<div dir="auto">Richard,<div dir="auto"><br></div><div dir="auto">Clone winner failure is not about electing the wrong clone ... it's about none of the clones of the erstwhile winner being elected. That is the spoiler problem. </div><div dir="auto"><br></div><div dir="auto">If you want a method that is both clone winner compliant and IIAC compliant, Approval Sorted Margins (ASM), or Majority Judgment Sorted Margins (MJSM) is what you need. </div><div dir="auto"><br></div><div dir="auto">FWS</div><div dir="auto"><br></div><div dir="auto"><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">El mar., 2 de nov. de 2021 9:02 p. m., Richard, the VoteFair guy <<a href="mailto:electionmethods@votefair.org">electionmethods@votefair.org</a>> escribió:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">On 10/31/2021 5:04 PM, Forest Simmons wrote:<br>
> So the intractability issue is mostly an inconvenience ...<br>
<br>
I'm pleased that you, unlike many others, realize that the <br>
Condorcet-Kemeny method's long computation time for some possible cases <br>
is just an inconvenience, not a deal breaker.<br>
<br>
> but the clone dependence is a deal breaker ...<br>
<br>
I disagree that a non-zero failure rate for clone independence is a <br>
deal-breaker.<br>
<br>
The Beatpath (aka Schulze) method achieves a zero failure rate for clone <br>
independence, but I suspect that, as a result, it has a significantly <br>
higher failure rate for IIA -- Independence of Irrelevant Alternatives.<br>
<br>
This characteristic would match what happens with IRV -- instant-runoff <br>
voting. It has a zero failure rate for clone independence, but it has a <br>
high failure rate for IIA.<br>
<br>
The follow scatter plot shows this pattern:<br>
<br>
<a href="https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg" rel="noreferrer noreferrer" target="_blank">https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg</a><br>
<br>
FYI, the upper right corner is where there are zero clone failures and <br>
zero IIA failures. Most of the plotted methods, with the notable <br>
exception of plurality, can correctly handle two-candidate cases.<br>
<br>
If the Condorcet-Kemeny method were modified to reduce the failure rate <br>
for clone independence, that would increase its IIA failure rate.<br>
<br>
I believe this obviously follows from the fact that Arrow's theorum and <br>
other proofs tell us that no method can have zero failure rates for all <br>
of a set of specific desirable fairness criteria. So it follows that <br>
decreasing the failure rate for one fairness criterion will increase the <br>
failure rate for at least one other fairness criterion.<br>
<br>
This is why I've spent time calculating failure rates and plotting them <br>
on a scatter plot. I want to know the failure RATES, not just whether <br>
the failure rate is zero or non-zero.<br>
<br>
In my opinion the scatter plot clearly shows that the Condorcet-Kemeny <br>
method has the best compromise for clone independence and IIA.<br>
<br>
Specifically, look at the distance of the points from the upper right <br>
corner. The Condorcet-Kemeny points are closer than the other methods.<br>
<br>
As a clarification about the data for the STAR method: These <br>
calculations simulate sincere voting -- with no tactical voting -- so <br>
the points for STAR voting are idealized compared to actual elections <br>
where tactical voting would be involved.<br>
<br>
In contrast, the Kemeny, IPE (Instant Pairwise Elimination), and RCIPE <br>
(Ranked Choice Including Pairwise Elimination) method are more resistant <br>
to tactical voting compared to STAR voting, so tactical voting would not <br>
increase the failure rates for the same cases.<br>
<br>
Since these calculations are based on randomly generated ballots, the <br>
failure rates in real elections would be lower than this data measures. <br>
That's because most real elections have clearer patterns regarding <br>
popularity of candidates. So these simulations are like stress tests <br>
that look at performance under challenging cases.<br>
<br>
So, I disagree that "clone dependence is a deal breaker." Yes, clone <br>
independence is very important, but so is IIA.<br>
