is as good a friend as one who encourages me to
keep trying.
Forest
-Original Message-----
From: Forest Simmons [mailto:[EMAIL PROTECTED]]
Sent: Saturday, 13 January 2001 9:05
To: [EMAIL PROTECTED]
Cc: Francis Edward Su; Steven J. Brams
Subject: [EM] Proportional Representation vi
Just as the STV system of proportional representation uses the front end
of the Borda Count (ballots with the candidates ranked), so can the front
end of Approval Voting (ballots marked with approved candidates) be used
to achieve another system of proportional representation.
Think in terms of
Greetings to all election methods aficionados.
I'm a new guy on the list, so I hope it's OK to jump right in and join the
fun.
Here's a line of thought concerning voting methods in general, as well as
Approval Voting in particular, that some of you might find interesting:
The first time I
wins instead of
his true favorite (similar to single-winner approval voting).
Bart
Forest Simmons wrote:
Michael Welford has independently hit upon the same method as mine for
Proportional Representation via Approval Voting.
I'm forwarding his brief explanation, since I still
Craig, without trying all 56 possible subsets of size three I did verify
that under PAV the combination ABH wins against AEH, and even more so when
we assume that the voters approved half of the candidates.
I think this is reasonable for the following reasons.
The two combinations disagree only
, a complaint about existing PR methods is that they
require ad hoc solutions for the inclusion of candidates with broad,
middle of the road support.
Do we have something worth pursuing here?
Forest
On Fri, 19 Jan 2001, Forest Simmons wrote:
Craig, without trying all 56 possible subsets of size
Joe, I used to think like you do on this matter, and I like the civil
rights idea and the public appeal idea, but the voter who wants to exert
maximum influence on the results of the election will do better by voting
at the extremes.
It's refreshing that someone would sacrifice this influence
On Sun, 21 Jan 2001, Bart Ingles wrote in part:
Of course you need to count votes for combinations,
and not just for individual candidates. In which case complexity of the
count is definitely a concern. Administering the election must be
manageable, and the process must be
One of the reasons citizens don't vote is voter apathy born of despair:
"What good will it do, none of the candidates have my interest in mind."
A major objective of election reform is to overcome this despair.
Let Pij be the subjective probability in the mind of the i-th voter that
the j-th
On Tue, 23 Jan 2001, LAYTON Craig wrote:
It seems to me that there might be a "tragedy of the commons" dilemma
here. The voters know that if they all stick to their agreement to vote
their honest probabilities, the outcome for the group will be best,
This is difficult. Numerically
Lets see how PAV stacks up against list PR.
Suppose there are K seats to be filled in a multiwinner election, and that
there are M single minded factions with members in proportion n1:n2: ...
:nM . Suppose further that the sum n1 + n2 + ... + nM is exactly K, the
number of seats to be filled.
I thought this might be of interest.
Date: Thu, 18 Jan 2001 15:05:50 -0500
From: "Steven J. Brams" [EMAIL PROTECTED]
To: Forest Simmons [EMAIL PROTECTED]
Subject: Public Choice Society meetings
I thought I'd call your attention and Francis's to the upcoming
Public Choi
In a recent posting Mike Ossipoff mentioned that there are better
alternatives than the Borda Count for converting ranked ballots to
ratings.
I'm not sure what he had in mind, but here's one thought along those
lines.
Suppose that someone came running after a two winner election and told me
Thanks to everyone for their insights on the Borda Count.
I do not intend to propose the use of the Borda Count (or any other method
that converts rankings to ratings) as a practical election method. But
when someone (like Craig L.) proposes a hypothetical situation in terms of
rankings, and
the same result, except for borda, which produced a
wildly different result (out of six candidates, the candidate who won the
borda count came third in the rating system, and did even worse in some of
the others).
I thought it was quite interesting.
-Original Message-
From: Forest
Thanks to Bart for repeating a posting of Joe Weinstein.
I appreciate Joe's comments on terminology, especially that they should
somehow reflect both ballot type (whether rankings, ratings, pass/fail,
lone mark, multiple mark, etc.) and scoring method.
People tend to assume that each ballot
On Tue, 6 Feb 2001, LAYTON Craig wrote:
Billy would also be the Condorcet winner.
Well, yes, no and maybe.
