 |
| Voter White | ||
| Voter Black | 1 | 3 |
| Voter Robinson | - | - |
...and so on...
Voters Jones, Green and Black prefer Option A to Option B; voter Smith prefers Option B to Option A; voters Brown, White and Robinson express no preference between them. Continue in this vein for all the voters and come to a conclusion that some number preferred Option A to Option B, and some number preferred Option B to Option A. The Option out of these two which gained more preferences is the winner of this pair; there is no minimum size of victory. It is possible, but unlikely, for two Options to tie should exactly as many prefer each over the other (ie 14 prefer Option A to Option B and 14 prefer Option B to Option A).
You must proceed to declare a winner out of every possible pair of Options that can be drawn from the Options surviving from Stage One.
Hopefully, you will reach a situation where one Option is the winner of every pair of itself and any other surviving Option. This Option is your Condorcet Winner. For instance, if only Option A and Option B in the example above survived from Stage One, the winner of that pair would be the Condorcet Winner. Another case might see Option A, Option B and Re-Open Discussion surviving from Stage One, then the winner between Option A and Option B would also have to beat Re-Open Discussion in order to be the Condorcet Winner. This extends further if there are more than three Options surviving from Stage One.
The slightly conceptually scary thing about Condorcet is that it is possible there will not be a Condorcet Winner. However, this does require an unusual set of circumstances. Suppose, in a particular vote, Option B, Option D and Option E (only) survive Stage One. Suppose that furthermore, Option B is the winner of the Option B - Option D pair, Option E is the winner of the Option B - Option E pair and Option D is the winner of the Option D - Option E pair. As we do not have a single Option which is the winner of all the pairs of itself and the other surviving Options, we do not have a Condorcet Winner. Technically, we have a Condorcet Top Set of Option B, Option D and Option E. What happens in this circumstance is that Re-Open Discussion wins, regardless of whether it reached Stage Two or not (or even whether it appeared on the ballot paper or not).
It is also possible that two (or more!?) Options might tie against each other, but both be the winners of all other pairs of themselves and all other surviving Options. (For instance, Option A, Option B and Re-Open Discussion might all survive to Stage Two; if Option A ties with Option B and both Options A and B beat Re-Open Discussion, this situation would occur.) In this case, the tie shall be resolved by lot. This would result in uk.*'s biggest ever coin-toss - but that is a bridge we should cross only when we reach it.