[EM] Equal Ranking of some Candidates in a STV election

[Steve Eppley]

Mike O wrote:
> Some of us have found that 1-winner STV, promoted in the U.S. under
> the name Instant Runoff (IRV), could meet the criterion known
> as WDSC, or the Drastic Defensive Strategy Criterion, if voters were
> allowed to split their vote among more than one candidate, by ranking
> more than 1 candidate at a rank-position.
> 
> Let me repeat that criterion, which I'll call WDSC or DDSC.
> First, let me say that I at first called it Weak Defensive Strategy
> Criterion, because it's relatively easy to meet, and, in that sense
> is a weak criterion. But it's been suggested that "weak" could be
> taken as implying that the strategy is weak. Since the criterion is
> about the most drastic form of defensive strategy, another name was
> suggested that reflects that. I believe the suggested new name was
> Drastic Defensive Strategy Criteriion, which I'll abbreviate DDSC.

The suggested new name was the "Non-Drastic Defense" criterion.  
The name is intended to distinguish methods which pass from 
methods where a majority may need to employ the "drastic 
defense" of ranking a compromise *ahead of* a favorite (to 
defeat an alternative which is worse than the compromise).  We 
consider it "non-drastic" to rank a compromise equal to a 
favorite.

Mike's related criterion, which he originally called "Strong 
Defensive Strategy Criterion," also has a suggested new name: 
the "Minimal Defense" criterion.  Methods which satisfy Minimal 
Defense allow a majority to express their preference for their 
favorites over the compromise, and still allow them to guarantee 
the defeat of worse alternatives, and simultaneous majorities 
can simultaneously employ the minimal defense strategy: they 
merely downrank the candidate/s they want to defeat, if 
necessary, so that it/they are not ranked ahead of alternatives 
which might cycle with the compromise.  (When in doubt, leave it 
out.)

> Anyway, here's the criterion:
> 
>    DDSC: If a majority of all the voters prefer A to B,
>    then they should have a way of ensuring that B can't win,
>    without any member of that majority voting a less-liked
>    candidate over a more-liked one.
> 
> DDSC is met by Approval, Bucklin, & all the Condorcet versions,
> including SD, SSD, Tideman, DCD, & PC. 

By "all the Condorcet versions" I think Mike is not including 
methods which consider pairwise margins instead of pairwise 
majorities.

> IRV fails DDSC. But it has turned out that IRV could be made
> to meet that criterion merely by letting voters divide their
> vote among several candidates by ranking them equal. It would
> probably be enough to allow that only in 1st choice position,
> though it would make more sense to allow shared rank-positions
> anywhere in one's ranking. 
> 
> But no. All the IRVies to whom we've suggested this IRV mitigation
> have been unwilling to include it in their proposals. It would seem
> that IRVies are determined to impose all of their meritless method's
> worst problems on the voting public.
> 
> That mitigation, which we called "Nonstrict IRV", was one of several
> mitigations that we offered to the promoters who are pushing IRV.
> None of the mitigations were accepted, and now it's evident that
> there's no such thing as a compromise with IRVies, because they
> won't compromise their method's meritlessness.

There are two basic variations of Nonstrict IRV.  One gives the 
ballot's entire (remaining) weight to each of the equally-
highest-ranked non-eliminated alternatives, the other splits the 
ballot's (remaining) weight between them.  Both seem to pass 
DDSC.

I asked an IRV advocate in California to consider promoting one 
of these nonstrict variations instead "strict" IRV (which 
presumably will invalidate any ballot where a voter has more 
than one alternative ranked highest, in addition to its other 
problems).  He expressed a tentative interest, depending on 
whether a corresponding STV PR method could be implemented.  
(After all, IRV is useful only to educate the public about 
preference orders and STV PR.  :-)  If a computer tallies the 
ballots, then it's not hard to design reasonable nonstrict STV 
PR methods corresponding to both Nonstrict IRV variations.

An STV PR which splits the ballot's remaining weight equally 
among its equally-highest-ranked contenders is a no-brainer.  
That's a straight-forward feature to add to strict STV PR.  An 
STV PR which gives the ballot's full remaining weight to each of 
the equally-highest-ranked contenders requires a bit of extra 
thought: 

   1. To avoid electing two candidates who reached the quota
   only because some ballots were overcounted, elect at most 
   one candidate per iteration.  (For instance, the candidate
   having the highest count.)  

   2. When an elected candidate consumes (a fraction of)
   a "shared" ballot, the same fraction of that ballot's
   clones must be consumed, so no ballot will wind up 
   counting extra.

One last comment on computerizing STV and IRV.  The algorithms 
will probably run slower than the algorithms for pairwise 
methods.  This may run counter to conventional wisdom, since 
tallying pairwise methods by hand is too laborious to be 
practical in a large public election.  But if the ballots are 
computer-readable, pairwise methods need to read them from mass 
storage only one, whereas IRV and STV need to reread them 
multiple times.  (I'm assuming that in a large public election 
the ballots won't fit into RAM.  The pairwise table will easily 
fit into RAM.)  Since reading from mass storage is slow, 
pairwise methods can run much faster.  And if the IRV or STV 
algorithm is just a brute force translation from the traditional 
hand count, rather than a clever design, it may spend a lot of 
time writing to mass storage as well (which tends to be even 
slower than reading from mass storage).


---Steve     (Steve Eppley    seppley at alumni.caltech.edu)