He would be what we might call the "Borda/Condorcet winner", i.e. the
"Condorcet winner" based on the (very likely) insincere ballots intended
for a Borda Count. But it is not so
On Wed, 7 Feb 2001, Donald Davison wrote:
Dear Forest Simmons,
On the 26th of January, you sent a letter to me and to the
instantrunoff list. I made a reply, but I was waiting for the list to
publish your letter before I sent in my reply. I like to have a gallery.
Forest: Since you
Dear Ultra,
I hope you never go over to the dark side.
Forest
On Fri, 9 Feb 2001, Ultra Runner wrote:
Donald Davison wrote:
Approval Voting does subsidize the lower candidates while Irving
insists on treating all the candidates and all the parties and all the
voters with equality.
I would like to hear your idea.
Forest
On Fri, 16 Feb 2001, lvtinnin wrote:
Hello,
I am new here. I have an idea for improving the voting method a
little. It would not cover all areas of voting, but it would be
directed at eliminating ballots with too many votes for a candidate,
and
. Applying IRV to the reversed preference problem (to do the
eliminations) has improved on IRV itself.
Note that this process is ideally adapted to recursive programming.
On Wed, 21 Feb 2001, Forest Simmons wrote:
Can anything be salvaged from IRV? I think so: it's an ill wind indeed
that blows
Hi, I'm Forest. When you say "ties in voting preferences," I take it you
are talking about the individual voter filling out the ballot, and not
knowing what to do if he has no real preference in the case of two of the
candidates. Is that right?
The answer to this question is that some versions
] wrote:
Forest Simmons wrote
is it possible for IRV to pick the same candidate as both the best
and the
worst? In other words, is there a pair of examples which are
identical
except for the reversal of preference directions, that both have
the same
winner when IRV
As DEMOREP demonstrates below, IRV fails to successfully implement its
implicit ideal of eliminating the worst candidates before the final choice
stage.
And as I mentioned before, finding the worst is as hard as finding the
best, so only a recursive elimination strategy (which IRV is not) has
Any trivial method can correctly distinguish winner and loser in a two way
contest. How about a three way contest?
The answer is the same, yes, any old trivial method can correctly
distinguish winner and loser in a three way contest, IF (this is one of
those big IF's) the method is not just
The following email from me to Tony came back to me as undeliverable, so
I'm hoping he can get it in the [EM] list. Others can read, too.
Forest
-- Forwarded message --
Date: Fri, 23 Feb 2001 14:38:05 -0800 (PST)
From: Forest Simmons [EMAIL PROTECTED]
To: Anthony Simmons [EMAIL
That'll teach me to say,"Nobody can deny!"
On Fri, 23 Feb 2001, Bart Ingles wrote:
Forest Simmons wrote:
40 BUVWCXYZA
25 UVWCABXYZ
35 AUVWBXYZC
In this version (Blake's example with steroids) nobody can deny that some
of the candidates are much better t
Tony,
here's a simpler version of the Recursive Elimination Supervisor,
based on a suggestion of yours.
Step 1. Use the seed method in reverse to find the "Seed Loser" SL, from
among the N candidates.
Step 2. While the SL sits out, recursively supervise the seed method to
find an N-1 stage
ut (unless the winner
is the seed loser).
Forest
On Tue, 27 Feb 2001, Forest Simmons wrote:
Tony,
here's a simpler version of the Recursive Elimination Supervisor,
based on a suggestion of yours.
Step 1. Use the seed method in reverse to find the "Seed Loser" SL, from
am
What I call "strong IIA" says (roughly) that the winner of an election
shouldn't change if any of the other candidates is removed.
Strong IIA may be too stiff a standard by which to judge common methods.
If you point out to IRV supporters that IRV doesn't satisfy strong IIA,
they will say, "So
Thanks, and see clarifications below.
Forest
On Wed, 28 Feb 2001, MIKE OSSIPOFF wrote:
Forest wrote:
What I call "strong IIA" says (roughly) that the winner of an election
shouldn't change if any of the other candidates is removed.
Is it this?:
Deleting a loser from the
I have ambiguous feelings about my two favorite methods.
Sometimes it seems like Condorcet is over-elaborate, making fine
distinctions between the deck chairs on the sinking Titanic. (How's that
for a mixed metaphor?)
On the other hand, there are times when Approval strategy leaves me in a
Thanks to Martin Harper and Craig Layton for valuable critiques.
In particular, Martin is right. The voters should be able to make
distinctions among their unapproved candidates, too.
