[EM] minmax is not a good public election method

Kevin Venzke stepjak at yahoo.fr
Tue May 31 22:09:59 PDT 2005


--- James Green-Armytage <jarmyta at antioch-college.edu> a écrit :
> James:
> >> 	My point is that as long as you are in a political climate that will
> >> welcome a pairwise count method, you should choose a good pairwise count
> >> method, one that at least passes Condorcet, Smith, MMC and CL. These
> >> failures of MMPO are an absolutely unnecessary liability.
> >> 	If A beats B, and B has absolutely no beatpath to A, then in my opinion
> >> no good pairwise count method will elect B.
> Kevin:
> >
> >I suggest using CDTT,MMPO instead, then, so that MMC is satisfied. 
> 	If the electorate is ready for something as complicated as that, then
> beatpath(wv), ranked pairs(wv), and river(wv) will be viable options.
> Aren't these methods more elegant than CDTT,MMPO?

Why do you think so? Finding the CDTT is considerably easier than finding
the Smith set, since you don't even have to check which side wins each
pairwise contest. When you calculate MMPO scores you don't even have to
consider which candidates are in the CDTT.

With RP, River, and one way of doing beatpath, you are repeatedly checking
for cycles.

I don't think "elegance" is the main point; I bring up CDTT,MMPO as an
attempt to preserve MMPO's good qualities, not to compete with Schulze,

> >I don't
> >agree that even weak defeats need to be acknowledged, particularly if
> >something else is gained by it, such as LNHarm.
> 	You mean non-majority defeats, right?

Not necessarily, since MMPO's mechanism also tends to ignore weak wins.

> Does CDTT,MMPO retain both FBC and LNHarm?

In the general case, no. That's why it's a trade; you get Minimal Defense
and lose some LNHarm. However, I've posted some messages detailing the
circumstances under which CDTT(,MMPO,FPP) fails LNHarm with four 
candidates, and I'm pretty satisfied that it's still worthwhile. In a
comparison with Schulze(wv), the failure rate was cut to 7% of that
method's, IIRC.

FBC performance is probably also decent; there seems to be a relationship
between LNHarm and FBC with pairwise methods. LNHarm says increasing v[a,b]
can't hurt C, and FBC implies that increasing v[a,b] can't help {a,b}.
Since CDTT satisfies LNHarm strictly in the 3-candidate case, it also
satisfies this latter condition (obviously, if you think about it).

> Kevin:
> >That is barely true. Any example needs a majority-strength cycle.
> 	Yes it does, and bare majority strength cycles are more probable than
> supermajority strength cycles. How likely are majority strength cycles,
> occurring naturally? Not very likely, perhaps, but once again I think that
> the liability is unnecessary.

Well, obviously it's unnecessary if you don't think LNHarm is valuable, which
clearly you don't, since you value criteria that avoid rare but really bad
situations, more than criteria which (according to me) provide guarantees
that are almost always useful.

> >> 	So, in choosing MMPO instead of something like beatpath, you are
> >>willing to trade Condorcet, Smith, MMC, CL, and IC for later-no-harm and 
> >> what I call elimination of compromising-reversal incentive (and you call 
> >>FBC). I
> >> don't know if I can change your mind about this, but at least I can
> >> voice my opinion that this is a very misguided trade.
> Kevin:
> >
> >I wonder if you realize how related those five criteria are.
> 	I believe that Smith implies Condorcet, MMC, and CL. I don't think that
> IC is as closely related to the other four.

Well, if you want to insist on Smith, why do you bother to type out 
"Condorcet," "MMC," and "CL"? Just to have a long list?

> James:
> >
> >> 	Why do you think later-no-harm is so important?
> Kevin:
> >
> >Because it gives voters the ability to safely rank all of their
> >preferences. 
> >It reduces defection incentive (that is, defection by truncation). And as
> >a result, it is more likely that MMC will be satisfied in practice.
> 	It is not always safe for voters to rank all preferences in MMPO. As in
> WV, truncation (equal ranking) can still be useful (arguably necessary in
> some cases) as a deterrent counterstrategy.

Great... I've already said all of that. In any case, I don't think this
weakens my point much.

> >I'm not sure about this. What if you don't expect that your favorite
> >candidate
> >will win? Then ranking him above or equal to your compromise choice can do
> >little other than frustrate your compromise's ability to be elected.
> >
> 	If your favorite candidate (F) really doesn't have enough support to be a
> viable candidate, then s/he is unlikely to have a beat against your
> compromise candidate (C), in which case C can't be harmed by your
> expressing an F>C preference (in Smith-efficient methods). (Thus, your
> preference won't cause the election of a greater evil (E).) 

I know it's unlikely. But it would be nice if the voter could be assured
that he can always rank his favorites at the top.

Kevin Venzke


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