Voting system R&D (Re: 2017 update to the SPI voting algorithm for Board elections)

[Barak A. Pearlmutter]

Dimitri,

Of course we're discussing multiwinner systems: systems that elect
k-of-n people to a board, where k>1.

As you note, when k=n the election is uncontested so there is no need
for any voting system.

In the Burlington election discussed, k=1 and n=3. That's about the
simplest situation you can have, so any credible multiwinner system
should perform flawlessly in that degenerate case, one would hope!

For a bit of background, all the systems we're considering have the
following basic character. (I'm going to simplify a bit.) They use
some "underlying single winner" system to elect a candidate, then they
adjust the ballots in some way to account for that, and iterate this
process until k candidates have been elected.

The multiwinner system called STV uses IRV for the underlying
single-winner system.

The multiwinner system called RRV uses RV (range voting) for the
underlying single-winner system.

STV does the "adjust the ballots" step by basically removing a certain
number of ballots that supported the candidate that just won.

RRV does the "adjust the ballots" step by putting a numeric weight on
each ballot, and lowering the weights of ballots that supported the
candidate that just won.

IRV successively discards the lowest-number-of-first-position
candidates until one candidate has a majority of first-rank positions
across ballots, with struck-out candidates not considered.

RV chooses the candidate with the highest average (weighted, in this
case) score.

Let me note a few things.

FIRST, these systems are not really so different when looked at from
such a high level.

SECOND, any problems with the underlying single-winner system will
necessarily cause problems with the multiwinner system.

THIRD, these systems were designed at very different times, with very
different goals and constraints. IRV and STV were designed to be easy
to perform by tired humans with trays of ballots. STV (and also IRV)
was designed to be easy to explain to a Victorian voter using a
natural intuition (namely that each person should get to vote for
exactly one candidate, but if the person they really want is knocked
out of the running they should get to switch that vote to someone
else); and to be easy to process by hand using trays and sheets of
paper. RRV was designed to be very easy to implement on a computer, to
avoid pathologies as much as possible, to be amenable to mathematical
analysis, and to perform well in simulated elections.

Cheers,

--Barak.