[EM] Instant Pairwise Elimination (IPE) vote-counting method

[VoteFair]

Based on Kristofer's feedback (below), here are the criteria that I 
suspect the Instant Pairwise Elimination (IPE) method fails:

Majority: fail
Majority loser: fail
Mutual majority: fail
Condorcet: fail
Smith/ISDA: fail
LIIA: fail
IIA: fail
Cloneproof: fail
Monotone: fail
Consistency: fail
Reversal symmetry: fail
Later no harm: fail
Later no help: fail
Burying: fail

I'm guessing that IPE fails these criteria:

Participation: fail ?
No favorite betrayal: fail ?

Of course IPE passes these criteria:

Ranks equal: pass
Ranks greater than 2: pass
Polytime/resolvable: pass/pass

I'm guessing that IPE passes this criterion:

Condorcet loser: pass ?

And here's my guess about summability:

Summable: O(N!) ?

On the surface, these characteristics do not look promising ...

... yet I'll say once again that what really matters is HOW OFTEN a 
method complies with the criteria. When we have that data we can more 
meaningfully compare different voting methods -- beyond just looking at 
checklists.

In fact, this topic, which I would call "Compliance Frequency," is being 
discussed on Reddit, with my suggestions at the following link:

https://www.reddit.com/r/EndFPTP/comments/afc9mm/quantifying_criteria_failure_rates/edy8gyh

I had intended to post these compliance-frequency suggestions here on 
this mailing list, but I seldom have time to write 
election-method-reform messages while at my PC, whereas I can type 
Reddit responses on my iPad while eating a meal.

Again, thank you Kristofer for your very useful feedback! (And no I had 
not already figured out the details that you clarified.)

Again, thanks to all for considering this suggested method. I'm assuming 
from the lack of criticism that the method is not as seriously flawed as 
IRV, which means it deserves attention as an alternative when a city 
considers adopting something better than plurality voting.

My next question is whether anyone wants to put the IPE method on the 
Electrowiki (or Electorama) site? (I tried using my login info from long 
ago, but with no success.) I can supply edited text if that's helpful. 
In advance, thanks!

