Dear stv-voters and Voice4Allers,

As I've occasionally complained on these lists, I have had an ongoing
dissatisfaction with most choice voting/STV procedures. What I've really
wanted is one that:

1. Has a short, self-evident list of rules
2. Provides a traceable link between an individual voter and a single
winning candidate.
3. Does not involve fractions or randomness in the tally (this is about
the same as #2). Randomness is OK for breaking ties.
4. Only exhausts ballots if they don't rank any of the winners, giving a
good measure of "none of the above" votes.
5. Gives results very close to true proportionality, ignoring a minimum
number of votes. (A STV algorithm called "Meek" gives proportional
results but throws lots of votes into a garbage can in the process; I'd
like something that outperforms this.)
6. Ideally makes minimal use of lower rankings.
7. Maintains the principle of lower choices not hurting higher choices.

I'd like to dub any STV procedure that takes on these weighty challenges
"courageous", and I'll outline one here.

Based on #5, the ideal outcome is one where each winner has
(cast votes)/(seats) votes ("cast votes" means without exhausted ballots;
this number is often called the "dynamic Hare quota"). So this is a good
quota to try for surplus transfers: if a candidate gets more votes than
this, those votes are transferred to other choices. This ideal is
ordinarily difficult to achieve because too many votes get tied up with a
few strong candidates.

To get past this, we can take advantage of the fact that candidates with
more than the Droop threshold (cast votes/(seats+1)) are going to win, so
it is a better use of one's vote to use a lower choice unless the ballot
lists no other remaining candidates. This can loosen things up enough to
achieve #5 in a sufficiently competitive election where voters rank a
sufficient number of candidates.

To achieve #3 and #4, we can prioritize ballots for surplus transfers
based on the ability of their next choices to help someone win. When
doing this, you may have to look at successively lower choices (which
maintains #7 because the higher rankings are the same). At some point,
ballots may all look identical, making them impossible to prioritize. In
this case we just take as many as we need; this breaches #2 somewhat, but
it's about as good as it gets. (One could get an improvement by looking
at higher rankings or those of eliminated candidates, but let's not bother
at this point.)

Some people think that fractional transfers are more "fair" than this, but
I like the above transfer approach because, in addition to satisfying #3
and #4, it simulates what the voters would choose to do as a group if
given the opportunity to manually transfer the ballots according to their
own rules. It also reduces the number of wasted transfers due to ballots
that exhaust.

By now, it probably sounds like #1 is a lost cause, but here is what I
have come up with so far:

--------
Rules for Courageous STV 1.0:

Voters: rank candidates you support in order of preference.

Definitions:
"Enough" votes is the number of votes cast for the remaining candidates
divided by the number of seats plus one: if a candidate has this many
votes, s/he is guaranteed to win, and if all winning candidates have more
votes than this, then a majority of the elected board represents a
majority of voters.

"Too many" votes is a number exceeding the number of votes cast for the
remaining candidates divided by the number of seats (the "cap"). If any
candidate has too many votes, then it is impossible for all candidates to
have the same number of votes.

A "surplus" is a number of votes in excess of the cap.

A "remaining" candidate is one who has not been eliminated.

To tally:

1. Count each ballot toward its highest-ranked candidate.

2. If any candidates have a surplus (taken in decreasing order):

(a) Sort the candidate's ballots into piles according to their next
choices, as follows:

(i) Attempt to assign the ballot to its highest-ranked remaining
candidate who does not have enough votes. If this fails:
(ii) Attempt to assign the ballot to its highest-ranked candidate with
more than enough votes, but less than the cap. If this fails, put it in
the 'none of these' pile.

(b) Identify:

(i) the pile that could give its candidate the most votes (without
using more ballots than the surplus), and
(ii) the number that can be transferred: the smallest of the surplus,
the number of ballots in that pile, and the number needed to give that
candidate enough votes.

(c) If the whole pile can be transferred, do that; if all of the ballots
in the pile are indistinguishable, transfer the appropriate number.
Otherwise, repeat steps (a) through (c) using this pile.

(d) Repeat steps (a) through (d) until the candidate no longer has a
surplus.

3. If there are more candidates than seats, eliminate the last-place
candidate and transfer the candidate's votes as follows:

(a) Attempt to assign the ballot to its highest-ranked remaining
candidate who does not have enough votes. If this fails:

(b) Attempt to assign the ballot to its highest-ranked remaining
candidate with more than enough votes, but less than the cap. If this
fails:

(c) Attempt to assign the ballot to its highest-ranked remaining
candidate. If this fails, put it in the 'none of these' pile.

Then return to step 2.

If a tie occurs at any stage, compare the tied candidates after
successively previous numbered steps, or by random lot if that fails.

--------

I have implemented this (with the exception of tie breaking) as an
appendage to the DemoChoice software package. You can run any poll from
that site through this algorithm by finding the poll's label and going to

http://www.demochoice.org/courageous.php?poll=mylabel

You can find a poll's label by going to its ballot or results page and
looking at the URL. It can take around 10 seconds to run some of the
longer polls and there is no fancy interface; it just spits out some
tables of text and numbers. (Please don't run the Meath poll, which puts
a large load on the server.)

