[EM] Comments on a posting from Benjamin Grant
dickburkhart at comcast.net
Mon Jan 6 13:52:31 PST 2014
The restricted Borda that I recommend is similar to Approval with rankings.
It does not require sincere voting. For example, in a 3 positions contest,
suppose group I with 55% of the vote wants to elect candidates A, B, and C,
while group II with 45% of the vote prefers candidates D, E, and F but
decides to focus on candidate D so as not to be shut out. That is, group I
could vote strategically by random ranking of A, B, C in hopes that they
could use their majority status to win all 3 positions. But this yields an
average of 2.0 tallies per candidate, or a vote proportional to 0.55 * 2.0
= 1.10, while candidate D wins with 0.45 * 3.0 = 1.35.
4802 S Othello St, Seattle, WA 98118
206-721-5672 (home) 206-851-0027 (cell)
dickburkhart at comcast.net
From: Michael Ossipoff [mailto:email9648742 at gmail.com]
Sent: January 06, 2014 12:41 PM
To: Dick Burkhart; election-methods at electorama.com
Subject: Re: [EM] Comments on a posting from Benjamin Grant
Others have very nicely laid Borda to rest, and so there's ittle if anything
for me to add on that matter.
I'll just say that in at least some of Myerson's & Weber's articles,
probably including the one in which the introduce their "Voting Equilibrium"
(now often called Myerson-Weber equalibrium), they mention that Borda
achieves the distinction of actually being worse than Plurality--as regards
such things as electing two unliked parties forever at Myerson-Weber
equilibrium., or encouraging corruption (the subect of another Myerson-Weber
Could Borda be recommended for anything, under any conditions, for some
applicaton. Maybe under certain circumscribed conditions.
I like Approval for things like Academy Awards, or for family voting on a
movie. Advise people to only approve what they consider to be "Excellent".
That's what an approval would mean. Assume that people won't "lesser-evi"
strategize. So we elect the movie that is considered excellent by the most
people. Mediocrity shouldn't help when awarding the Academy Awards or voting
on the choice of a movie.
Of course the trouble with Approval, when there are only a few voters, is
that's it's tie-prone under those conditions.So, to avoid ties, one could
propose Score instead. Hopefully it would be sincerely-voted Score, not
strategically-voted Score. So, to avoid ties, we let mediocrity into the
So say there are only a few voters, suggesting the choice of Score as the
voting system, but suppose voters don't want to rate the alternatives
(movies or whatever). A very rough approximation to Score can be achieved by
Borda. So, under thoses circumstances, Borda might be a good choice. Note
that we're talking about a non-strategizing, sincere-voting electorate.
By the way, I don't think that Score would be the best way to maximize SU,
if that were one's goal. The CW usually maximizes SU, and a good ideal
majoritaian method (MAM is the best one) would be the best way to maximize
Say the electorate are a family who have no inclination to cheat eachother
by misrepresenting their utilities in Score. But if they're
altruisticallly-inclined, then might they not misrepresent their
utility-ratings in order to benfit others? I've observed that in a family
vote. That's another reason why I'd rather use MAM than Score, even if it's
desired to maximize SU. An ideal majoritarian method, MAM, is what I'd
prefer for family or organizational voting, under ideal majoritarian
conditions, or even under non-majoritarian, unselfish conditions, where
altruism could distort Score ratings. The exception would be for choices
where all we're interested in is excellence, in which case Appoval would be
my first choice, unless there are few voters and its tie-proneness is a
If MAM has a lot of mid-count ties, &/or a tied-outcome, and if it's desired
to avoid that, then that could be a reason to use Score or Borda, which,
might be less tie-prone. Speaking for myself, I'd use MAM in preference to
Borda, and even in preference to Score.and so I agree that, even for the
situation described above, Borda wouldn't be my favorite choice.
Of course, if people objeced to MAM's midcount ties, or tied-outcomes, then
Score, or Borda (if people insist on ranking instead of rating) could be
So I'm not saying that Borda can't be considered for anything. But for
official public political elections? Forget it.
I've defined, at EM, a Borda version that I called Summed-Ranks (SR), which
was intended to minimize its Borda problems.
On Sat, Jan 4, 2014 at 2:50 PM, Dick Burkhart <dickburkhart at comcast.net
<mailto:dickburkhart at comcast.net> > wrote:
The fundamental problem with criteria based on "X over Y" preferences
(Condorcet, Mutual Majority, etc.) is that all such criteria ignore the
intensity of the preference (a ranking of 5 to1 counts the same as 3 to 2,
for example). This is why Borda-type methods are superior - they don't throw
away critical information. Donald Saari explains the mathematics of this
well in "Decisions and Elections".
