[EM] STV - CV hybrid elections

[Tom Ruen]

My name is Tom Ruen and I was on this list last year in March and April. I
had to leave after 6 fun weeks because it was too distracting from the rest
of my life with so many interesting messages to read and think about.

I return now because I need some help.

As of Friday, I convinced important people at the small private company I
work for to consider changing the board election (stock share based votes)
from a Cumulative Vote to Single-Transferable Vote.

We'll be having a vote sometime in the coming months to decide if we want to
replace CV in our bylaws for board elections.

I have some influence to deciding how the proposed STV is implemented.
(Although it is to my advantage to support a version of STV with practical
historical use elsewhere.)

The primary failing I see of STV is that it forces a full vote on one
candidate which is a distortion of a voter's true preferences that might be
seen in a sincere rated preference vote. This distortion, pushing full vote
on the top choice, runs the risk that a strong compromise candidate (overall
high second rank support) may be eliminated early in STV, but might have
survived and flourished under CV which allows a vote to be divided.

I want a system that will fix the failings wasted votes on excess winners
and weak spoilers if CV. I don't want to introduce new failings that didn't
exist under CV!

I've considered a hybrid election method which allows voters to offer
weighted preferences (like CV but the voted sum need not equal the total
votes). Actual votes are computed by normalizing the weights to sum to the
total remaining vote each round and remaining candidates supported.

I successfully tallied ballots from last year's board election with CV
ballots using this method. I can call this method CTV - Cumulative
Transferable Vote, and it follows the same rules as STV except it counts
votes by normalized weights of remaining candidates and remaining votes.
Surplus votes are transferred by proportion of weights given on remaining
candidates. Eliminated candidates transfer votes simply by reducing the
normalization factor.

The drawback of the pure CV election with transfers is that when all
nonzero-weight candidates are elected or eliminated, the remaining surplus
vote can't be transferred anywhere.

Now I see it is possible to mix vote weights and ranks of STV as one final
step to a flexible voting method.

I'm talking now at a theoretical level, only hopefully practical. My best
hybrid system would give each voter a matrix to fill out, each column is a
given rank, and each row is support for a given candidate. A vote is divided
in proportion among all candidates with nonzero weights in the highest rank
with remaining candidates.

Example ballot: (ranks by column, candidates by row)
C/R 1   2    3    4
A    2   0    0    0
B    3   0    0    0
C    0   1    0    0
D    0   0    1    0
E    0   0    0    1

These numbers are weights. The actual vote is divided in proportion to the
weights of candidates remaining in the highest rank.

This ballot says:
1. Put 2/5 vote of my vote on A, 3/5 vote on B. (Redistribute remaining vote
on other if either wins or loses)
2. If A and B both have won/lost, move my remaining votes to C
3. If C also has won/lost, move remaining votes to D.
4. If D also has won/lost, move remaining votes to E.

This would seem to be the best possible CV with elimination and surplus
transfer. Voters have full control where and when their vote is distributed
in the election process.

This is the full system I would choose to call Cumulative Transferable Vote
(CTV).

Optionally ranked ballots with ties could be used (instead of a matrix) if
it is decided sufficient to allow voters only equal divisions of their vote
at any given time. I might call this Equal-and-Even CTV.

In this given CTV system, we can say last-place elimination is a fair step
since no candidate should be left unsupported merely due to limits of how
people can vote. A candidate will be last place because voters didn't choose
to split their vote to support him or her. If I want to protect any set of
favorites I am free to give them all a fraction of my support. I can do this
fearlessly knowing my vote redistributes among the other candidates in my
top remaining rank set. There is always a gamble with fractional support,
but a true relative preference is the optimal vote for getting what I want,
assuming I'm seriously interested in more than one choice.

This would seem to be as close to supporting sincere (normalized) "ratings"
as a "one-person, one-vote" voting method can get.

If anyone would like to comment on this CV-STV hybrid system, I'd really
appreciate it.

Questions about definitions? Is it a good hybrid? Is it simple enough for
voters in a small election (50 voters)? Do you think voters will appreciate
and (well) use this power if offered?

Thanks for listening!

Sincerely,
Tom Ruen

P.S. I offer this system primarily for multiseat elections, but I'm not
convinced it is valueless in single winner elections that would use IRV.
These split vote are added to solve unfair elimination of good compromise
candidates, and that failure exists under BOTH IRV and STV. At least here
(in CTV) voters are free to support as many candidates as they like at once.
That seems a good power to me.