Michael Ossipoff email9648742 at gmail.com
Tue Oct 29 08:28:08 PDT 2013

 On Sun, Oct 27, 2013 at 2:49 PM, Chris Benham <cbenhamau at yahoo.com.au> wrote:

> I have a standard that says that if a method isn't at least as resistant to
> the Burial
> strategy as the "Benham" method (if there is no CW, do IRV-style
> eliminations until
> among remaining candidates there is), then if there is a candidate X that is
> uncovered
> and positionally dominant it must elect X.

If chicken-dilemma defection isn't a problem, and CD isn't needed (but
it is here, now)--and of course if FBC isn't needed either--then we're
free to gain more majority-rule guarantees than would otherwise be
possibe...like SFC and SDSC. We're free to use an all-pairwise

Of course the choice depends on the goal. If the goal is to encourage
sincere voting, to avoid incentives or needs to vote other than
sincerely, to allow a majority to get the best they can without
strategy, to let the electorate elect the CW without strategy: Then
compromise is important. Fully and eqully counting preferences at
various different levels is important. I suggest that "all-pairwise"
methods are what do that. WV pairwise methods like RP and River.

But one could propose for different conditions, in which majorities
aren't trying to get the best they can for themselves, and electorates
aren't going to do whatever it takes to elect the CW. In other words,
one could propose for a non-majoritarian electorate.

That would be a fourth kind of conditions, in addition to the three
that I've already listed:

4. Sincere-rating, non-majoritarian conditions:

instead of wanting to get the best they can for themselves, as members
of majorities, and intstead of doing whatever it takes to elect the
CW, the best that they can get, people just want to rate the
alterntives sincerely, in order to collectively optimize the _overall_
satisfaction and good in some specified way (such as maximizing
social-utility (SU), or minimizing the greatest harm, a la Rawls).

I suggest that #4 is a lot farther away than #3 (Ideal Majoritarian).
But they're all hypothetically worthwhile for dicusion.

I suggest that there could be about 3 versions of #4:

4a) Linear.

That's ordinary Score voting and counting.

4b) Near Rawlsian:

Dislike is much more stongly-counted than like. The obvious way seems
to be to let a zero rating represent "Ok, but not particulary good or
bad", and then allow positive and negative ratings for paricular like
or dislike. In some way, count the negative ratings much more

Of course that could be done in several ways:

A monomial function of the negative rating:


...where A and p are constants, and x is the voter's rating (these are
negative ratings).

Or an exponential function, with its constants chosen to give desired
results. That would make strong dislike even more strongly-counted, in
comparison to weaker dislike.

Some form of:

-A  * exp(B*(-x)),

...where A and B are constants, chosen to suit.

If the above functions (F) could ever be less negative than x, then say:

F2 = min(F, x)

...and use F2 for that voter's final counted rating of that alterntive.

4c) Rawlsian:

The same positive and negative rating scale as above, but just
interpret the ratings linearly,  and elect the alternative whose
lowest rating (from some individual voter) is the highest.

4c is the ideal best, it seems to me. But it also seems impractical,
because one mistaken individual, or one individual who isn't really as
unselfish as the rest, could spoil the result.

So 4b seems more feasible and practical than 4c.

I empasize that #3 is far away, and that #4 is much farther away.

#2 is what's relevant for practical voting-system reform discussion,
because #2 is what would come next, from where we in this country now
are, and #2 is when voting-system reform could become possible at all.

> The  Strategy-Free Criterion can demand that such a candidate X lose, so I
> reject the
> idea that meeting it is especially desirable.

It depends on which is more important:

Letting majorities get what they want without strategy, letting people
elect the CW without strategy ...to the greatest extent possible,


Positional considerations and the cover-relation.

It seems to me that before we reach #4, strategy-freeness should be the goal.

And, after we reach #4, why would we care about anything other than
sincere ratings and (in some way) optimizing the overall satisfaction?

In other words, why would we choose a combination of pairwise and
positional considerations?

Well, conceivablly such a combination could be chosen, for an
experimental partial transition from #3 to #4.

> 25 A>B
> 26 B>C
> 23 C>A
> 26 C
> 100 ballots.
> B>C 51-49,  C>A 75-25,  A>B 48-26.
> Top Ratings:   C 49,   B 26,   A 25
> Inf. Approval: C 75,   B 51,   A 48.
> MPO:              C 51,   B 48,   A 75
> C is uncovered and positionally dominant, but SFC says it isn't allowed to
> win.

Of course, if we want to minimize strategy-need for majorities who
want the best that they can get, and for peope who want to elect the

C has a lot of people who have indicated that they don't want it. B
has fewer people who have indicated that they don't want it.

Minimizing strategy-need requires compromise, and giving precedence to
pairwise-votes. That's why I say that, for #3, ideal-majoritarian
conditions, the pure-pairwise methods are the best, with RP and River
being the best recommendations.

But something else might be good for an experimental transition from #3 to #4.

I admit that, in your example, it looks as if C should win, because we
naturally highly value positional dominace, and the optimization of
overall satisfaction with sincere ratings.

By the way, one more thing about 4a:

Maybe people would rather rank than rate. Maybe rating is more
difficult to do, or problematic to interpret.

In that case, Borda would be a good 4a method.

I suggest, as the Borda version, my Summed Ranks (SR) method:

Rankings. Equal ranking and truncation allowed:

The winner is the alternative that has fewest instances of someone
being ranked over it, summed over all of the ballots.

Power-truncation is in effect:

Any alternative that you don't rank is counted as having all the other
candidates ranked over it, on your ballot.

[end of SR definition]

The reason for that method of counting, and the power-truncation, is
that even with 4a, linear interpretation of ratings, it's still very
important fully count dislike, and to give voters full opprtunity to
express it.

> MMPO (IA>MPO)  elects B, but if 4 of the 26 C voters change to A then C
> wins.

MMPO deserves come consideration as an alternative to ICT and
Symmetrical ICT, for current conditions (That's conditions #1). I
prefer ICT and Symmetrical ICT because of MMPO's bottom-end

Additionally, others have pointed out that MMPO's plurality-failure
could take a form that could be devastatingly used against it by
heaviy-funded opponents.

Michael Ossipoff

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