Richard Fobes


On 1/13/2019 3:10 AM, Kristofer Munsterhjelm wrote:
> On 13/01/2019 04.44, VoteFair wrote:
>> Here's a suggestion for an easy-to-understand vote-counting method that
>> produces very fair results for single-seat elections:
>>
>> Voters rank the candidates using up to 7 ranking levels (or 5 ranking
>> levels if ovals are marked on a paper ballot and space is limited).
>> During counting, each elimination round eliminates the candidate who
>> loses every pairwise contest against every other remaining candidate. If
>> an elimination round has no pairwise-losing candidate then, for that
>> round, each ballot gives one count to the lowest-ranked remaining
>> candidate on that ballot, and the candidate with the highest such count
>> is eliminated.  The last remaining candidate wins.
>
> This seems very close to Smith//Coombs, but it's not exactly the same
> thing. I think it may fail Smith, even.
>
> Suppose that we have a nested inequality situation with an ABCA cycle
> and candidates DEF are all beaten by {ABCA} but have a DEFD cycle among
> themselves. Then the Smith set is {ABCA}, and the Antiplurality
> elimination stage triggers because nobody is beaten by everybody else.
> The Antiplurality elimination stage might then eliminate one of ABCA,
> and in the worst case, might sequentially eliminate all of them, making
> the method fail Smith.
>
> It's probably not monotone either, as very few candidate elimination
> methods are, and probably fails independence of clones since both
> Antiplurality and Coombs do.
>
>> Unless someone recognizes it as having a different name, I suggest
>> calling it Instant Pairwise Elimination (IPE).  The word "instant"
>> indicates that this method is similar to instant-runoff voting (IRV) in
>> the sense of "instantly" doing multiple elimination rounds.  The word
>> "pairwise" makes it clear that the eliminations use pairwise counting,
>> rather than the less-fair counting method used in IRV.
>>
>> This is a hybrid of Condorcet-loser elimination and the Coombs method.
>> For fun, someone on Reddit (u/jpfed) suggested calling it "Coombsdorcet".
>>
>> This is not a Condorcet-compliant method!  A test has already found a
>> case where the IPE winner is not the Condorcet winner.  Also note that
>> the description does not introduce the word Condorcet, even though it
>> eliminates Condorcet losers.
>
> Oh, oops. You already figured out what I wrote above :-)
>
> Both Nanson and Baldwin (Borda-elimination methods) are Condorcet
> without having an explicit Condorcet step or using a Condorcet matrix.
> So are methods of this type:
>
> Arrange the candidates in a line according to some initial ordering.
> Start with the last candidate in line, and compare him to the
> second-to-last. Eliminate the one of the pair who is beaten one-on-one
> by the other. If they tie each other, use whatever tiebreaker you want.
> Keep on going up the line until only one candidate is left; he wins.
>
> (Those methods are Smith. They're also summable as long as the methods
> used for tiebreaks and initial ordering are.)
>
>> I suggested it on Reddit in the r/EndFPTP subreddit because the
>> single-seat voting methods being discussed there most often are
>> approval, score, STAR, and IRV, which are easier to understand than
>> Condorcet methods, but they have one or both of these disadvantages:
>>
>> * Quite vulnerable to tactical/strategic voting
>>
>> * Do not work in situations that involve general/runoff elections
>>
>> The IPE method seems to be easier to explain to typical
>> (non-math-oriented) voters than any of the Condorcet methods (including
>> my favorite, the Condorcet-Kemeny method), yet it comes close to
>> providing the fairness of Condorcet methods.
>>
>> The inspiration for this method is the relative success of the STAR
>> method, which is a hybrid of score and runoff.
>>
>> Based on the surprisingly favorable response on Reddit, apparently most
>> voters are more trusting of a method that eliminates one candidate at a
>> time in a way they understand.  This contrasts with Condorcet methods,
>> which can identify the winner just by "looking at" a table of pairwise
>> counts.
>>
>> Also, explicitly identifying "losers," and identifying them one at a
>> time, seems to be emotionally appealing to voters.  Perhaps this is part
>> of why IRV is seen as appealing.
>
> Do you think the line method above would be received favorably? It is
> very simple but has a less explicit loser elimination component.
>
>> Yes, this method is vulnerable to the burial tactic, at least from the
>> voter's perspective.  Yet when voting methods finally get measured for
>> HOW OFTEN each method fails each fairness criterion, I suspect that this
>> burial-criterion failure will not affect the results often enough to be
>> significant, especially compared to IRV’s frequent fairness-criteria
>> failures.
>>
>> In fact, the method may appeal to some voters because it will give them
>> the emotional satisfaction of burying "enemy" politicians.
>
> Every voting method permits an angry voter to decide "I'm going to
> punish X" and change his vote from A>X>B>C to A>B>C>X. Pervasive burial
> susceptibility is more problematic when it creates a feeling that "I
> need to put the frontrunner I like the least at the very bottom or he'll
> win"; and then everybody does that, and a nobody wins.
>
> I generally think Condorcet methods are (on the whole) robust enough to
> disincentivize such massive burial sprees, but I haven't done any
> analysis on IPE in particular.
>
>> Please correct me if I'm wrong, but I believe that -- unlike IRV -- use
>> of the IPE method would enable polling places to start by sending their
>> pairwise counts to the central counting location, and the winner can be
>> identified quickly in most(?) cases.  Of course some elections
>> (especially if they are highly competitive) will require more ballot
>> data to be sent to the central counting location before a winner can be
>> calculated.  In elections that involve lots of candidates, the original
>> pairwise counts might clarify the elimination sequence for the
>> less-popular candidates, which would reduce the amount of ballot data
>> that needs to be sent quickly to determine the winner.  By contrast, IRV
>> needs almost all the raw ballot data, and the full ranking data with
>> lots of candidates does not lend itself to being compressed or summarized.
>
> If there's a clear Condorcet order, then you're right. But as soon as
> the Antiplurality elimination step comes into play, the districts will
> have to send their ballot data over to the center (or do two-way
> communication like in IRV). The reason is that who is next to be
> eliminated depends on which candidates have been eliminated so far in a
> way that can't be handled by a summed array -- just like IRV.
>