Here's a more ideal version of a compromise between Condorcet and
Approval, which could be considered a dyadic
On Fri, 2 Mar 2001, Forest Simmons wrote:
Thanks to Martin Harper and Craig Layton for valuable critiques.
In particular, Martin is right. The voters should be able to make
distinctions among their unapproved candidates, too.
Here's a more ideal version of a compromise between Condorcet
to
aggregate individual utility into social utility.
Forest
On Fri, 2 Mar 2001, Forest Simmons wrote:
One other thing. In a zero information election, start by expressing your
utilities in binary rounded to three binary digits, this takes you
directly to the second representation of the dyadic
I would like to make a suggestion for a multiple winner proportional
method that is as good or better than any I have heard proposed so far,
short of the Proportional Approval Voting (PAV) that Michael Welford and I
proposed several weeks ago. (Full strength PAV would involve checking all
of the
Craig, thanks for the critique.
I mentioned in one posting that I owed Joe W., Bart I., and Martin H. for
certain insights that led to the need for (and certain features of) a
finer resolution dyadic system.
I also owe you for your excellent example with utilities and poll results
that showed
On Tue, 6 Mar 2001, MIKE OSSIPOFF wrote:
When I mentioned strategies for 2-balloting Approval, where the
1st balloting doesn't elect anyone unless they have a vote total
equal to half the number of voters, or more, from an article
by Tideman and (I believe it was) Merrill, I should have
On Sat, 3 Mar 2001, Joe Weinstein wrote (in part):
On Fri. 2 March (or Sat. 3 March in Sydney) Craig Layton wrote:
"Joe wrote (in relation to Forest's Condorcet//Approval compromise):..."
My query: Joe who? Not I.
Craig was thinking of Martin Harper's response to my first
versions
In his masterful article at
http://www.barnsdle.demon.co.uk/vote/noagree.html
Mike Ossipoff proposes a clever meta-method called "voter's choice" to use
when there is no agreement among knowledgeable voters on which method to
use. I think Nobel Prizes have been given for less ingenuity.
Each
Here's a simple example that I hope will be of interest to those who
believe that there can be valid distinctions in levels of approval:
Utilities: 3 210
--
Faction 1: AB C
Faction 2: CB A
Assume zero information from polls,
On Tue, 6 Mar 2001 Mr. Demolition Repo Man wrote:
Mr. X wrote about vote intensities.
Again- a scale vote goes from plus 100 percent to minus 100 percent.
Simple example-
Votes Percent Scale
2 A (1)
1 B (100)
Sorry for the intense B supporter (could be B him/her
On Thu, 8 Mar 2001 [EMAIL PROTECTED] wrote (in part):
---
D- The default vote is obviously minus 100.
Votes Percent Scale
2 A (1) B (-100)
1 B (100) A (-100)
3 Voters
Same result.
The respective averages for A and B are -32.7 and -33.3,
Good discussion, but don't you think that it would be easier to infer
all of the other ballots from CR than from a pure ranking?
On Wed, 7 Mar 2001, MIKE OSSIPOFF wrote (in part):
I like Voter's Choice for situations where people don't agree on a
voting system. Of course if they don't agree
Dear EM list members, this is a draft of an article that I am sending to a
progressive newsletter that I subscribe to. Before I submit it, I would
like your comments and suggestions.
Thanks to all of you for ideas you have already given me.
Sincerely,
Forest
Thanks, Martin, I'll incorporate both of those suggestions.
Forest
On Fri, 9 Mar 2001, Martin Harper wrote:
two points.
Forest Simmons wrote:
By way of comparison the Approval ballot would look like this:
Candidate | Oval
---
Bush
I see your point. And I also see that there could be several different
reasonable versions of Voter's Choice, any one of which would be an
elegant way to resolve the lack of concensus on method.
The amount of variation in ballot types would have to be a function of the
time and energy that was
Dear EM folk,
here's my second draft. I still need suggestions, especially for websites
for people to get more information on pro's and con' of different methods.
Thanks,
Forest
---
Dear Editor:
As mentioned more than once in your newsletter an important
Thanks Richard, I'll incorporate all of your valuable suggestions one way
or another.
I guess that "Instant Runoff Voting" is intended to be a simulated version
of a certain kind of actual runoff where the voters are required to go to
the polls up to N-1 times when there are N candidates.
It's
On Wed, 14 Mar 2001, LAYTON Craig wrote:
Forest wrote:
Would "instant voteoff" be too suggestive of elimination (even though it
naturally includes full Condorcet through the round robin playoff analogy
mentioned above)?