<br>
In fact, the failure of IRV in Burlington is an IIA failure! I regard <br>
that IIA failure to be more important than the failure to elect the <br>
Condorcet winner. Of course in that case if the "Condorcet loser" <br>
(actually the "pairwise losing candidate") had been eliminated instead <br>
of eliminating the Condorcet winner, then the Condorcet winner would <br>
have won.<br>
<br>
In other words, it was the presence of an irrelevant candidate (the <br>
pairwise losing candidate) in the top 3 that blocked the Condorcet <br>
winner from reaching the top 2.<br>
<br>
The elimination of "pairwise losing candidates" is why the RCIPE method <br>
performs better than IRV.<br>
<br>
And because the Condorcet-Kemeny method looks so deeply into ALL the <br>
ballot preferences on all the ballots, I suspect that it eliminates <br>
"irrelevant alternatives" better than a method that has a zero failure <br>
rate for clone independence.<br>
<br>
Also consider that when an election has rock-paper-scissors (Condorcet) <br>
cycles (that involve the most popular candidates), ignoring irrelevant <br>
alternatives helps the method deal with near clones.<br>
<br>
Admittedly I'm less concerned about the handling of *exact* clones <br>
because those are almost impossible in a real election.<br>
<br>
Yet if an election did have almost exact clones, I'm willing to accept <br>
electing the wrong clone. That's better than if a method gets "confused" <br>
by an irrelevant alternative.<br>
<br>
Richard Fobes<br>
The VoteFair guy<br>
<br>
<br>
On 10/31/2021 5:04 PM, Forest Simmons wrote:<br>
> Richard,<br>
><br>
> Twenty years ago I was excited to learn about K-Y because a topologist<br>
> is always on the lookout for interesting metrics on multidimensional<br>
> spaces. The NP complete intractability intrigued me without discouraging<br>
> me because in practice with hundreds of ballots the one among them with<br>
> the minimum average distance to the other ballots would be the actual<br>
> global minimum or very close to it ... after all, billions of such<br>
> averages can be calculated every second ... the problem is the sheer<br>
> number of finish orders that need to be checked to be absolutely sure<br>
> that you got the right one .... for 30 finalists it would be about 2.65<br>
> times 10^32 different orders ... but that is just a messy inconvenience<br>
> for picky people to worry about ... anybody who thinks they have found a<br>
> better solution can easily check it ... and then (if it pans out) easily<br>
> prove it by one additional average distance calculation ... a drop in<br>
> the bucket compared with the millions of such calculations required for<br>
> an exhaustive search for the winning order, even in an election with<br>
> only ten candidates, for example.<br>
><br>
> So the intractability issue is mostly an inconvenience ... but the clone<br>
> dependence is a deal breaker ... the whole impetus for single winner<br>
> election method reform is the spoiler problem ... an example of clone<br>
> winner failure.<br>
><br>
> K-Y fails clone winner because the Kemeny distance itself, the<br>
> fundamental basis of the method, is distorted by cloning.<br>
><br>
> There is a way to declone the Kemeny metric, but at a sacrifice of<br>
> monotonicity and simplicity .... in fact, any Universal Domain metric<br>
> will result in a monotonicity failure, a clone independence failure, or<br>
> both. What is needed is a way of reducing the cost of shuffling clones<br>
> around within their own clone set ... ranking clones equally would do<br>
> that, but with a loss of ability to help decide which of them wins if<br>
> the set had a chance of producing a winner. Also is needed a way for<br>
> non-clones to pass through the clone set at a discount.<br>
><br>
> However, going outside of Universal Domain by allowing one or more<br>
> approval cutoff (or other virtual) candidates (as ASM does) makes<br>
> decloning more or less automatic as long as clone sets more or less<br>
> respect these cutoffs, and in the case of Kemeny distance, a<br>
> transposition with a cutoff candidate is significantly more costly than<br>
> a normal transposition....[The Kemeny Distance between two candidate<br>
