[EM] FWD - The search for perfect STV, with ties allowed
Venus Greenhouse
donald at mich.com
Mon May 22 17:46:53 PDT 2000
----------- Forwarded Letter -----------
From: Alejandro Solá <ajsola at yahoo.com>
To: <loringrbt at aol.com>, <donald at mich.com>
Subject: The search for perfect STV, with ties allowed
Date: Sat, 20 May 2000 18:07:06 -0400
I suggest the following system for multi-member elections. Please relay to
the Elections Methods List and other interested parties. [ok]
1. Ballot paper
1.1. Whether on paper or on screen, the "ballot paper" lists the candidates
in columns, one for each political party. Independents are listed on a
separate column. Voters enter the number of their preference besides each
candidate's name. I choose to call these "individual preferences" (ie,
preferences for individual candidates). Up to now, exactly the same as in
STV.
1.2. But at the bottom of each party's column, there is a slot for "all
other candidates for this party". And at the very bottom of the ballot,
there is a slot for "all other candidates". I choose to call these
"collective preferences". The advantages of collective preferences,
especially on very long ballots (such as those necessary in a single
national constituency, which I advocate), are twofold:
a) allows party voting for those voters who don't know candidates well enough;
b) allows easy ranking of most disliked as well as most liked candidates.
Simply mark your first preferences for the candidates you like most, then
rank "all other candidates", and lastly rank those you like least.
1.3. Apart from the ties implied by collective preferences, candidates can
indicate ties by ranking equally several preferences (individual and/or
collective). Each tied entry is given an equal fraction of the vote.
1.3.1. Ties consisting exclusively of individual preferences are
considered individual preferences.
1.3.2. Ties consisting wholly of individual preferences are considered
collective preferences.
1.3.3. Ties including both individual and collective preferences are
apportioned between individual and collective preferences. In these
preferences, each individual and collective mark account for an equal
fraction of the vote (ie, if it so appears, my entry for William Hague
weighs the same as my same-ranked preference for "all other Labour Party
candidates").
1.3.4. Any individual preference tied with a collective preference
including it (ie, the voter ranked equally Tony Blair and "all other Labour
Party candidates") is "submerged" within the collective preference (ie,
only the ranking for "all other Labour Party candidates" remains).
1.3.5. The "all other candidates" option is apportioned equally between
the "all other candidate" option for each party and between each
independent candidate.
2. Initial tally
2.1. All valid votes are counted and divided by the number of seats to
obtain a Hare or Droop quota (the difference is very small in large
districts, as you will see). The quota remains the same at each round of
voting, ie, incomplete ballots do not result in a reduction of the quota.
This is to avoid candidates being elected with different numbers of votes.
In standard STV this would result in some unfilled seats. With this method
this should also happen, but to a lesser degree.
2.2. First preferences are examined. Only individual preferences are considered.
2.2.1. Non-tied individual preferences are counted. Candidates who reach
quota are elected. Their surpluses go (in proportion to the excess, as in
fractional STV) to their second preferences, which may be either individual
or collective.
2.2.2. Tied individual preferences (including the "individual" fractions
of "mixed" preferences) are counted next. For each vote, they are
distributed equally between the tied unelected candidates. Candidates who
reach quota at this stage are elected as well, but their surpluses are
distributed immediately and equally between the remaining candidates of the
tie. Candidates who reach quota in this way are elected as well and their
surpluses distributed equally between the remaining candidates of the tie.
This goes on until no candidate reaches quota.
2.2.3. Steps 2.2.1 and 2.2.2 are repeated with the following individual
and mixed preferences. For each vote, the cycle stops when a collective
preference is reached. This round of counting finally stops when no further
candidates reach quota.
2.3. Collective preferences (including the "collective" fractions of
"mixed" preferences) are examined next. In each round of counting:
2.3.1. Ties between collective preferences (ie, between different
parties) are apportioned equally between the parties.
