...

of course the only difference in behavior will be when there is a case like Burlington where a Condorcet winner exists but does not make into the final round with Hare IRV.  i dunno the details of your simulation but i might wonder how many (as a percent) times that happens and how many times a cycle occurred.

my sole selling point (maybe this becomes 4 or 5 selling points as i have enumerated in my paper at https://drive.google.com/file/d/14assN41UL7Mib9PpwsjM63ZT17k9admC/view ) is that plain-language advantages of RCV that are presented to the public are going to be better attained with a Condorcet method.  but most people following RCV don't know what that is.  so i translate "satisfy Condorcet criterion" to "Majority Rule" and i translate "satisfy IIA" to "eliminate the Spoiler Effect" and the only voting tactic i worry about is "compromising" because that is the most common problem and is directly related to the spoiler effect.  and i am also trying to appeal to the Precinct Summability issue because it relates directly to transparency in elections and decentralization of the tallying of ballots.  that speaks to election integrity and puts up another bulwark against hacking and corruption in elections.

in other words, i want to make RCV live up to its promise.

Here is a Vermont update:  Because, because city charter changes require state legislative approval and because of heavy load on the legislature regarding covid and the economic consequences, the Gov Ops committee was too busy to deal with the RCV charter change even though it passed the voters of Burlington with a 64% majority.  Some legislators read my paper and it has influenced them.  It is not dead, but it is in hibernation until 2022.  Then we're gonna have a big fight and, again, I will be asking for help in advocacy.  https://vtdigger.org/2021/05/21/burlington-charter-change-package-stalls-in-committee/

BTW, i got involved in a Ranked-Pairs advocacy group centered mostly in Madison Wisconsin, but they got Nicolas Tideman in it.  People here might remember that before I was told about BTR-STV (which is the name I am giving it), that RP with margins was my fav Condorcet method (only because I saw it as simpler than Schulze and easier to sell).  But BTR-STV is even simpler and even easier to sell.  And I can compare it directly to Hare STV.

My hope is that when the "big presentation" happens at the Statehouse in 2022, that I might be able to get both Nicolas and Markus and Richard and some others here to testify (via Zoom) before the committee.  I need to fight off the accusation that I am a constituency of 1 and that nobody else cares about this "detail".

Thank you to all for your help and encouragement.  That FairVote train is rolling with a lot of momentum.

--

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

I have updated the scatter plot that charts Clone Independence and IIA
(Independence of Irrelevant Alternatives) for various methods.  The
scatter plot is (still) at:

https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg

Here are the most important changes to the software and chart:

• The Clone Independence test now categorizes the case of a clone
  candidate displacing the similar candidate as a success, not a failure.
  This interpretation was requested on the r/EndFPTP subreddit, and it
  makes sense to me.  The other three kinds of CI failures continue to be
  categorized as failures.  This means that when the original candidate
  who is similar to the clones (is there a name for this candidate?) wins
  without the clones, and then loses to one of the clones (when they are
  added), that displacement is not regarded as a failure of clone
  independence.  The wording in the Wikipedia article on Clone
  Independence implies that such displacements are failures, so that's the
  interpretation I originally used.  I'm not suggesting that the Wikipedia
  wording is incorrect; rather I'm suggesting that when measuring CI
  success/failure rates it's important to also measure how often each kind
  of CI failure occurs (which is what I wrote earlier), and because this
  scatter plot is intended to be a meaningful summary of the measurements.

• Because of this change, the success rates for the Condorcet-Kemeny
  method and the Borda count method are much higher.

• The success rates for the Condorcet-Kemeny method are now very similar
  to the Instant Pairwise Elimination (IPE) success rates.  This is not
  surprising to me because I designed opposition counts -- which are used
  in the IPE method -- as a quick way to estimate Condorcet-Kemeny
  results.  (I had been surprised by the earlier results.)

• The Instant Pairwise Elimination (IPE) method calculations now
  correctly eliminate Condorcet losers when they occur.  The previous
  calculations just used the pairwise opposition counts.  The resulting CI
  and IIA measurements remain about the same.  (Typically when there is a
  Condorcet loser, the Condorcet loser has an opposition count that is
  very close to the highest opposition count.)

• I've eliminated the Approval method from the plot.  As someone pointed
  out on r/EndFPTP, converting ranked ballots into Approval ballots is not
  meaningful.  This is especially true for these tests because my counting
  software is separate from the ballot-generation software, so the clone
  candidates often do not get the same approval rating as the original
  similar candidate.

• Minor change: Now that the Approval results are gone, the scale starts
  at 50 percent compliance.

Additional details are in the software, which is on Github here:

https://github.com/cpsolver/VoteFair-ranking-cpp/blob/master/generate_random_ballots.cpp

As a reminder (and because someone on Reddit asked), I chose CI and IIA
because they measure vulnerability to strategic nomination, which is
easily exploited through the control of campaign contributions.