That sounds a bit Survivor.
By the way, I'm no sports fan, but
Tom Ruen has recently reminded us of the possibilities of Approval Runoffs
or "Freedom Voting" in committee meetings and similar situations.
For the record I would like to explain how this type of runoff can be
simulated instantly from Dyadic Approval ballots as easily (and
accurately) as IRV
e an entry recording how many labels
of each type, and there are 2^N different possible labels when there are N
candidates.
On Wed, 14 Mar 2001, Forest Simmons wrote:
Tom Ruen has recently reminded us of the possibilities of Approval Runoffs
or "Freedom Voting" in committee meetings an
Dear Hugo,
I suggest getting a preference ballot from each official involved in the
determination of the ballot order.
Have them order the candidates by preference and, in addition, indicate
the boundary line between approved and unapproved candidates.
Use the approval scores to get a
position) should be allowed to rotate
down.
Peace,
Forest
On Wed, 14 Mar 2001, Forest Simmons wrote:
Dear Hugo,
I suggest getting a preference ballot from each official involved in the
determination of the ballot order.
Have them order the candidates by preference and, in addition, indicate
On Wed, 14 Mar 2001, MIKE OSSIPOFF wrote (among other things):
I was surprised disappointed to find out that, with very few voters
the above-mean strategy isn't valid in Approval. I kept denying it
for a long time, not because it was something I didn't want to believe,
but because it
I have some comments on Mike's response to Bart. See below.
On Sat, 17 Mar 2001, MIKE OSSIPOFF wrote (in part):
My 2 main points about the Condorcet badexample apply here:
1. The voter median will be a popular crowded place, and if you think
the only candidate there will be someone who is
On Thu, 15 Mar 2001, MIKE OSSIPOFF wrote (in part):
WDSC says:
If a majority of all the voters prefer Smith to Jones, then they
should have a way of voting that will ensure that Jones won't win,
without any member of that majority reversing a sincere pairwise
preference ordering.
On Sat, 17 Mar 2001, MIKE OSSIPOFF wrote:
Demorep said:
It is not *average* utilities that are important.
I think Demorep has a point here. Instead of optimizing average SU
someone might want to optimize median SU, or most likely SU, or minimize
the likelihood of SU below some cutoff
Mike, the definition of Dyadic Approval has evolved slightly since the
original, so I welcome this chance to summarize to date. Plus I know that
Tom Ruen and other recent list members are interested, too.
Dyadic Approval is a generalization of both Approval and Condorcet.
It generalizes
On Fri, 23 Mar 2001, Tom Ruen wrote:
Anthony,
I appreciate your defense for approval. I'm not surrendering full-vote
Approval as a good concept. I agree with your defense for one vote per
candidate in approval.
Plurality and approval are different systems and I don't think you can
Another way to look at Approval in terms of one vote per voter:
Suppose there are N candidates. Count each approval as exactly one Nth of
a point. That way no man can vote a total of more than one point. (And
he's a fool to vote a full N/N .)
You can vote less than one point if you want, same
factor.
--
Martin
Forest Simmons wrote:
Consider the following summary of 90 preference ballots:
40 C A B
20 A B C
30 B C A
IRV gives the win to B. Reverse all of the preferences and IRV still
gives the win to B. However, we cannot fault IRV in this case because
ion is due to computational complexity, exponential
in the number of winners.)
I guess grading too many finals brought out the worst in me.
Just be glad you're not one of the students in the last class to get
graded.
Peace,
Forest
On Sat, 24 Mar 2001, Forest Simmons wrote:
Tom, I am cur
Xander,
I want to elaborate a little on one point that I passed over rather
glibly.
Forest
Xander wrote (in part):
I see the potential failings of IRV, but it does allow us to show our
support and greatly reduces the odds, if not eliminate them altogether,
of
spoiling. My question about
, 27 Mar 2001, Martin Harper wrote:
Forest Simmons wrote:
I like your idea. But I still think there is no stigma attached to
failing the reverse symmetry criterion when there is no (unique) Condorcet
winner, so I would suggest that you throw those out of the count.
Forest
Hmm - I'm
On Tue, 27 Mar 2001, MIKE OSSIPOFF wrote:
"What's wrong with, instead of 'One person one vote', 'One person
one equal supply of votes, of which one may use as many as one wishes?"
