Dear EM aficionados,
Here's a method that elects the candidate with the best ratio of offensive
strength to defensive weakness. Until a better name comes up, call it
Offense/Defense or O/D.
For each pair of candidates X and Y, let F(X,Y) be the number of ballots on
which X is ranked equal
A while back Kevin came up with an interesting method that he called Gradual
Information Approval.
There are both ranked ballot and ratings versions of this method.
If there are K candidates then K-1 approval rounds are simulated.
In round m, the 1+K-m most approved candidates in the previou
Title: [Condorcet] Re: why the Schulze Method is a Better Proposal
Somehow this message didn't
pass muster for the Condorcet list.
From: Simmons, Forest Sent: Wed
9/28/2005 2:31 PMTo: [EMAIL PROTECTED]Subject: RE:
[Condorcet] Re: why the Schulze Method is a Better Proposal
Jeff
Title: Re: [Condorcet] A "Condorcet" by any other name still smells as sweet?
Markus wrote ...
"To be honest, I believe that whatever Condorcet methodwe
will propose, the chances that the state of Washingtonwill adopt the
proposed Condorcet method are not verygood."
Unfortunately, I thin
In the recent message quted below there are two questions.
1. What should we call the Approval method that allows an extra mark to
identfy the favorite candidate, thus satisfying the Approval voter's urge to
give more moal support to Favorite than to Compromise?
I suggest "Approval Plus" or
From: [EMAIL PROTECTED] on behalf of [EMAIL PROTECTED]
Sent: Sun 9/25/2005 12:00 PM
To: election-methods-electorama.com@electorama.com
Subject: Election-methods Digest, Vol 15, Issue 53
I had written ..
> Note that in ordinary Bucklin the ordinal informat
Title: [Condorcet] Re: why the Schulze Method is a Better Proposal
On Sun, 25 Sep 2005, Jeff Fisher
wrote:>> Cycles (Condorcet paradoxes) still exist in DMC whether
it recognizes> them or not. To avoid discussing them would be possible
but dishonest.>> DMC's tendency to hide cycles rather
Title: Election-methods Digest, Vol 15, Issue 50
Someone wrote:
I think the "+" to show "I like B better than A even though
I ranked A=B" disingenuous and unnecessary. If you prefer one of the equally
ranked alterntatives more than the other, just don't rank them equally.
Forest Answers
Put some ideas from MDDA, Bucklin, and MMPO together, and what do you get?
I'll let Ted Stern name it, but here it is:
Collapse the top ranks as in Bucklin until (according to the collapsed ballots)
there is a candidate undefeated by a majority.
If, at that point, there is more than one cand
Adam wrote:
I haven't been following this line of threads terribly closely, so I just
want to be clear that I understand. The way I think about Bucklin is an
approval election where the approval cutoff bar on everyone's ballot keeps
getting lowered until we have a majority approved winner. It s
I like the modified ER Bucklin Whole version that Kevin and Mike have been
considering.
I have two suggestions that might make it more viable as a public proposal:
1. Keep the number of possible distinct ranks down to seven or eight, for
ballot simplicity.
2. Allow a special mark "+" to b
Here's an interesting example with four candidates, in which (under Shulze) an
order reversal between Favorite and Compromise would give the win to Compromise
(instead of a third candidate D) even though Compromise already beats Favorite.
In other words, there seems to be incentive to betray Fa
Kevin wrote (>) in response to my (>>):
>Also, there's a second election at this convention! Supposing the method used
>at
>this convention satisfies weak FBC, what have we gained (in terms of FBC
>compliance)
>by voting for delegates first?
>> Or are you just saying that although this method m
Mike suggest that the best public proposals are ...
"Best: MDDA, or maybe MDDB, which combine FBC with SFC, thereby accomodating
the needs of different kinds of voters. It now seems to me that MDDA is
better than MDDB. I'd said that SR would be a good proposal under certain
conditions, when peopl
I sympathize with Rob's complaint about the meaning of approval versus
disapproval in Approval.
There is a trade-off, a price for the simplicity of Approval.
However, DMC takes the pressure off this question because in DMC, approval is
only used to eliminate enough of the Smith set for an un
Here's the weakness of SR:
60 ABCDEF
40 BCDEFA
Here A should be the winner, but B has by far the best SR score of only 60
versus A's lousy 200.
I believe that this defect is called "teaming."