2.3.2. Within each party, each vote or fraction thereof goes to the
unelected candidate who (a) is not ranked lower as an individual and (b)
had most votes from step 2.2.
2.3.3. If the candidate from step 2.3.2 reaches quota, she is elected and
her surplus goes to the next most voted unelected candidate of the party
(or the succeeding one if the vote ranked him lower as an individual), and
so on until nobody else is elected for that party.
2.3.4. The same is done for all parties.
3. Elimination of least-voted candidates
3.1. The candidate with least votes is eliminated. If in a vote he is part
of a tie, the surplus is distributed equally between all the other
unelected candidates and parties tied. If in a vote he is not part of a
tie, the surplus goes to the next preference.
3.2. Step 2 is repeated all over again (but this time should be much shorter).
3.3. Steps 3.1. and 3.2 are repeated until no unelected candidates remain.
No candidate is ever elected, on any round, unless he reaches quota.
____________________________________________________________________________
__________________________
I also want to call your attention to the following possibility of
strategic voting in fractional STV (including the version above):
If my first preference is a very popular candidate, bound to win, I do not
vote for her. She will get elected anyway, but my vote will not lose value
when it is transferred to my next preference.
Regards,
Alejandro Solá.
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META content="text/html; charset=iso-8859-1" http-equiv=Content-Type>
<META content="MSHTML 5.00.3013.2600" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV align=justify><FONT face=Arial size=2>I suggest the following system for
multi-member elections. Please relay to the Elections Methods List and other
interested parties.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2><STRONG>1. Ballot
paper</STRONG></FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>1.1. Whether on paper or on
screen, the "ballot paper" lists the candidates in columns, one for each
political party. Independents are listed on a separate column. Voters enter the
number of their preference besides each candidate's name. I choose to call
these
"individual preferences" (ie, preferences for individual candidates). Up to
now,
exactly the same as in STV.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>1.2. But at the bottom of each
party's column, there is a slot for "all other candidates for this party".
And at the very bottom of the ballot, there is a slot for "all other
candidates". I choose to call these "collective preferences". The advantages of
collective preferences, especially on very long ballots (such as those
necessary
in a single national constituency, which I advocate), are twofold:</FONT></DIV>
<DIV align=justify><FONT face=Arial size=2>a) allows party voting for those
voters who don't know candidates well enough;</FONT></DIV>
<DIV align=justify><FONT face=Arial size=2>b) allows easy ranking of most
disliked as well as most liked candidates. Simply mark your first preferences
for the candidates you like most, then rank "all other candidates",
and lastly rank those you like least.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>1.3. Apart from the ties implied by
collective preferences, candidates can indicate ties by ranking equally several
preferences (individual and/or collective). Each tied entry is given an equal
fraction of the vote.</FONT></DIV>
<BLOCKQUOTE style="MARGIN-RIGHT: 0px">
<DIV align=justify><FONT face=Arial size=2>1.3.1. Ties consisting exclusively
of individual preferences are considered individual preferences.</FONT></DIV>
<DIV align=justify><FONT face=Arial size=2></FONT> </DIV>
<DIV align=justify><FONT face=Arial size=2>1.3.2. Ties consisting wholly of
individual preferences are considered collective preferences.</FONT></DIV>
<DIV align=justify><FONT face=Arial size=2></FONT> </DIV>
<DIV align=justify><FONT face=Arial size=2>1.3.3. Ties including both
individual and collective preferences are apportioned between individual and
collective preferences. In these preferences, each individual and collective
mark account for an equal fraction of the vote (ie, if it so appears,
my entry for William Hague weighs the same as my same-ranked preference
for "all other Labour Party candidates").</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>1.3.4. Any individual preference
tied with a collective preference including it (ie, the voter ranked equally
Tony Blair and "all other Labour Party candidates") is "submerged" within the
collective preference (ie, only the ranking for "all other Labour Party
candidates" remains).</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>1.3.5. The "all other candidates"
option is apportioned equally between the "all other candidate" option for
each party and between each independent candidate.</FONT></DIV></BLOCKQUOTE>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2><STRONG>2. Initial
tally</STRONG></FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>2.1. All valid votes are counted and
divided by the number of seats to obtain a Hare or Droop quota (the difference
is very small in large districts, as you will see). The quota remains the same
at each round of voting, ie, incomplete ballots do not result in a reduction of
the quota. This is to avoid candidates being elected with different numbers of
votes. In standard STV this would result in some unfilled seats. With this
method this should also happen, but to a lesser degree.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>2.2. First preferences are examined.