Richard Fobes

On 5/26/2021 9:17 AM, VoteFair wrote:

On 20.06.2021 02:41, VoteFair wrote:

I'd say the three clone failure types are:

Suppose A is cloned into A1 and A2. Then, for any two other candidates B
and C from the original election:

1. If A won before cloning, but B wins after, that's vote-splitting.
2. If B won before cloning, but A1 or A2 wins after, that's teaming.
3. If B won before cloning, but C wins after, that's crowding.

Everything else (A->A1, A->A2, B->B, C->C) is a pass.

James Green-Armytage's paper on IRV shows that even though IRV is
theoretically cloneproof, it's unusually vulnerable to candidate exit
(where similar candidates leave the race to get a candidate elected).
Does your plot try to find such "near clone independence" failures?

If it doesn't, then something's still off: IRV is strictly speaking
clone independent, so its clone independence rate should be 100%.

On 6/20/2021 6:53 AM, Kristofer Munsterhjelm wrote:

I see four categories:

1. A wins without clone, but B wins with clone: clone "hurts" similar
   candidate (yes usually because of vote splitting but I'm not sure that's
   always the case)

2. B wins without clone, but A or A1 or A2 wins with clone: clone
   "helps" similar candidate (A/A1) (yes usually intentionally if teaming
   used, but can be accidental)

3. B wins without clone, but C wins with clone: similar to IIA (I don't
   have a name for this category)

4. A wins without clone, but A2 wins with clone: clone "displaces"
   similar candidate

No it does not try to isolate this kind of failure.  Instead, the IIA
(independence of irrelevant alternatives) test does this kind of testing
where removing any candidate is a failure.  In the IIA tests there are
no clones, so no my tests don't measure this specific kind of failure.
Such failures would just contribute toward the IIA failures.

This bothers me too, yet I've looked for bugs that might affect this and
I haven't found any -- although of course that doesn't mean they aren't
there.

If I were only testing IRV failures without comparing the results to
other methods using the same ballots, then I could simply ignore cases
where there is a tie for the fewest transferred votes (during any of the
intermediate, but not final, elimination rounds).  And then it would
have 100% clone independence.

How does the academic paper resolve such ties?  Or does the math assume
such ties do not occur?

I do ignore cases where IRV yields a tie for winner.  And also I ignore
cases where the Condorcet-Kemeny method or plurality yield a tie for who
wins.  That makes sense because those cases are actual ties.

But I can't justify ignoring cases that are problematic for just one
method.  That could cause higher failure rates for the other methods,
especially the ones that include tie-breaking rules.  That would not be
a fair comparison across the different methods.

I regard this as one of the reasons why such measurements have not
already been done.  It's challenging!

Yet being able to yield numeric comparisons is essential to move beyond
the simplistic zero versus non-zero failure-rate arguments.

Kristofer, as always I greatly appreciate your wise feedback!!

Richard Fobes

On 6/20/2021 6:53 AM, Kristofer Munsterhjelm wrote:

On 22.06.2021 20:36, VoteFair wrote:

The third category is usually called "crowding". This terminology seems
to be due to Blake Cretney, see
http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-February/105357.html.
The earliest instance I can find of his jargon page is this:
https://web.archive.org/web/19991001204109/http://www.fortunecity.com/meltingpot/harrow/124/defn.html

As for the fourth, I don't think that's a failure, because for any
election where A is cloned into A and A2, there's an equivalent election
where A is cloned into A2 and A. Since clones only obey the property
everybody ranks them next to each other, it's not possible to determine
who's the original and who's the clone; to distinguish A and A2 would be
a failure of the neutrality criterion.

Or to put it differently, suppose you have an election like this, call
it election eX:

45: A>B>C
33: B>C>A
30: C>A>B

Without loss of generality, suppose A wins. Now make two clone
elections, eY:

45: A>A2>B>C
33: B>C>A2>A
30: C>A>A2>B

and eZ:

45: A2>A>B>C
33: B>C>A>A2
30: C>A2>A>B

Now in eY, either a member of the clone set wins with positive
probability, or someone outside the clone set does. If it's the latter,
you have a straightforward clone failure. So suppose the winner/s in eY
is/are part of the clone set.

If A and A2 tie, then A has gone from winning with certainty to winning
with 50% probability, which is a failure of the fourth criterion. If A2
wins, then it's also a failure of the fourth criterion. This only leaves
the possibility that A wins in eY.

But if A wins, then by neutrality A2 must win in election Z, which would
be a failure of the fourth criterion. So no method can be cloneproof: it
will either fail when going from eX to eY, or when going from eX to eZ.

