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Tom Monto

This STV fable shows the random-ness of FPTP and the reliability of STV

B C A D A B A B A C C B B C D C A D B A B E D B D


This odd list records the party of choice of 25 voters in a fictitious province or country.


When the story starts, the voters are voting in elections conducted using First Past The Post. The voters find that the government they elect does not have the support of a majority of the voters so they complain.


When the next election approaches, the non-partisan electoral commission attempts to provide fairer representation by re-districting. It moves district boundaries to put different voters together in different districts.


And the next election the voters vote exactly the same way, and oddly the election produces a different government. This happens four times. Each time despite the Commission's efforts, the majority of the voters find that they have not voted for the successful party.


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You can see this for yourself.

Divide the 25 voters into five-voter districts from left to right, and you will see five different governments elected depending on where the district boundaries are placed.


Do not change the order of the voters. It is outside the jurisdiction of the Commission to actually ask voters to move house just to achieve better representation. Although not explicitly stated, giving such power to a government body or board is clearly against the Canadian Bill of Rights and Freedoms!


The winner is the party with the most votes in a district.


To make the model work - a province or country of only 25 voters is pretty minimalist - I have given three seats to each district, thus electing a 15-member government. In case of ties for the most popular party in a district, give two seats to A or the party alphabetically closest to A, and one seat to the other party in the tie.


You will find that, depending on where you place the district boundaries - without changing the order of voters - you will produce five different governments. Voters at the left end of the line are moved to the right end of the line to make up whole five-member districts as needed.


To test the validity of the election result, you can calculate how many voters cast Effective Votes where they assisted in the election of representative and how many votes were wasted.

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The 25 voters grew weary and anxious of the sheer random-ness of the election results.


They cast about for an alternative.


Finally, they learned about the form of proportional representation named Single Transferable Voting.


They realized that it would take just a couple changes to adopt STV in their elections. Each voter would retain his or her single vote. And the number of representatives in the legislature would remain the same.


But districts would have to be made larger so that multiple representatives would be elected in each district. Under the new system, each district would elect a mixed crop of representatives. More representatives would be represented in each, and thus there would be less waste of votes. With less waste of votes, the results in each election would be more stable and less seemingly-random than elections under FPTP.


The first STV election they tried saw a very different result from the previous FPTP elections.


And the change became permanent, to all the voters' satisfaction.

Under STV, the most-popular party was assured of majority or minority government status.

The next party knew that if it could raise its vote count past that of the leader, it instead would form government.

The smaller parties on occasion were able to change the winner through their vote transfers, thus helping achieve the success of a mostly-favoured party over a less-liked party. Meanwhile, they had a chance to get more votes. Voters no longer shied away from wasting their vote on a long shot. With STV, strategic voting was un-necessary. Voters could cast their vote for whom they truly wanted to elect.


After several democratic elections under STV, the voters in this fictitious place wondered how they had ever accepted the almost-random results of elections using FPTP.


(The End)



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You too can produce STV elections in this fictitious place using the same voters:

B C A D A B A B A C C B B C D C A D B A B E D B D.


You just need to group all 25 voters into one district or into two or three districts each containing more than five voters. Thus, more than one representative would be elected in a single district election.


Transfers are not necessary to create this effect. You may assume that no voters marked back-up preferences (or that the election is held using Single Non-Transferable Voting).


If all voters are taken at-large (in one district), the parties' votes tallies are:

A 6, B 8, C 5, D 5, E 1.

You find that A gets 4 seats, B 5 seats, C 3 seats and D 3 seats. Thus a B minority government.


If divided into three five-member districts, say one district with 7 voters and two districts with 9 voters each, you will find that no matter how you arrange the districts (without changing the order of voters in the line) that each district will elect candidates belonging to three or four parties, thus ensuring mixed roughly proportional representation.


The district results added together will produce a pretty consistent and narrow range of results:

B will always take more seats than any other party.

A will take more seats than C or D.

E will not take any seats. There are always losing parties even under STV. But each substantial party will be rewarded with seats under STV.


Calculation will show that a majority of voters cast their votes for the party or party that receives a majority of the seats. The results under STV are thus more representative than the result under FPTP.


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Try a variety of voter profiles


Any string of letters may work as well.

Interestingly, a version of the ancient incantation "Abracadabra" yields just as odd a collection of governments when divided into various single-member districts.