Only individual preferences are considered.</FONT></DIV>
<BLOCKQUOTE style="MARGIN-RIGHT: 0px">
<DIV align=justify><FONT face=Arial size=2>2.2.1. Non-tied individual
preferences are counted. Candidates who reach quota are elected. Their
surpluses go (in proportion to the excess, as in fractional STV) to their
second preferences, which may be either individual or collective.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>2.2.2. Tied individual preferences
(including the "individual" fractions of "mixed" preferences) are
counted
next. For each vote, they are distributed equally between the tied unelected
candidates. Candidates who reach quota at this stage are elected as well, but
their surpluses are distributed immediately and equally between the remaining
candidates of the tie. Candidates who reach quota in this way are elected as
well and their surpluses distributed equally between the remaining candidates
of the tie. This goes on until no candidate reaches quota.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>2.2.3. Steps 2.2.1 and 2.2.2 are
repeated with the following individual and mixed preferences. For each vote,
the cycle stops when a collective preference is reached. This round of
counting finally stops when no further candidates reach
quota.</FONT></DIV></BLOCKQUOTE>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>2.3. Collective preferences
(including the "collective" fractions of "mixed" preferences) are examined
next. In each round of counting:</FONT></DIV>
<BLOCKQUOTE style="MARGIN-RIGHT: 0px">
<DIV align=justify><FONT face=Arial size=2>2.3.1. Ties between collective
preferences (ie, between different parties) are apportioned equally between
the parties.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>2.3.2. Within each
party, each
vote or fraction thereof goes to the unelected candidate who (a) is not
ranked
lower as an individual and (b) had most votes from step 2.2.</FONT></DIV>
<DIV align=justify><FONT face=Arial size=2></FONT> </DIV>
<DIV align=justify><FONT face=Arial size=2>2.3.3. If the candidate from
step 2.3.2 reaches quota, she is elected and her surplus goes to the next
most
voted unelected candidate of the party (or the succeeding one if the vote
ranked him lower as an individual), and so on until nobody else is
elected for
that party.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>2.3.4. The same is done for all
parties.</FONT></DIV></BLOCKQUOTE>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2><STRONG>3. Elimination of
least-voted
candidates</STRONG></FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>3.1. The candidate with least votes
is eliminated. If in a vote he is part of a tie, the surplus is
distributed
equally between all the other unelected candidates and parties tied. If in a
vote he is not part of a tie, the surplus goes to the next
preference.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>3.2. Step 2 is repeated all over
again (but this time should be much shorter).</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>3.3. Steps 3.1. and 3.2 are repeated
until no unelected candidates remain. No candidate is ever elected, on any
round, unless he reaches quota.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial
size=2>_____________________________________________________________________
_________________________________</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>I also want to call your
attention to
the following possibility of strategic voting in fractional STV (including the
version above):</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>If my first preference is a very
popular candidate, bound to win, I do not vote for her. She will get elected
anyway, but my vote will not lose value when it is transferred to my next
preference.</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2>Regards,</FONT></DIV>
<DIV align=justify> </DIV>
<DIV align=justify> </DIV>
<DIV align=justify><FONT face=Arial size=2><EM>Alejandro
Solá.</EM></FONT></DIV></BODY></HTML>
More information about the Election-Methods
mailing list