Forest
<>
Election-methods mailing list - see http://electorama.com/em for list info
Perhaps we could distinguish "sincere approval strategy" from merely
"consistent approval strategy" according to whether both or only the first of
Chris' conditions are satisfied.
I agree strongly with Chris' remark concerning the advantage of DMC zero info
strategy over Shulze(WV) zero info s
Forest claimed:
> That said, an even simpler method comes closer to satisfying the Strong FBC
> than any of these
> other more complicated methods: Asset Voting:
>
> Voters vote for their favorite, who represents them by proxy in an election
> completion
> convention. Write-ins are allowed.
eally care about the most.
From: [EMAIL PROTECTED] on behalf of
Simmons, Forest Sent: Sat 9/17/2005 3:00 PMTo:
election-methods-electorama.com@electorama.comCc:
[EMAIL PROTECTED]Subject: [Condorcet] Favorite Betrayal in
DMC
One of the nice things about DMC is that it is easy to pinpoint
Title: [Condorcet] RE: Approval Strategy in DMC
Rep. Nixon rightly opined that Approval would not
be favored as a proposal because people want to be able to distinguish
their favorite from their lesser evil compromise.
Although Approval satisfies the weak Favorite Betrayal
Criterion (FBC
One of the nice things about DMC is that it is easy to pinpoint the precise
circumstances in which there is a Favorite Betrayal incentive, i.e. where
Favorite Betrayal is more likely to payoff than not. It seems to be much
harder to pin this down in Schulze.
Here are the conditions that must
Title: [Condorcet] Re: Voting as duty (was ties & truncation)
Somebody thought that the
candidates would frequently fail to be ratified by the electorate.
Well, if the statisticians
take this into account properly, and submit for ratification only those
candidates that have a 99 percent
dates, and truncate all others. I'm not sure.
Forest
Kevin replied to the following:
Forest,
--- "Simmons, Forest " <[EMAIL PROTECTED]> a écrit :
> Kevin, your ICA method interests me. In particular, your creative use of
> "equa
Title: Election-methods Digest, Vol 15, Issue 33
Here's the corrected strategy for the case where you
have enough polling information to discern the Smith set:
First identify (with the letter
C) your favorite member of the Smith set (or, if possible, the
uncovered set).
Put your app
Recently Rob Lanphier asked how to determine the strategically optimal approval
cutoff when voting under DMC.
Here are my suggestions:
(1) For the case where you have enough polling information to discern the Smith
set:
First identify (with the letter C) your favorite member of the Smit
Woops, now I see that step 3 puts all defeats in cycles, so disregard my
objection.
Forest
I had written:
The plain English description of Shulze is pretty good except for the last step
(5), which is incorrect. In Shulze you nullify the weakest defeat in a cycle.
The "in a cycle" part
I meant to say that you could use matrices M and PM (not CM) to formulate ICA,
in the last paragraph quoted below.
Sorry for the confusion.
Forest
I suggest that we consider methods that sum two modified pairwise matrices in
addition to the basic pairwise matrix:
(This description is at th
Title: [Condorcet] Plain English description of Schulze(wv)
The plain English description
of Shulze is pretty good except for the last step (5), which is incorrect.
In Shulze you nullify the weakest defeat in a cycle. The "in a
cycle" part is extremely important.
To see this point supp
Title: Re: [Condorcet] Ties & Truncation: Information Loss
The main reason that "lazy"
voters don't take the time to study up on and carefully rank all of the
candidates is that they know that in these large scale elections the chance that
their vote will be pivotal is practically nil.
S
Another measure of logical complexity of a method is the number of alternations
between quantifier types, from universal to existential and back, in the
complete definition of the winner.
For example MinMax is more complex in this regard than DMC, because the MinMax
winner is the candidate C s
Title: RE: [Condorcet] Can we come to consensus? (ICA)
Kevin, your ICA method interests me. In
particular, your creative use of "equal ranked top" might be called "power top"
analogous to what Mike Ossipoff recently called "power truncation" for equal
(non)ranking at the bottom.
I sugge
Title: Re: [Condorcet] Why Schulze is Better than DMC
There are other
objective measures of complexity besides the ones mentioned by Jobst. (He
mentioned computational complexity from the point of view of the smallest
accurate description of the method or algorithm, as well as the minimal
rongenst beatpath C(80)F(70)A(65)D
through the candidates.
If I am not mistaken, River, Beatpath, and Ranked Pairs all agree
on C as winner.