Final-round results for the real datasets I have are pasted below. The
main observation is that all winners achieve the Hare quota in all but
two cases, where the candidates were still well above the Droop quota.
These differences occur when the last candidate with too many votes has no
support in lower rankings for the below-Hare candidate.

"Ambiguous transfers" is comparable to the number of votes that get
fractionated in a traditional STV procedure. It is the sum of the piles
in which ballots were effectively identical when trying to prioritize them
for surplus transfers. Some ballots may have been counted toward this
total more than once if they ended up in more than one of these piles.

"Ballot depth" (shown on the courageous.php output page, but not here)
provides a measure of #6. The results are very similar to those observed
using the normal DemoChoice procedure.

Probably the next step (after pondering your constructive feedback) is to
run the procedure with less realistic polls that push its limits and see
where and how it breaks down. But just from this it appears to perform
quite well compared to traditional STV procedures against the above
criteria.

Cambridge School Committee 1997
label: cambsc97
Ballots: 16386
Droop quota is 2283
Hare quota is 2662
2662 Grassi, Joseph
2662 Harris, Robin
2662 Maher, David P.
2662 Segat, Susana
2662 Simmons, Denise
2666 Turkel, Alice
410 None of these
1538 ambiguous transfers

Cambridge School Committee 1999
label: cambsc99
Ballots: 17961
Droop quota is 2439
Hare quota is 2844
2847 Fantini, Alfred B.
2844 Grassi, Joseph G.
2844 Segat, Susana M.
2844 Simmons, Denise
2844 Turkel, Alice L.
2844 Walser, Nancy
894 None of these
2600 ambiguous transfers

Cambridge School Commitee 2001
label: cambsc01
Ballots: 16489
Droop quota is 2292
Hare quota is 2674
2674 Fantini, Alfred B.
2674 Grassi, Joseph G.
2674 Harding, Richard, Jr.
2674 Price, Alan C.
2674 Turkel, Alice L.
2674 Walser, Nancy
445 None of these
2011 ambiguous transfers

Cambridge School Committee 2003
label: cambsc03
Ballots: 18698
Droop quota is 2632
Hare quota is 3070
3070 Fantini, Alfred B.
3070 Grassi, Joseph G.
3070 Harding, Richard, Jr.
3070 Lummis, Ben
3073 McGovern, Marc C.
3070 Walser, Nancy
275 None of these
5675 ambiguous transfers

Cambridge City Council 1999
label: cambcc99
Ballots: 18777
Droop quota is 1825
Hare quota is 2027
2027 Born, Kathleen Leahy
2027 Braude, Jim
2121 Davis, Henrietta
2027 Decker, Marjorie C.
2027 Galluccio, Anthony D.
1936 Maher, David P.
2027 Reeves, Kenneth E.
2027 Sullivan, Michael A.
2027 Toomey, Jr., Timothy J.
531 None of these 531
3012 ambiguous transfers

Cambridge City Council 2001
label: cambcc01
Ballots: 17125
Droop quota is 1677
Hare quota is 1863
1863 Davis, Henrietta
1863 Decker, Marjorie C.
1863 Galluccio, Anthony D.
1863 Murphy, Brian
1766 Pitkin, John
1863 Reeves, Kenneth E.
1863 Simmons, Denise
1960 Sullivan, Michael A.
1863 Toomey, Timothy J., Jr.
358 None of these
2227 ambiguous transfers

Cambridge City Council 2003
label: cambcc03
Ballots: 20080
Droop quota is 1922
Hare quota is 2135
2135 Davis, Henrietta
2135 Decker, Marjorie C.
2135 Galluccio, Anthony D.
2135 Murphy, Brian
2135 Pitkin, John
2135 Reeves, Kenneth E.
2135 Simmons, Denise
2135 Sullivan, Michael A.
2139 Toomey, Timothy J., Jr.
861 None of these
1587 ambiguous transfers

Dail - Dublin West 2002
label: DublinWest02
Ballots: 29988
Droop quota is 7111
Hare quota is 9480
9482 Burton, Joan (Labour)
9480 Higgins, Joe (Socialist)
9480 Lenihan, Brian (Fianna Fail)
1546 None of these
9416 ambiguous transfers

Dail - Dublin North 2002
label: DublinNorth02
Ballots: 43942
Droop quota is 8402
Hare quota is 10502
10502 Glennon, Jim (Fianna Fail)
10503 Ryan, Sean (Labour)
10502 Sargent, Trevor (Green)
10502 Wright, G.V. (Fianna Fail)
1933 None of these
5147 ambiguous transfers

Dail - Meath 2002
label: Meath02
Ballots: 64081
Droop quota is 9904
Hare quota is 11883
11883 Brady, Johnny (Fianna Fail)
11883 Bruton, John (Fine Gael)
11883 Dempsey, Noel (Fianna Fail)
11887 English, Damien (Fine Gael)
11883 Wallace, Mary (Fianna Fail)
4662 None of these 15
5767 ambiguous transfers