And if you want to elect a minority party candidate for President, Borda
might do it (by many second place rankings), but not IRV. For electing a
single position I recommend Borda using the top 3 rankings (assigning 3
tallies, 2 tallies, 1 tally respectively). To elect 'n' positions, I
recommend Borda using the top 'n' rankings (but at least 3), unless you want
truly proportional representation.
In Seattle this kind of Borda is often used at community meetings for the
public to advise on alternative courses of action. It is correctly preserved
as fair and works very well.
4802 S Othello St, Seattle, WA 98118
206-721-5672 <tel:206-721-5672> (home) 206-851-0027 <tel:206-851-0027>
dickburkhart at comcast.net <mailto:dickburkhart at comcast.net>
From: election-methods-bounces at lists.electorama.com
<mailto:election-methods-bounces at lists.electorama.com>
[mailto:election-methods-bounces at lists.electorama.com
<mailto:election-methods-bounces at lists.electorama.com> ] On Behalf Of
Sent: January 04, 2014 10:44 AM
To: election-methods at electorama.com <mailto:election-methods at electorama.com>
Subject: [EM] Comments on a posting from Benjamin Grant
Let's say that election after election people
see that more and more people are voting for Nader,although he is not
winning. Thinking optimistically (as some people like to) that this might
be the year that Nader could take it all, they put all their money on Nader
- they vote Nader, but *not* Gore. The result? Gore's numbers drop, Nader's
numbers rise a little, but Bush still get's the most!
That's the old standard criicism against Approval. The answer to it hasn't
changed, over all the thousands of times that objection has been made.
Approval isn't a pairwise-count methods. Approval doesn't aspire to, or
claim to achieve, the pairwise-cound ideal, whereby we can help Compromise
against Worst, while also helping Favorite against Compromise.
For that, we need rank-balloting. That's why, for the Green scenario, which
I've defined here, I recommend IRV, Benham, and Woodall. But preferably
Benham and Woodall, because of their Condorcet Criterion compliance. All of
the party platforms that offer a better voting system offer IRV. Though not
as good as Benham and Woodall, IRV is nevertheless an excellent choice for
the Green scenario (in which a progressive party has been elected, and its
progressive government and policies are in effect).
Brief IRV definition:
A candidate tops a ballot iff s/he is ranked (not necessarily along) at
first rank position on that ballot.
Determine which candidate currently tops fewest rankings. Delete hir from
all of the rankings.
Repeat till only one candidate remains un-deleted. Elect hir.
[end of IRV definition]
1. "X beats Y" means that the number of ballots ranking X over Y is greater
than the number of ballots ranking Y over X.
2. Do IRV till there's an un-deleted candidate who beats each of the other
un-deleted candidates. Elect hir.
[end of Benham definition]
1 The Smith set is the smallest set of candidates such that every candidate
in the set beats every candidate outside the set.
2. Do IRV till only one initial Smith set member remains un-deleted. Elect
[end of Woodall definition]
IRV, Benham, and Woodall meet the Mutual Majority Criterion and are free of
the chicken dilemma. Benham and Woodall additionally meet the Condorcet
Criterion. (In fact, they meet the Smith Criterion, which implies compliance
with the Condorct Criterion and the Mutual Majority Criteion).
There's much complain about IRV, when it fails the Condorcet Criterion (CC).
But if you're in a mutual majority, then you have no need to not rank
sincerely. Every mutual majority is assured that the winner will come from
its majority-prefered set (the set of candidates whom that majority prefer
to everyone else),merely by their ranking sincerely. ...even while freely
voting _among_ that preferred set sincerely.
That's the rank-balloting ideal, and the Mutual Majority Criterion (MMC)
guarantees that, provided that mutual majorties' sincere voting isn't
spoiled by media-induced favorite-burial, or the chicken dilemma. The Green
scenario premise says that we no longer have disinformational media, or a
public who could be deceived by them. IRV, Benham and Woodall have no
Therefore, IRV, Benham, and Woodall fully offer the rank-balloting ideal,
for mutual majorities.
And, if your preferred proposals are any good, and if others' judgement is
as good as yours, then you'll be in a mutual majority. So stop worrying.
Summary: Yes, the rank-balloting ideal would be good, and it's available to
mutual majorites. So you're right: IRV, Benham, and Woodall would be better
than Approval,for the Green scenario.
And the Green scenario is the relevant condition for whicho evaluate and
compare voting systems.
This seems almost worse than plurality, in a way, because at least with
plurality we all knew and admitted that we need to vote against the spoiler
effect, but Approval voting may actually suffer from it just as much while
not as obviously - meaning people may vote against there interests more by
not seeing that.
No. In Approval, if you thought you needed to help Gore :-) against Bush,
then you can still fully support Nader. Nader's support wouldn't be hidden.