I hope that this earns some respect for DMC's Favorite Betrayal
resistance :-)
My Best,
Forest
From: Adam Tarr
[mailto:[EMAIL PROTECTED]Sent: Fri
I believe that most voters would feel worse about having to rank Favorite equal
with Compromise than they would about ranking Favorite ahead of Compromise
while approving both.
If you collapse the order, then nobody can tell from your ballot which you
prefer, unless (somehow) approval can dist
I wrote ...
> Yes, this is the measure of defeat strength used in AWP, but here's the
> question: Is AWP based
> on River the same as AWP based on MinMax?
>
> Somewhat surprisingly, the answer to the analogous question for "winning
> approval" as a measure
> of defeat strength is affirmative
Title: Re: [Condorcet] Can we come to consensus?
Jeff Fisher recently opined that DMC voters would
likely adopt the strategy of approving all candidates that they considered
certain to be beaten pairwise by their Favorite. This
would put these candidates in a better position to doubly de
James has asked for evidence that "winning votes" (as a measure of defeat
strength) gives more incentive for insincere rankings than "winning approval"
does.
Adam and Kevin have argued that Winning Approval tends to encourage Favorite
Betrayal more than Winning Votes does.
But a thorough ex
Kevin has written (in response to)
>--- "Simmons, Forest " <[EMAIL PROTECTED]> a écrit :
>> This brings up a question. How good is MinMax(Approval Against)?
>>
>> By "Approval Against" I mean number of ballots on which X is approved and Y
Title: Re: [Condorcet] Can we come to consensus?
Jeff wrote ...
Now that we have presented a
few favorites and examined them, I hope we allat least understand each
other, even if we do not yet agree. It now lookslike we have the
following:* DMC has one ardent supporter and several contrib
Title: Re: [Condorcet] Comment on DMC
Here is an "ABC" example that illustrates
Jeff Fisher's concern as I understand it (see below):
Sincere zero info ballots:
45 A>>C>B
20 C>>B>A
35 B>>A>C
Pairwise cycle is
A>C>B>A.
Approval order is A>B>C.
So the sincere DMC winner is B.
But in
Dear James,
as I said in a recent message, I also think that AWP is more resistant to
burying than DMC. But until there is a simpler description of AWP, I will
support DMC over AWP in the category of "Condorcet Public Proposals."
This brings up a question. How good is MinMax(Approval Agains
Title: Re: A class of ballot set with "unbeaten in mean lotteries."
The following lottery method is easier to explain in
terms of ratings (range ballots), but can (and should) be adapted to rankings
(ordinal ballots) by modifying the following definition.
Definition 1: Lottery L1 beat
s are immune to strategic
> voting when there is a Condorcet winner (that is, voters cannot improve
> the election result from their perspective by voting insincerely). Is
> there
> an appropriate paper to cite that makes this argument clearly? Thanks
> much,
>
> -- Andrew
>
My two cents worth on utility:
1. Utility can be a useful concept for an individual to use in making a
decision, even though it may be impossible to calculate. For example, if
candidates A, B, and C have equal priors of winning, and my preference order is
A>B>C, then I might decide to approv
Warren,
Neither Jobst nor I think that Condorcet methods are the ultimate. In
particular there is a conjecture on the EM list that no Condorcet efficient
method can satisfy the FBC, so we shouldn't expect that of DMC.
If this conjecture is proven false, and it turns out that a reasonably sim
To the message from T.S. copied below, I would like to give a little more
background.
A few months after I came up with the idea of bubble sorting the approval
order, I came across an article at
http://www10.org/cdrom/papers/577/
in which the authors suggested bubble sorting the Borda order an
Title: Re: [Condorcet] Comment on DMC
Here's something I posted
today on the Condorcet list.
Forest
From: Simmons, Forest Sent: Tue
8/30/2005 1:36 PMTo: [EMAIL PROTECTED]Subject:
Recent History Perspective on Condorcet Methods
As most of you know, the
Election Methods grou
Warren (wds) asked if I could be more precise about reason #17.
> 17. It is resistant to the burying strategy that plagues some
> Condorcet methods. This is related to reason number 9.
The expert on burying in Condorcet methods is James Green-Armytage, who
invented a method called "Cardinal W
Suppose that ...
1. there are three candidates A, B, and C,
2. ballot rankings are strict,
3. in each ordinal faction second ranked candidates are distributed uniformly
between the other two,
and
4. there is a beat cycle A>B>C>A .
