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A blog: I'm going to China. Starting in Vienna with a TEDx talk, I then head to Belgrade, Sarajevo, Tbilisi, Baku and Kabul, before catching a bus across Tajikistan to Kashgar, 喀什, in Xīnjiāng, 新疆, where I hope to buy a bicycle.  https://debordaabroad.wordpress.com/2017/09/07/de-borda-abroad/

 

38 DEGREES   -   PETITION

Mulit-option and Preferential Referendums

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DECISION-MAKER
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www.decision-maker.org

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The Hospital for Incurable Protestants

The Mémoire of a Collapsed Catholic

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The de Borda Institute aims to promote the use of inclusive voting procedures on all contentious questions of social choice.

This applies specifically to decision-making, be it for the electorate in regional/national polls, for their elected representatives in councils and parliaments, for members of a local community group, for members of a company board, for members of a co-operative, and so on.

 

 

 

The director alongside the statue of Jean-Charles de Borda, capitaine et savant, in l’École Navale in Brest, 24.9.2010. Photo by Gwenaelle Bichelot. 

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Welcome to the home page of the de Borda Institute, a Northern Ireland-based international organisation (an NGO) which aims to promote the use of inclusive voting procedures on all contentious questions of social choice. For more information use the menu options above or feel free to contact the organisation's headquarters. If you want to check the meaning of any of the terms used, then by all means have a look at this glossary.

As shown in these attachments, there are many decision-making and even more electoral systems.  Sometimes, for any one voters' profile - that is, the set of all their preferences - the outcome of any count may well depend on the voting procedure used.  In this very simple example of a few voters voting on just four options, and in these two hypothetical examples on five, (word document) or (power-point) in which a few cast their preferences on five options, the profiles are analysed according to different methodologies, and the winner could be any one of all the options.  Yet all of these methodologies are called democratic!  Extraordinary!

The electorate decides...

Let us assume that the ballots have been printed and distributed and that an electorate of five persons - Messrs J, K, L, M and N - have voted by giving a 1 to their first preference, a 2 to their second preference, and so on.

Let us imagine that they voted as follows:

Preferences

Ms. J

Mr. K

Ms. L

Mr. M

Ms. N

1st

A

A

D

D

C

2nd

B

B

B

B

B

3rd

C

C

 

C

 D

4th

D

D

 

A

 A

 

Please note that Ms L only gave her first and second preferences; but that, of course, is her prerogative and is accepted by the software package.

Recording the votes...


To enter each voter's preferences, we click on the ‘Ballot Entry’ tab and enter the votes, one at a time:

In this example we have enter Ms J’s votes which were 1, 2, 3, 4. We then click 'Submit Vote'.

This is procedure is carried out in turn for each of the five voters. Decison-maker provides a tally of the number of stored votes.

Determining the final results...


Finally, we click on the ‘Results’ tab and this presents an analysis of the votes according to eight different voting methodologies:

The methodologies are mentioned here and described in the analysis.

Majority (Plurality) Voting is used in most parliaments and most referendums.

Two-Round Voting is used in some referendums, eg, in New Zealand.

Approval Voting is sometimes used in the UN, though mainly as an electoral system.

Alternative Vote is used, in its PR form, in most elections in Ireland, North and South.

The Borda Count is a French methodology, used in part in Austrian elections.

The Borda Preferendum allows for partial voting in the Borda count.

Serial Voting is used in some Scandinavian parliaments, eg, in Sweden.

A Condorcet count is another French methodology.


All of these methodologies are described as democratic, yet in many instances, different counting procedures will lead to different results. In our own example, the ‘most popular’ options are:

 

VOTING PROCEDURE

WINNER(S)

RUNNER(S)-UP

Plurality Voting

A and D =

 

Two-round voting

D

A

Alternative Vote (AV) or STV

D

A

Approval Voting

B and D =

 

Borda Count (BC)

B

D

Modified Borda Count (MBC) or Preferendum

B

A, C and D =

SerialVoting

B

C

Condorcet

B

C

 

In analysing the vote, we must examine each methodology in turn. But first, we repeat the voters' profile, like this:

 

Preferences

Ms. J

Mr. K

Ms. L

Mr. M

Ms. N

1st

A

A

D

D

C

2nd

B

B

B

B

B

3rd

C

C

 

C

D

4th

D

D

 

A

A

 

or in a slightly different style.

 

 

Preferences of:

Options

Ms. J

Mr. K

Ms. L

Mr. M

Ms. N

A

1st

1st

-

4th

4th

B

2nd

2nd

2nd

2nd

2nd

C

3rd

3rd

-

3rd

1st

D

4th

4th

1st

1st

3rd

 

Majority (Plurality) Voting considers only the first preferences, so while two people consider option A to be the best, and hence its score of two, the fact that two other people think it is the worst is not taken into account.

Two-Round Voting takes the two leading options from the plurality vote, and takes a straight majority vote between the two. Messrs J and K prefer A to D but Messrs L, M and N all prefer D to A, so D wins by 3 to 2.

In the Alternative Vote, option B is again (as in the plurality vote) considered to be the worst with a score of 0. Option C is the next least popular, and when its vote is transferred according to Mr. M's preferences, it goes to D. So D wins.

In Approval Voting, any preference expressed is regarded as a mark of approval, so in this analysis Options B and D gain the maximum score of 5 approvals.

A Borda Count is a straight points system with, in this instance, 4 points for a first preference, 3 for a second, and so on. And B wins.

In a Borda Preferendum, a partial vote is given a correspondingly partial score but, in this instance, the winner is still B.

Serial Voting considers the four options as if on an axis, and takes a majority vote between the two extremes first: A v D. A loses, so its then B v D. B wins this vote, so it's then B v C and again, B is the winner.

A Condorcet count is a series of pairings - A v B, A v C, A v D, B v C, B v D and C v D; the options which wins the most pairings is the winner and, in our example, it is again B.