This "equal supply of votes" would go well with the tradition of having
more than one race on the same
Tom,
Bart Ingles has the best introduction to Approval that I have ever seen.
Be sure to get him to send it in.
Forest
Tom, in your example below you keep switching between 546 and 526 for the
size of the A + C faction. (It doesn't make any difference in the winners
by the two methods.)
Here's my two cent's worth:
I don't think that the same population of voters would have voted the same
on their ballots under
Hi, again. Martin asked how one would calculate the winner. Sorry, I got
distracted before making that clear.
I'm making this cumulative, so skip down to third installment for the
answer.
First Installment:
Dyadic Approval is a generalization of both Approval and Condorcet.
It generalizes
Mike O. recently reminded us that it seems impossible to get IRV
supporters to budge on anything. I think it is a sign of insecurity.
Before Mike reminded me of that, I was thinking of a method based on
preference ballots that might have some of the same psychological
attraction as IRV and still
I'm keeping this cumulative, so skip down to fourth installment for the
new stuff.
---
First Installment:
Dyadic Approval is a generalization of both Approval and Condorcet.
It generalizes Condorcet by allowing expression of
Demorep has a good point here, namely that election dynamics tend to make
certain kinds of distributions of candidates and voter preferences more
likely than others, as they evolve with time.
For example, suppose that we start with two major parties, P1 and P2, and
that in the process of
Craig, I like analogous ideas. They often yield insights about each other.
Here's my take:
We have triathlons, pentathlons, decathlons, etc. Let's imagine an
hectathlon with 100 events ranging from snowboarding, waterskiing,
archery, calf roping, sky diving, wind surfing, etc. to ice skating,
I want to thank Tom for the stimulation he has brought to this EM list.
Thanks, Tom.
I know you have grave reservations about IRV, but you see some value in
runoffs of various types, and you are willing to explore areas that we may
have neglected too much, if there is even a slight possibility
More thoughts on Universal Approval:
If there are N candidates, and two of them are A and B, then there are
2^(N-2) subsets that contain both A and B. Therefore ...
1. The maximum number of points that a candidate could get from one
pairwise comparison on one ballot would be 2^(N-2).
2. If m
, but sure beats IRV by a
long shot. And it does satisfy WDSC.
Forest
On Mon, 2 Apr 2001, Forest Simmons wrote:
Mike O. recently reminded us that it seems impossible to get IRV
supporters to budge on anything. I think it is a sign of insecurity.
Before Mike reminded me of that, I was thinki
Let me explain what I mean by the following phrase from a recent posting:
the inexorable, myopic, unidirectional march of an
elimination method.
Imagine a road rally on the west coast where the winning team is the one
that can get the furthest east of the starting point (in a specified
Thanks Mike, your summary about making unnessary irrevocable decisions
based on a fraction of available information early in an important project
gets straight to the point.
Forest
On Sat, 7 Apr 2001, MIKE OSSIPOFF wrote:
Good analogy. I often ask people if, in an important project,
I should have thought of that. Every method needs two names, one for
public consumption and one for scientific classification, like the latin
names for plants and animals.
I think the best one for public consumption would be "Instant Majority
Runoff" (IMR).
Forest
On Sun, 8 Apr 2001, Martin
Here's a single winner method with five distinctive slots for the
candidates.
Here's how you fill in the slots:
First put your favorite and worst candidate, respectively, in slots one
and five.
Next put the better and worse of the two front runners, respectively, in
slots two and four.
Then
Anthony, you missed your calling!
On Tue, 10 Apr 2001, Anthony Simmons wrote:
So Forest's new system should be called SuperVote
EM, and STV should be called SuperVote Plus with
DoofusGuard*.
(* failure to follow instructions may result in
election of imbeciles)
On Wed, 11 Apr 2001, Martin Harper wrote:
[snipped]
I would call your suggestion "Smith//Plurality" - the Smith Set is the smallest
possible set of candidates such that all members of the Smith Set pairwise beat
all non-members.
I *think* it's monotonic, but I'm not sure: Plurality
approved member of the
original Smith Set as the winner.
There are other variations, too.
Forest
-- Forwarded message --
Date: Wed, 11 Apr 2001 15:21:52 -0700 (PDT)
From: Forest Simmons [EMAIL PROTECTED]
Reply-To: [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]
Subject
In my conversations with fellow Greens I've learned that they can live
with non-monotonicity, they can live with elimination of Condorcet
Winners, and they can live with low average social utility.