Let (alpha, beta, gamma) equal
(m(B
Three more reasons:
16. Like any method that makes germane use of both ordinal and approval
information it is well adapted to three-slot ballots, i.e. voters that don't
want to submit complete rankings can opt to have their approval order extended
by the order of their favorite.
17. It is
Under the heading
4 - DISCUSSION OF ALTERNATE NON-GRAPH-BASED ALGORITHMS
Adam said ...
"Warren Smith has proposed an alternate solution, which has been
brought up before on the EM list, of simply dragging a "cutting edge"
across the state to make a division at the proper population ratio,
a
In his response under this subject heading Mr. Lomax seemd to think that I was
advocating Cumulative Voting, then he offered what amounted to a plausibility
argument for my assertion that Cumulative Voting is strategically equivalent to
Plurality. I'm slightly miffed that he would imply that I
Mr. Lomax wrote:
"Asset Voting, per se, was invented by Warren Smith, though it strongly
resembles delegable proxy (which seems to have been invented independently
by a number of people, I know I did not get it from anyone else). "
I reply:
It's true that the name "Asset Voting" was invented b
In a recent message, partly quoted below, Adam Tarr outlined an NP hard
optimization approach to redistricting. He suggested that a genetic
optimization algorithm might be used for practical purposes.
It has been suggested before that in such cases anybody with a proposal found
by any means (
Title: Re: A class of ballot set with "unbeaten in mean lotteries."
Jobst and All:
I did make one
(inconsequential) boo boo. The normalization factor for the weights x+y-z,
y+z-x, and z+x-y should be 1/N, not 1/(2N), since the sum of these weights is
x+y+z=N.
To physically carry out t
Title: Re: [EM] 0-info approval voting, repeated polling, and adjusting priors
Let x, y, and z be positive integers such that
x+y+z=N, and max(x,y,z)
x: A>B>C
y: B>C>A
z: C>A>B
Further assume that the cardinal ratings of the middle
candidate within each faction are distributed uniformly
Abd ulRahman Lomax proposed:
The proposal is that the ballots might be counted first as ordinary
approval. If a majority appears from this process for a given candidate in
a single-winner election, the candidate would be elected. If not, then the
ballots would be retabulated as fractional approval
Asset voting (in its lone mark version) is one of the few methods simple enough
to have a decent chance among lazy U.S. voters, and it would be the greatest
possible improvement consistent with the simple lone mark ballot.
In Asset voting you vote for the candidate that you think would represen
The approval strategy that maximizes voting power (thus minimizing the
probability of an approval voter's regret) in a close three way race is this:
First decide your preference order among the three major candidates, say A>B>C.
Of course you should approve A and leave C unapproved. Approve B
Title: Re: [EM] 0-info approval voting, repeated polling, and adjusting priors
As usual, Jobst has given us lots of food for
thought.
First I would like to compare Joe Weinstein's approval
strategy with its marginal version based on tie probabilities.
The marginal version is to approve
Title: Re: [EM] 0-info approval voting, repeated polling, and adjusting priors
Jobst gave examples in which optimal approval strategy
for someone with preferences A>B>C>D would be to approve only A
and C.
Mike Ossipoff and Richard Moore first made me aware of
these counterintuitive pos
Title: Re: [EM] 0-info approval voting, repeated polling, and adjusting priors
Jobst wrote ...
Dear Forest,I'm not sure what you mean by the red marble
thing or how it clarifiesthe meaning of the priors in zero-info
strategy.
I reply:
I'm not sure either. I'm stabbing around in
the dark
What I wrote below doesn't make sense because I got two different ideas mixed
together.
I wrote (emphasis added to highlight the mistake):
Suppose for example, that at each stage a marble is drawn (with replacement) at
random from a bag containing one red and 999 green marbles, and that the f
Title: RE: [EM] 0-info approval voting, repeated polling, and adjusting priors
Jobst wrote ...A point which troubles me is
this: The justification of placing the approval cutoff at the expected or median
utility according to the current priors is based upon the two assumptions that
(1) giv
Title: Re: [EM] 0-info approval voting, repeated polling, and adjusting priors
Here's a two line description of the simplest method
that Jobst's proof applies to:
1. Ballots are ordinal with approval
cutoffs.
2. In each round (and on each ballot) the approval
cutoff is adjusted by movi
when there are a finite number of voters.]
Forest
From: Jobst Heitzig [mailto:[EMAIL PROTECTED]
Sent: Wed 8/3/2005 11:03 PM
To: Simmons, Forest
Cc: election-methods-electorama.com@electorama.com
Subject: Re: [EM] 0-info approval voting, repeated polling, and adjusting prio
s.]
