[EM] Scatter plot of clone independence versus IIA

[Kristofer Munsterhjelm]

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%.