> rankings is the number of transpositions required to convert one into<br>
> the other.]<br>
><br>
> K-Y started out in the old Universal Domain ... strict rankings<br>
> required... so I am happy to hear that it has been adapted to the<br>
> relaxed UD rules allowing equal rankings and truncations ... but that is<br>
> not far enough to solve the clone problem of K-Y or to distinguish<br>
> between ballot sets resulting from burial attacks and chicken attacks<br>
> ... even clone-free UD constrained methods like River, CSSD, and Ranked<br>
> Pairs are incapable of making that distinction, as I have reminded<br>
> readers of the EM list many times.<br>
><br>
> The next step in UD rules relaxation should be either general allowance<br>
> of virtual candidates or else Ranked Rankings ballots that allow<br>
> expressions of relative strength of preference to be utilized.<br>
><br>
> Then, for example, clone free metrics can be used, and Borda can be<br>
> decloned without sacrificing monotonicity. Many of the excuses for the<br>
> (purportedly psychologically stressful) requirement of cardinal ratings<br>
> would vanish.<br>
><br>
> So that you can judge for yourself rather than rely on what somebody<br>
> else told you about the seriousness of K-Y's spoiler problem, here is an<br>
> example ...<br>
><br>
> 40 A>B>C<br>
> 30 B>C>A<br>
> 30 C>A>B<br>
><br>
> A wins according to K-Y rules and any other method anybody has ever<br>
> invented based on Universal Domain rules.<br>
><br>
> So according to clone-winner, a member of A's clone set should win if A<br>
> is cloned.<br>
><br>
> Suppose the A faction ranks the clone members in the order a1>a2> ...<br>
> a9, but the other factions rank this clone set in the opposite order<br>
> a9>...>a1. This will be the Kemeny order among the clones ... in fact,<br>
> to change from one clone order to the other takes a minimum of 36<br>
> transpositions... so changing all 60 of the reverse orders would require<br>
> 60*36 while changing the other 40 ballots would require only 40*36. The<br>
> difference is 36*20 or 720, a great cost (i.e.distance) saving by<br>
> rejecting the A faction order.<br>
><br>
> This puts the A faction ballots at a significant disadvantage compared<br>
> with the other two orders, so one of them will be the winning order<br>
> after the dust clears.<br>
><br>
> The A faction would claim that a2, a3, ...a9 spoiled the chances of<br>
> their favorite a1. That's why clone winner failure is referred to as<br>
> the spoiler effect.<br>
><br>
> That's not the only kind of clone dependence suffered under K-Y ... it<br>
> also suffers from crowding, for example; If B were cloned, and the C and<br>
> B faction ranked the clones in the same order and A in a significantly<br>
> different order, that could cost A the election.<br>
><br>
> On the other hand if we were not constrained by UD, the factions could vote<br>
><br>
> 40 a1>a2> ...a9>>B>C<br>
> 30 B>C>>a9>...>a1<br>
> 30 C>>a9>...>a1>>B<br>
><br>
> for example, and the extra cost of moving {A} around could save the<br>
> first faction order.<br>
><br>
> Does that help clarify the situation?<br>
><br>
> Thanks!<br>
><br>
><br>
><br>
> El vie., 29 de oct. de 2021 4:29 p. m., Kristofer Munsterhjelm<br>
> <<a href="mailto:km_elmet@t-online.de" target="_blank" rel="noreferrer">km_elmet@t-online.de</a> <mailto:<a href="mailto:km_elmet@t-online.de" target="_blank" rel="noreferrer">km_elmet@t-online.de</a>>> escribió:<br>
><br>
> On 10/29/21 8:09 PM, Richard, the VoteFair guy wrote:<br>
><br>
> > > (2) it fails clone independence,<br>
> ><br>
> > It has a nice balance between clone independence and independence of<br>
> > irrelevant alternatives. "Fails" just means the failure rates are<br>
> not<br>
> > zero.<br>
><br>
> I'd rather pick a Condorcet method with Condorcet methods' IIA<br>
> resilience (when there is a CW) *and* full clone independence, than one<br>
> with the former but not the latter. :-)<br>
><br>
> Since that option is available, I mean.<br>
><br>
> -km<br>
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><br>
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</blockquote></div>