[EM] Scatter plot of clone independence versus IIA

[VoteFair]

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


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

 > 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?

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.

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

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 20.06.2021 02:41, VoteFair wrote:
>> 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.
>
> 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.
>
>> * Because of this change, the success rates for the Condorcet-Kemeny
>> method and the Borda count method are much higher.
>
>>
>>
>> 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.
>
> 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%.
>