Forest
From: Jobst Heitzig
[mailto:[EMAIL PROTECTED]Sent: Wed 8/3/2005 11:03 PMTo:
Simmons, Forest Cc:
election-methods-electorama.com@electorama.comSubject: Re: [EM]
0-info approval voting, repeated polling, and adjusting
priors
Dear Forest!You wrote:> At each successive stage
we
Title: 0-info approval voting, repeated polling, and adjusting priors
Thanks to one and all (in
both private and public communications) for the creative small group
ideas,
Jobst asked about repeated approval polling
ideas that might converge.
Here's an approach that I would like
to se
I'm interested in hearing a variety of ideas for voting in small groups where,
for example, hands can be raised, repeated balloting is not a problem, etc.
One application I have in mind is text book selection. At PCC all sections of
Calculus 251 must use the same text book. The math Subject A
As in all my postings, my main objective is to encourage mental limbering up,
so that we don't get bogged down in a lack of imagination and thereby overlook
the wide variety of possibilities whose surface we have barely scratched.
All elections are influenced by biased random bits of informatio
>From his remarks below I think that Lomax would agree with me that candidate A
>in the following example would likely be better for the electorate than
>candidate M:
Sincere
55 M>A>>B
45 B>A>>M
On the other hand, M would be more likely to win the approval election, unless
a significant perc
On 20 Jul 2005 at 18:51 UTC-0700, Abd ulRahman Lomax wrote:
>At 03:47 PM 7/20/2005, Dan Bishop wrote:
>>[...]I think a good solution would be for elections to have two rounds:
>>
>> 1. A qualifying primary, done entirely with write-in ballots, and
>> counted using Approval. Candidates with a su
I like James' sample ballot and accompaning explanation at ...
http://fc.antioch.edu/~james_green-armytage/vm/rank-cutoff-ballot.htm
Forest
<>
Election-methods mailing list - see http://electorama.com/em for list info
Jobst!
Here's a connection to approval.
A lottery L is undefeated in mean iff every candidate would end up with less
than 50 percent approval if voters were to use above mean approval strategy
(based on prior winning probabilities borrowed from L) .
A lottery L is undefeated in median iff e
Jobst,
I'm still digesting this. I'm always interested in potentially good "lottery
methods."
Here's my latest attempt:
Voters first submit approvals, and the candidates are listed in order of
approval.
Each voter then submits a number between 1 and the number of candidates (to be
used
Random ballot satisfies the Strong FBC, but it is too promiscuous with the
probability for most situations.
Here's a small group method that is much more frugal with the probability
while still satisfying the FBC, if not the Strong FBC.
1. List the alternatives in order of approval on the bl
Jobst,
I don't know that this criterion has been discussed in general. The CR example
I gave came up a few years ago when were comparing cumulative votes and
ordinary CR, whose ballot restrictions correspond to L(1) and
L(infinity) norms, repectively. It was noted that for these norms the o
Very interesting, Jobst.
Suppose that ratings are between zero and 100.
On each ballot normalize these ratings by shifting to the left by its mean
rating and then dividing by the root mean square of those ratings.
This ballot contributes its normalized ratings to the respective candidates.
Mike asked: Is Clone-Winner the same as the Independence from Clones Criterion
(ICC)?
I reply: I understood it to mean that if a winner is cloned, then the winner
must come from the new clone set.
I intended the votes-only version of this in my posting.
Kevin asked, "Any thoughts?"
Forest replies:
Suppose that you modify MDDA by specifying a three slot, MCA style ballot, i.e.
allowing voters to rank as many alternatives as they like in first and second
place, but all other candidates are considered equally ranked and unapproved.
Call the
Jobst recently gave a nice, but rather elaborate geographical example with
different winners for different methods.
With a more limited objective in mind (showing the inadequacy of mere ordinal
information) I present a simpler example:
This example is in the form of two related scenarios that
Subject: RE: [EM] Fall Back Approval
To: [EMAIL PROTECTED]
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset=iso-8859-1
Forest,
--- "Simmons, Forest " <[EMAIL PROTECTED]> a écrit :
> In the first round only the alternatives ranked first (or equal fi
Ballots are ordinal with truncation and other equal ranks allowed.
In the first round only the alternatives ranked first (or equal first) are
counted as approved, i.e. a tentative cutoff is placed immediately below the
top rank on each ballot.