The one feature that they cannot live with is the spoilage problem. They
don't want ever again to
This is more of a query about Lori Cranor's method than anything else.
If it really gives no strategic incentive for distorting ratings, it
sounds like the ideal way to use CR ballots.
Here's what puzzles me. On the one hand, it seems like any method like Ms
Cranor's that uses CR ballots to
for (or even trust) analysis that involves more than two steps of
logic. If the board is set up for checkmate in three moves, they won't
believe the analysis until two of the moves have been made.
Forest
On Thu, 19 Apr 2001, Anthony Simmons wrote:
From: Forest Simmons [EMAIL PROTECTED]
Subject
really is (in an SU sense, that is).br
br
Richardbr
br
br
Forest Simmons wrote:br
blockquote type=cite
cite=[EMAIL PROTECTED]">mid:[EMAIL PROTECTED];pre
wrap=This is more of a query about Lori Cranor's method than anything
else.brbrIf it really gives no strategic incentive for di
None of the Above by setting a
quota, which seems simpler than adding a fictitious candidate to the
ballot.
There may be other advantages to None of the Above which I am not aware
of (other than the fun that novelty always brings).
Forest
On Mon, 23 Apr 2001, Bart Ingles wrote:
Forest
, but
I don't know enough about bridge to conjure one up.
Richard
Forest Simmons wrote:
I'll be more specific. Suppose that there are three candidates A, B, and
C , of which your favorite is A, and that there are five voters. You ask
the other four ahead of time what their utilities
Yes, I keep coming back to the five slot method too. It really gives ten
choices if you count AB as half way between A and B, and you count no
grade as below F. That should be plenty of choices for any single winner
election.
I'm beginning to like Cranor's method which starts with CR ballots,
I like this ACMA method. It requires more marks on the ballot, but they
are easy to make, and their purpose is clear. The thing I like best is
that it is an Approval completed Condorcet method, so it satisfies the
Favorite Betrayal Criterion (FBC) and more.
In fact, if I am not mistaken, it
(Buchanan).
Forest
On Thu, 26 Apr 2001, Martin Harper wrote:
Forest Simmons wrote:
In any case, if Cranor's method were used in public elections, there
should be a little check box on the ballot that asks if you want your
ballot Cranor optimized or not. If you check yes, then your
On Thu, 26 Apr 2001 [EMAIL PROTECTED] wrote:
I would suggest limiting NOTA variations to executive and judicial office
elections.
Legislative bodies do not (and never should) go out of existance and can fill
any vacancies if the voters reject all of the executive and judicial office
On Thu, 26 Apr 2001, Bart Ingles wrote:
NOTA may be feasible if the office to be filled is considered optional,
so that if NOTA wins (or at least wins repeatedly), the office is left
vacant. But in that case, the office doesn't sound very important in
the first place, and probably
The purpose of this posting is to answer Demorep's concerns (see below)
about the complexity of the Five Slot Ballot, and to advocate another use
for it (simpler than my median method that he refers to) as our best
chance of making Approval psychologically palatable to citizens of the IRV
satisfies IRV psychology.
There may be other better solutions, but I doubt that they will be as
simple as this and still beat IRV in every category.
Forest
On Fri, 20 Apr 2001, Blake Cretney wrote:
On Thu, 19 Apr 2001 15:27:41 -0700 (PDT)
Forest Simmons [EMAIL PROTECTED] wrote:
In my
I would like to make a couple of suggestions relating to Approval Runoff
that address your questions.
1. The natural ballots for Instant Approval Runoff are Dyadic Approval
Ballots. At each stage of the runoff the coarsest remaining inequality is
the current approval cutoff.
Remember that on
:
Forest Simmons wrote:
Medians are more democratic measures of general utility than are means.
A problem regarding medians was pointed out to me a couple of years ago,
when I had claimed that,
Medians are a natural way of evaluating rated examples,
since a candidate with the highest
On Tue , 1 May 2001, Martin Harper wrote:
Forest Simmons wrote:
I will argue in another posting that in general maximizing mean utility is
less democratic than maximizing median utility, which in turn is less
democratic than maximizing (number of voters receiving) acceptable
I should have defined democratic .
My conception of democracy is what Noam Chomsky describes as a society
in which a decent person would want to live.
In such a society, there would be lower priority for advancing the rich
(in utility) to ever greater hights, and more effort would be focused
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