In "A B R A C C A D D A B B R A B B R A C A D D A B D," A is the most popular party. But never is it elected to a majority government. Of the five options, in only one does it even elect a minority government.


This string of letter, derived from abracadabra, results in five different governments when divided into five districts in five different ways.


A B R A C C A D D A B B R A B B R A C A D D A B D

The vote tallies for each party are: 8As, 6Bs, 3Cs, 5Ds, 3Rs


Three seats for each district. The most popular party takes all three seats.

In case of a tie, allocate two seats for D or the party farthest from A, and one seat to the other party in the tie. Except R never takes more than one seat in case of a tie.


A B R A C C A D D A B B R A B B R A C A D D A B D

The results in the five districts using each group of five starting at the extreme left is:

Winners are: A A/D B A D

Thus these are elected: 7A, 3B, 5 D A minority government


If the district boundaries are moved one to the right, we have five new districts and a very election result.

Districts are: B R A C C A D D A B B R A B B R A C A D D A B D A

Winners are : C D B A A/D

These are elected: 4 A, 3 B, 3 C, 5 D D minority government


R A C C A D D A B B R A B B R A C A D D A B D A B

Winners are: C B/D B/R A/ D A/B These are elected: 2 A, 4 B, 3 C, 4 D, 2 R

This produces a government where B and D are tied with the most seats. One or the other would form a minority government propped up by the C, D, or R members.


A C C A D D A B B R A B B RA C A D D A B D A B R

Winners: C B B D B Electing 9B, 3C, 3D forming a B majority government


C C A D D A B B R A B B R A C A D D A B D A B R A

Winners: D/C B B D A

Electing 3A, 6B, 2C, 4D forming a B minority government.


Thus

an election held with voters "A B R A C C A D D A B B R A B B R A C A D D A B D"

may produce an

A minority government

B majority government

B minority government,

or a D minority government.


STV elections

While under SNTV or STV (leaving aside vote transfers),

with this vote profile: 8As, 6Bs, 3Cs, 5Ds, 3Rs

in an at-large election: you would elect

5 A, 3 B, 3 D, and 2 C and 2 R members, electing a minority A government.


in a three-district election, with a 7-seat and two 9-seats districts,

each district electing five members,

A B R A C C A D D A B B R A B B R A C A D D A B D

Winners: 3A, 2C 3B, 1A, 1D 3 D, 2 A Total elected: 6 A, 3 B, 2 C, 4 D, 0 R. Minority A government (again)


with boundary moved to the right one space:

B R A C C A D D A B B R A B B R A C A D D A B D A

Winners: 3 C, 2 A 3 B, 1 A, 1R 3 A, 2 D Total elected: 7 A, 3B, 3 C, 2D.

Minority A government (yet again).


And so on. Try it for yourself.


Note that in each district:

Parties are fairly elected with their relative strength reflecting their relative vote tallies.

The most popular party gets more seats than the next one. (Excepting ties)

And the two most popular parties get more seats than the rest.


And many voters see their vote used effectively.

With this scheme: B R A C C A D D A B B R A B B R A C A D D A B D A

In the first district four of the seven voters voted for parties that had candidates elected.

Second district - eight of the nine voters voted for parties that had candidates elected.

Third district - seven of the nine voters voted for parties that had candidates elected.


STV, no matter how you draw districts, produces a relatively-consistent representation, where the party with the most votes takes the most seats and the votes of a large majority of voters have an effect on who is elected.


Thanks for reading.

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The story behind the fable

The idea of the 25-member electorate came from a so-called "PR Wheel" illustrated in an old electoral reform book. The wheel is slid around in front of a background and numbers appear in little windows showing how the shift in the district boundaries produces different governments.

The book states that the relevance to an examination of proportional representation is that under forms of proportional representation the opportunity to distort the boundaries is reduced. Elections in multiple-member districts or even state-wide (at-large) basis rarely reflect narrow voter characteristics. In a small district where an industrial site and working community overshadows a suburban community, the suburbanites will rarely have representation. But with a multiple-member district, there may be elected representatives from both the right and left.


Under FPTP, when two parties are evenly balanced in he number of their votes, one party takes most or all of the seats sometimes, and the other party takes most of the seats the other times, depending on how the districting is done.


But the result under STV, when two parties are almost evenly balanced in the number of votes, would be that one would take only slightly more seats than the other, no matter how the districting is done.


The info is from Terry Newman's book Hare-Clark in Tasmania (1992) p. 110-111.


Thanks for reading.

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