In subsequent rounds the tentative cutoff is move
Near the end of his message Mike wrote ...
It seems to me that the first step of sprucing-up was to eliminate every
candidate who isn't in a certain selection set. The set of candidates who
could win without violating BC? And then was that followed immediately by
the collapsing of beat-clone-se
I don't have much time right now, but here are a few brief replies to Mike's
comments and questions.
>From: "MIKE OSSIPOFF" <[EMAIL PROTECTED]>
Subject: [EM] MMPO
As you know, MMPO can be introduced to people very briefly:
Voters rank as many or as few candidates as they want to. Eq
This looks promising. I like this kind of creativity.
Three Questions:
1. Exactly how do you define correlation?
2. Do you re-calculate the correlations after each elimination?
3. What about clone triplets, quintuplets, etc.?
Forest
<>
Election-methods mailing list - see http://el
Kevin, thanks for supplying the details of MMPO's FBC compliance.
I never doubted it since I suggested it back in March 2003, inspired by your
"median winner" method for two slot ballots.
http://listserver.dreamhost.com/pipermail/election-methods-electorama.com/2003-March/009575.html
I was d
I agree that non-deterministic methods are hard to sell to the wider public.
I think that's why Jobst is suggesting small group scenarios.
<>
Election-methods mailing list - see http://electorama.com/em for list info
In the context of this thread Chris wrote ...
Normally if there is a lot of ill-will between rigid majority and
minority factions, then the majority will not assent to a raffle, and if
there is one the losing side will suspect that it was
rigged.
I reply:
Jobst's example could be something like a vote to determine where the olympic
games or some world wide conference was to take place.
Notice that the question, "Which is the best city for this purpose?" has
different answers for different voters, as opposed to some voters being right
and some b
From: Chris Benham <[EMAIL PROTECTED]>
Subject: [EM] Re: "Approval Later-no-Harm",
...
I am of the view that it is possible and desirable to have the situation
where the big majority of voters
are innocent of strategy and/or not interested in strategy, and I
strongly believe that the "officia
If ballots are ordinal with approval cutoffs, and alternative A pareto
dominates alternative B, then B cannot have more approval than A.
If B has approval equal to A's, then the tie should be broken by random ballot.
In that case alternative A will beat B, since A is ranked higher than B on
e
Sometimes when a concept is presented fuzzily it stimulates more creative
thought than when it is set forth more definitively.
This percentage support idea reminds me of an observation made by Martin Harper
a few years back.
If you list the candidates in order of approval, and then assign e
Russ said ...
I'd label it something like "[End Approved Candidates]".
Forest replies...
I like your"End Approved Candidates" or perhaps "Approval/Disapproval Cutoff
Rank."
How about, "I disapprove candidates ranked after this rank:"?
Some other suggestions that have been entertained ar
Date: Fri, 22 Apr 2005 18:42:16 -0700
From: Russ Paielli <[EMAIL PROTECTED]>
Subject: [EM] auto-truncation
To: [EMAIL PROTECTED]
Note, however, that the added equipment requirement for an approval
cutoff could delay the adoption for decades, but I won't get into that now.
Forest replies:
Well said, Mike.
Every time I hear that the program I was listening to on Public Radio was
supported by a generaous grant from the Rockefeller Foundation I think of the
workers and their families who were shot by private security forces (Brinks)
and national guardsmen for striking or being wit
than the late Hugh W. Nibley, the old adage
"The idle shall not eat the bread of the laborer" originally meant that the
idle rich should not be eating the bread of the working poor.
Forest
Simmons, Forest simmonfo-at-up.edu |EMlist| wrote:
> My idea is that in a large enough el
Title: Election-methods Digest, Vol 10, Issue 25
Below where I wrote "99% confidence" I should have specified the
confidence interval:
If n= 1,the the standard deviation is 100*SQRT(P*Q) which is less
than 50, as long as P and Q are positive numbers that sum to unity. Here
P is th
Recently someone asked about the best way to collect ordinal information.
Jobst and Ted have recently suggested methods that use the basic information
theoretic principle of encoding the most likely messages with the smallest code
words, and getting approval information as a bonus. [The most li
Both DFC and DMC make use of the set P of all alternatives that pairwise defeat
the alternatives that have greater approval.
I would like to define another set which I will call BP consisting of all
alternatives that have beat paths to every alternative with greater approval.
In other words,
1 - 100 of 103 matches
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