It certainlly was, with Plurality voting strategy combined with
What makes Pluralilty so beautifully perfect for protecting the status-quo
is that it can keep on electing two unliked parties forever, at
Myerson-Weber equilibrium. It has been demonstrated that Approval won't do
Another way of expressing the usual Approval criticism is that Approval
won't immediately elect the voter-median candidate. No, Approval will
quickly (in a few elections) home in on the voter-median, and then stay
there. But it won't elect the voter-median in the first election. It won't
guarantee MMC compliance, or guarantee majority rule in the 1st election. If
you're in a hurry, then you want IRV, Benham or Woodall in Green scenario
conditions; and ICT in current conditions; and MAM in ideal majoritarian
conditons (but don't hold your breath waitng for ideal majoritarian
conditions in U.S. official public poitical elections).
This notion of first geting a better voting system, in order to elect a
better government is backwards: We won't get a better voting system under
the current government. Why should this government's owners allow a better
voting system? If we can actually vote for what we want in Plurality, then
we can get a better government. (if we've insisted on, and gotten, a
some of us may find that a
system in which people must accept that voting sincerely is not in their
best interest is not as good a system as one in which that is less likely.
Then support the best rank-method, for the paricular kind of conditions that
you want to recommend for.
And the only point I was making is for the 3rd party supporter (when there
are two stronger parties)
Perhaps he meant "two parties that are represented in the media as more
publicly-preferred, and are winning due public belief in the media's claims,
and possiby due to unverifiable vote-count results."
, there is no practical difference between
Approval and Plurality - either way, if he votes smart, he helps Gore beat
Bush, and Nader doesn't win.
Benjamin means "if you vote timid and gullible".
If he votes less smart, he can even
regrettably (from his point of view) help Bush beat Gore by only Approving
Benjamin means "If you aren't willing to vote for sleaze, or if you're
willing to give the other voters a little credit for not preferring sleaze
(in spite of what the media claim)."
So the fact that he is penalized by support Nader *over* Gore by getting
his last choice Bush is something that I thought Approval (and by
extension, Range/Score) were supposed to fix.
You thought wrong. I'm glad that you expressed that notion, giving me the
opportunity to disabuse you of it.
Approval is _not_ supposed to achieve the rank-balloting ideal.
What is Approval supposed to do?
1. Not force anyone to ever bury their favorite in orde to help a
2. Quickly (in a few elections) home in on the voter-median, and then stay
No, Approval isn't deluxe. If you want deluxe, look elsewhere, choosing a
good rank-method appropriate for the conditions for which you want to
Since this isn't fixed, tell me what the benefit of Approval is in the real
world over Plurality?
See immediatey above.
I want to be CLEAR about this, so please let me: I
am not asking how the what supporters of Approval voting promise will
happen, nor what Approval voting's creators intentions are - I am ONLY
asking about pragmatic and real-world RESULTS.
People would find out the extent to which other voters want the same thing
they want. Progressives would find out how many other voters want a
progressive party (Greens, Justice, Pirate, etc.). When it's clear that
there's no compelling need to help one sleaze beat another sleaze, because
the progressive parties are showing to be at least as popular, then, people
could start having the courage to actually stop voting for the sleaze who
(supposedly) isn't quite as bad as the other sleaze. Dare we hope??
For current conditions, ICT, or Symmetrical ICT is the best. It's better
than Approval because 1) It is free of chicken dilemma; and 2) It lets you
fully and fully-effectvely support both Favoite and Compromise, if that's
what you chose to do, while also allowing you to, instead, sincerely rank
Favorite over Compromise--thereby helping to make Compromse beaten and
Favorite not beaten, and by helping Favorite's top-count against Compromse's
top-count. ICT accomodates both kinds of voting.
But Approval is, of course simpler and easier to propose, and simpler and
easier to implement. Approval is the minimal improvement in Plurality. For
those reasons, I say that Appoval is the best voting-system for current
But, as I said, I don't there's any point in discussing voting-systems for
current conditions. The Green scenaio is the condition for which it's
relevant to discuss voting-system.
That's why I ignore Approval these days, and emphasize the best methods for
the Green scenario: IRV, Benham, and Woodall.
We have a great head-start in that regard, since IRV is the only voting
system proposed in party platforms (at least five of them, in the U.S.). And
Benham is a minimal change from IRV, making Benham the most ahievable, most
likely, improvement in IRV.
It is easy I think to see that with the Gore/Nader/Bush example, a Nader
supporter has to choose between stopping Bush and voting his true
preference. It seems to me that whatever the criterion is named that
covers that, that's an important one to embrace.
Of course it's desirable. I don't think it's a criterion, but it's
desirable. I call it the rank balloting ideal. In the Green scenario, IRV,
Benham, and Woodall offer it for you if you're in a mutual majority.
-------------- next part --------------
An HTML attachment was scrubbed...
More information about the Election-Methods