Suppose that you break ties with a tiebreaker that itself is cloneproof.
Then the cloning doesn't get someone who would've been eliminated later,
eliminated earlier (since there's no teaming or crowding in either the
tiebreak or in Plurality). So the elimination order is the same up until
either A or A2 is eliminated and the other one remains. After that
happens, the remaining candidate gets all of the clone set's first
preference votes and the method proceeds as it would without the clone.

Finding an appropriate tiebreaker is the difficult part. I don't know
how JGA did it, but here's a suggestion that should be cloneproof.

Let's say the tiebreaker consists of a ranking, where in a tie between
some candidates, you eliminate the tied candidate that's ranked last on
that ranking. You have one ranking before the cloning and another one after.

Then the proof says that as long as you eliminate candidates one at a
time, and the rankings before and after are the same, except that the
candidate cloned is replaced with the clone set in some order, IRV will
be cloneproof.

The usual way to get such a ranking would be to pick a random ballot and
use the ranking on that ballot (completing it with random voter
hierarchy if there's equal-rank or truncation:
https://electowiki.org/wiki/Maximize_Affirmed_Majorities#Random_Voter_Hierarchy_tiebreak_procedure).

So you could implement this using random ballot to create the ranking
before the cloning, and use the exact same ballot to create the ranking
after the cloning.

One could argue that this leaves too much to chance: it could be that
IRV is cloneproof only for some random ballot rankings, but not for
every such ranking. But the proof shows that it's either cloneproof for
none of them or for all of them. So in the particular case of IRV, this
will suffice to show that IRV is cloneproof - the randomness has no
effect as far as clone resistance goes.

I think you can handle clone failure in the presence of winning ties.

If the winner set doesn't contain A, you clone A, and now it contains A,
then that's teaming.

If the winner set contains A, you clone A, and A is kicked off the set,
that's vote-splitting.

If you clone A and someone who isn't A is either kicked off or added to
the winner set, then that's crowding.

This doesn't properly classify some clone failures, but some of them
defy classification into just one category when you're dealing with
winner ties. For instance, suppose the winner set before cloning is A
and B; and after, it is A, B, and C. This has aspects both of
vote-splitting (because the chance of a tie-breaker choosing A is
reduced) and crowding (because C got admitted).

More generally, suppose you have a cloneproof tiebreaker like Random
Ballot (choose a random ballot, pick the winner who's listed first on
it). Then something like:

• if the probability that the winner comes from the clone set after
  cloning is reduced, that's vote-splitting;

• if the probability that the winner comes from the clone set after
  cloning is increased, that's teaming;

• and if the conditional probability of electing some candidate X not in
  the clone set, given that you elect a candidate outside the clone set,
  changes, that's crowding.

There's another problem as well that I've been mentioning numerous times
:-) When you count "how often" or "how likely", you have to assume some
probability distribution - i.e. how often a particular election is going
to appear. This probability distribution may well change as voters come
to learn the method.

FairVote makes a big deal (as I understand it) about IRV tending to
elect Condorcet winners. However, this is under the probability
distribution inherited from Plurality, where you have two large parties
and a bunch of fringe ones whose only danger is splitting the vote of
major-party voters.

Given some time, the voters may think that now they can vote for third
parties without any harm; but when a third party gets large enough and
is everybody's second choice, cue Burlington.

How often does IRV fail to elect the Condorcet winner? That depends on
whether there are any third parties around.

So any "how often" calculation should be qualified by noting just what
kind of distribution/voter behavior the calculation assumes. Whether
it's uniform utilities, impartial culture, something spatial, or based
on polling data like Armytage's analysis.

Thank you. :-)

-km

On 6/27/2021 10:32 AM, Kristofer Munsterhjelm wrote:

My simulations have a fully random distribution, without any tactical
voting. Specifically each ranked ballot is generated randomly without
any interaction with any other ballot, and without any knowledge about
how the ballots will be counted. (And without any knowledge of what the
candidates represent.)

Of course in real elections voters will use tactical voting if they
believe that tactical voting can make a difference in the results.

To repeat, my simulations do not attempt to measure cases that involve
tactical voting.

(In contrast, I noticed that your software does perform measurements
regarding tactical voting.)

Perhaps a useful analogy is the tossing of a coin to determine a pattern
in the results. Of course the pattern of the results can have a
distribution (such as a "normal" distribution). Yet there is no pattern,
specifically no distribution pattern, in generating the random ballots.

To repeat what I've written before, these simulations are like stress
tests. They are not intended to represent real elections. Instead they
are intended to push election-counting methods into a zone where the
methods are forced to reveal how they differ from one another.

Switching to the other topic in your reply, I agree with your
categorization of clone failure types.

Richard Fobes

On 6/27/2021 10:32 AM, Kristofer Munsterhjelm wrote: