Googling DYN shows that these initials are already spoken for (though
not in the context of voting).
The initials PXSV are not spoken for, so unless someone comes up with a
better set of letters, I would like to use these letters for "PSX
Voting".
These letters have the advantage of being very
Chris B wrote...
>
>Regarding "social utility", I'm of the school that says that to the
>extent that it is a real and wonderful thing it will look after itself
>if we do
>our best to ensure that the election method is as fair and
>strategy-resistant as possible.
Random Ballot is already fair a
One of the basic theorems of Linear Programming is that when there is
an optimal value of a linear objective function it will occur at least
one corner of the feasible region.
In the rare cases that it occurs at two corners of the feasible region,
it will also occur at every point on the line
Mike,
Thanks for reminding us of the basic approval strategies that are easy
to apply.
Still there are those who would rather have a strategy free method
without having to rank all of the candidates, while still being able to
give their favorite candidate special support above mere approval.
Mr. Schudy's article reinforces the rationale behind DYN: that with
reliable partial information, Approval does as well or better than
Condorcet.
Mr. Schudy treats the case in which there is a clear frontrunner and a
clear runnerup. In that case he shows that (what we usually call)
"approval
In further response to Juho's question about candidates making their
approval choices before versus after the partial count, here's a
compromise:
Require the candidates to publish their candidate rankings before the
election, and then (after the partial info is available to them)
require them
True, it would be confusing to explain DYN as a form of asset voting,
but it could be done. Here is its purest form:
Each voter gets one vote per candidate. The voter delegates each vote
to a candidate (the one that she wants to make responsible for
getting a Y or N attached to that vote).
In response to Juho's questions:
There are various possible versions of DYN. But if the candidates were
required to give their approvals before learning the partial results,
then there would be little point in delegating votes; the voters could
just copy the candidate recommendations onto thei
Delegable Yes/No:
Each voter has a Yes/No vote to cast for each candidate. The voters
can delegate some of these votes to candidates (including write-ins),
if they so desire. The candidates cast the delegated votes after the
rest of the votes have already been counted.
Thus the voters that h
Raphfrk had a question about Declared Strategy Voting.
Yes, originally DSV was limited to Batch and vote-by-vote versions of
plurality strategies applied to ordinal ballots.
But on this election methods listserv we have expanded DSV to include
any method that takes rankings or ratings and autom
;From: [EMAIL PROTECTED]
>Subject: Re: [EM] election-methods Digest, Vol 37, Issue 4
>To: election-methods@electorama.com
>Message-ID:
Designated Strategy Voting (DSV) methods relieve the voter of repeated
returns to the polls for each iteration of the feedback loop, and also
solve the anonimity requirement, but as has been noted, methods that
are supposed to iterate unto an equilibrium may not converge.
[What follows requires
Mike,
Yes, the approval strategist would do well with this method.
Those who like to strategize can do so, and those who don't like to can
just rank the candidates. Those who don't strategize will (by
definition) submit sincere rankings. Those who do strategize can do
most, if not all, of th
It appears that the answer to the question is no, but not too bad.
Taking into account suggestions by Warren, Mike, and Dave, I offer a
simpler version.
The basic ballot is ordinal. Everything else is optional.
Voters with opinions about who has the best chance of winning can put a
mark next t
It's true that there can be some incentive to lie about whom you think
is the most likely to win, but there is no point in lying about your
preference order.
Here's a version that reduces the incentive to lie about perceived
probabilities:
Each person indicates both a guess as to the winner, a
I was happy to see Alex Small's progress on the FBC.
It inspired me to take another crack at some way of getting around the
basic impossibility of manipulation free deterministic methods based on
standard ranked ballots.
Obviously, to surmount this basic obstacle we need other information
from
Suppose that candidate Y has the greatest pairwise opposition against
candidate X. Let the letter n represent the number of ballots on which
Y is rated strictly above X, i.e. X's maximum pairwise opposition.
If X is an approval equilibrium winner, then the equilibrium approval
of Y will be at
What is an approval equilibrium?
Is it possible to deduce an approval equilibrium from sincere rankings
or ratings?
These questions are amazingly slippery!
I won't attempt to survey the many answers that have been proposed, but
I would like to share a line of thought that came to me after pond
idates, and go with the winner of the
cycle that maximizes the min conditional approval of its cycle winner.
Forest
>From: Forest W Simmons <[EMAIL PROTECTED]>
>Subject: Re: [EM] Does this method have a name?
>
>
>The "reactive approval" of candidate X relative to
The "reactive approval" of candidate X relative to Y as defined below
is supposed to approximate the approval that X would get given only
that Y was ahead of all the other candidates in the polls.
In other words, if there were zero info up until someone reveals that Y
is the front runner, would
Here's an example that might clear up some questions:
Suppose that the original ballot is
A=B>C=D>E=F|G=H>I=J>K=L
where "|" is the voter's marked approval cutoff.
Then in calculating reactive approvals relative to C we move the
approval cutoff adjacent to but not past the position shared by C
's score is her minimum reactionary approval relative
to the other candidates. "
then we get another method not equivalent to MinMax in the complete
ranking case.
Forest
>From: Forest W Simmons <[EMAIL PROTECTED]>
>Subject: [EM] Does this method already have a name?
>To:
Ballots are ordinal with approval cutoffs.
The candidate with "Maximum Minimal Reactionary Approval" wins.
A candidate's "reactionary approval" relative to another candidate is
the approval she would get if the approval cutoff were moved adjacent
to (but not past) the other candidate's position
Warren,
I think I understand the source of our difference in thinking. I
haven't been taking "issue space" literally enough.
Or from another point of view, I haven't been thinking of the voters'
ratings as a function of position in issue space, but only as a
function of their distances from th
I would like to see how the Yee/BOlsen diagrams for this method
compare with those of IRNR (Instant Runoff by Normalized Ratings), for
example.
Chris Benham wrote:
>Hello,
>My current favourite plain ranked-ballot method is "Approval-Sorted
>Margins(Ranking) Elimination":
>
>1. Voters ra
For practical purposes any method based on rankings or range style
ballots, can be closely approximated by a summable version. Since
approval cutoffs can be incorporated into rankings and ratings, methods
that require approval cutoffs can also be efficiently accomodated.
It's based on the idea
Approval Margins should have been on my list of most promising, even
though it is not as well known as the three that I mentioned. Total
Approval would not be that well known except that DMC has received a
lot of attention, and DMC is equivalent to River(TA), etc. which,
admittedly, may not be
So far, the three most promising measures of defeat strength for
Beatpath and the other immune methods are ...
1. Winning Votes: the number of ballots in favor of the pairwise win.
2. Total Approval: the number of ballots on which the pairwise winner
is approved. The Beatpath, Ranked Pairs, an
This method was introduced in the middle of another thread, but not as
well as it deserved, so here goes again:
Ballots are range style.
Let R be the highest range value such that if all of the alternatives
that are rated at or above level R are advanced to Equal Top, then for
some alternative
I never claimed that EQTOP-MPO satisfied any strategy free criteria.
To the contrary I pointed out the drawback that it requires approval
style strategy even in the zero info case.
That method was just the introduction to a better method that
immediately followed it in the same message.
Here'
Thanks, Kevin, I should have known that Woodall would have already
considered this in his systematic way.
BTW, the more I think about MAMPO, the more I like it.
How about three slot MAMPO?
How about this variation of Chris Benham's idea?:
For each candidate X, let EQF(X) be the number of ballo
email, send a message with subject or body 'help' to
> [EMAIL PROTECTED]
>
>You can reach the person managing the list at
> [EMAIL PROTECTED]
>
>When replying, please edit your Subject line so it is more specific
>than "Re: Contents of election-method
This method has the same relationship to Beatpath that MMPO has to
MinMax.
Let's call the opposite of opposition, consent. Then MMPO which is an
abbreviation for Min Max (pairwise opposition) could be characterized
as Max Min (pairwise consent).
To be definite, the pairwise consent for A rela
Michael Poole worried that it might be impossible to find circuit
elements with the precise properties needed.
As always, theoretical circuits have elements with idealized
properties. An idealized diode of the kind we need with reisitance R1
in one direction and R2 in the other direction coul
Has anybody explored this idea?
Make an electrical circuit with a terminal for each candidate.
For each pair of terminals attach a diode that has a different
resistance in each direction: the resistance in the direction from
candidate i to candidate j is proportional to the number of ballots
Ballots are range with finite number of range choices.
Think of the cutoff between each range value as a virtual candidate.
List all of the candidates, virtual or not, in order of median range
value.
While any candidate pairwise beats its immediate superior, swap the
highest such pair in the l
If we include the approval cutoff "App" as a virtual candidate in DMC,
and elect the second place winner when App is the DMC winner, then
(since DMC is immune from second place complaints) the resulting method
can be described as follows without any mention of App:
List the candidates in order
Chris, this reminds me of something related I suggested last December in
http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-December/019070.html
under the title of
"[EM] carrying Warren's approval equilibrium idea to its logical
conclusion"
Here's an extract:
"... Amo
In my recent posting on this subject I mistakenly argued that if the
truncation cutoff was uncovered, then it was also unbeaten.
It is convenient to treat the truncation cutoff as a virtual candidate,
"trunc."
There are three cases to consider:
Case 1. Trunc is the beats all candidate.
Case
Various methods that make use of approval have alternative versions
that use truncation as the approval cutoff.
This suggests the concept of a virtual candidate "trunc" that is ranked
below the lowest ranked real candidate on each ballot, but above any
(and all) truncated candidates.
How could
Here's a version of Beatpath that always picks from the uncovered set:
As in Beatpath(margins) or Beatpath(wv) we define a relation R
on the candidates as follows:
X R Y iff and only if there is a stronger beatpath from X to Y than
from Y to X.
This relation is transitive, and when there are n
Here's a Monotone method (UncDMC) that chooses from the uncovered set,
and always picks the DMC winner in the three candidate case:
1. List the candidates in approval order, highest to lowest, top to
bottom.
2. Modify the list according to the following rule: as long as some
candidate in the l
list) adds only those candidates
to the chain that pairwise defeat each of the other candidates
currently in the chain.
How does TACC compare with ASM and DMC in other three candidate cases?
Forest
Chris Benham wrote:
>
>Forest W Simmons wrote:
>
>> Here's the quest
Suppose that the alternatives are three restaurants for lunch, and the
preferences of the two friends are:
1 Italian>Mexican>>Thai
1 Thai>Mexican>>Italian
[The second voter seems to prefer hotter spices.]
Under D2MAC they would always end up at a Mexican restaurant for lunch.
This is fine if t
Mike O. wrote ...
UncAAO, ASM, and DMC ignore defeat-magnitude and magnitude of pair-wise
opposition. They look at pair-wise vote totals in order to find out who
beats whom, but then they throw pair-wise vote total information away.
Throwing that information away has regrettable consequences.
Compare:
1. Adding an alternative may not change the winner unless it pairwise
defeats the old winner.
2. Adding an alternative may not change the winner unless it is an
essential link in the strongest beatpath from the new winner to the old
winner.
As you mentioned , DMC satisfies (1). I th
An observation on the ordinal version:
1 A>C>B
1 B>C>A
If the method is clone free and neutral, then the clone sets B'={A,C}
and A'={B,C} must have equal probability with B and A respectively.
This implies that C must have zero probability.
In the ratings version that Jobst specified in his s
1. Is C socially preferable to A? ___Yes
2. Is tossing a coin to decide between A and B socially preferable to
A? ___Yes
3. Is C socially preferable to tossing a coin to decide between A and
B? ___No,
although asymptotically the added variety of a lottery like (A+B+C)/3
might be preferable.
andidate. This candidate is the winner.
Forest
Chris Benham wrote:
>
>
>Forest W Simmons wrote:
>
>>UncAAO stands for Uncovered, Approval, Approval Opposition. Here's how
>>it works:
>>
>>For each candidate X,
>>
>>if X is uncovered,
>>
Mike,
That's right. The C voters still have to use defensive strategy, but
the moving the approval cutoff is sufficient.
When there are only three candidates, UncAAO is the same as Smith
Approval.
Here's another classical example:
49 C
24 B>A
27 A>B
Under wv, this is not a Nash Equilibrium,
Here are the main advantages of UncAAO over other Condorcet methods:
1. It is resistant to manipulation ... more so than Beatpath or Ranked
Pairs, if I am not mistaken.
2. It always chooses from the uncovered set.
3. It is at least as easy as Ranked Pairs to describe. No mention of
the pos
Forest wrote ...
>
>Is TACC monotone? It seems to me that the winner W could improve in
>approval enough to overtake and surpass some W' in approval without
>defeating W' pairwise, though W' covers W.
I see: then W wouldn't have been the original winner.
election-methods mailing list - s
Jobst,
You've probably already figured this out, but here goes:
UncAAO fails IDPA to the same extent that Approval does, because it is
possible (however unlikely) for a Pareto Dominated alternative to get
as much or more approval than an alternative that dominates it.
But note that if Y' Pare
Thanks to Jobst for clarifying the conditions under which various kinds
of individual and social utilities can be justified.
A most important idea is that for social utility the average of two
lotteries could have more utility than either lottery separately
because of the social value of having
UncAAO stands for Uncovered, Approval, Approval Opposition. Here's how
it works:
For each candidate X,
if X is uncovered,
then let f(X)=X,
else let f(X) be the candidate against which X has the least approval
opposition, among those candidates that cover X.
Start with the approval winner A
This is for those that didn't see this proposal buried in the details
of a longer posting. There it was called method 1' . Here I'll call
it UncAA for reasons that I will explain later:
>From each covered candidate draw an arrow to the most approved
candidate that covers it. Then start with
Chris B. should get more credit for MCA than I, since he has been more
active in bringing it to the fore.
What about 3-slot MAMPO?
Which would be better, 3-slot MAMPO or the following hybrid of MCA and
MAMPO?
Ballots are 3-slot.
If exactly one candidate gets into the highest slot on more than
Warren remarked that when we drive our families across town we are
risking their lives.
I reply: If the purpose of the trip is not infinitely valuable
compared to the value of one cent, then don't do it.
Forest
election-methods mailing list - see http://electorama.com/em for list info
Markus showed that some methods that pick from the uncovered set are
not monotonic. In fact, it's easy to create non-monotonic methods,
including (blush) the five that I recently claimed were monotonic. I
found a subtle hole in my proof. The lemma is sound, but not quite
sufficient to prove
I would like to mention that I proposed the first of these five methods
back in December of 2004:
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-December/014293.html
"Ballots are ordinal with approval cutoff, equal rankings allowed.
Let U(A) be the set of uncovered c
Candidate X covers candidate Y
if and only if
X defeats (pairwise) both Y and each candidate that Y defeats.
An uncovered candidate is one that is not covered by any candidate.
Method 1. If the approval winner A is uncovered, then elect A.
Otherwise elect the highest
Mike,
Don't forget that even with honest voters, Borda suffers from clone
dependence in a major way.
Forest
election-methods mailing list - see http://electorama.com/em for list info
Jobst,
If I understand your method correctly, it is a refinement of the
following method which is based on so called "ranked preferences"
wherein the voters have some way of expressing their own relative
preference strengths:
Three ballots i, j, and k are drawn at random. Let A, B, and C
desi
Jobst,
I'm still digesting your new method. It is starting to make sense to
me. It is extremely creative and ingenious, in my opinion. I just hope
that we haven't overlooked any subtle logical error.
I have one question, though. If best strategy is to report true
utilities, then what do you
Here's a slightly different approach to Hay Voting:
Suppose that a typical voter votes the range ballot v=[x1, x2, x3].
The ballot adds to the respective virtual accounts of the three
candidates amounts of
x1/r, x2/r, and x3/r ,
where r is the L_2 norm of the vector v.
A dart board is co
Actually, in Mark Livingston's simulation at
http://www.cs.unc.edu/~livingst/Banzhaf/#results
he did assume that each state voted as a block.
Perhaps you meant that the small population states voted together as a
block?
I can see where that is a possibility, since most of the small
population
I would like to express my admiration for the ingenuity of the Hay
Voting method.
In my opinion it is a great contribution to the theory of election
methods.
Forest
election-methods mailing list - see http://electorama.com/em for list info
Here's the link to the data supporting the fact that the defacto super
proportional representation of our small states is not enough to make
up for their Banzhaf Voting Power deficiency:
http://www.cs.unc.edu/~livingst/Banzhaf/#results
Thanks,
Forest
election-methods mailing list - see
Mike expressed concern about a bias in favor of the small states if we
were to minimize maximum under representation.
I would like to point out that even with their super proportional
representation (due to the mandatory two senators) the small states are
at a disadvantage in voting power.
For
I'm beginning to suspect that in the presence of equality and a
reasonable definition of the ICC in that context, the AFB (FBC) and the
ICC are compatible.
Consider River, for example, where the drainage system is set up
according to minimum opposition, i.e. the drainage follows the paths of
l
As Kevin pointed out in one of his posts I have been using a overly
difficult standard of Favorite Betrayal.
Here's a simpler proof based on the following definition of FBC:
Raising favorite to top rank must not decrease expected utility.
Given three voters with utilities consistent with the ra
Here's a slightly simpler approach for a slightly weaker result. I show
that (in the case of pure ordinal ballots) you cannot have all three of
Monotonicity, Clone Independence, Pareto, and the Strong FBC.
To be very careful we explicitly list the assumptions:
1. Strictly ranked ordinal ballots
MCA satisfies both conditions (clone free and avoidance of favorite
betrayal). It does use range style ballots, but it elects the
candidate with the greatest median rating. If there are several
candidates tied for greatest median rating, it elects the one with the
greatest number of ballots th
Chris,
as I remember, after MCA was invented various attempts at generalizing
it eventually resulted in ER Bucklin (whole) for ranked ballots, even
though strictly speaking (as you point out)that method is not a
generalization of MCA.
The nice thing about ER Bucklin (whole) was that it satisfi
This method is based on ranked ballots that (at least) allow truncation.
The candidate with the fewest truncations (i.e. the one that is ranked
on the greatest number of ballots) is designated c0.
Let c1 be the candidate (among those that cover c0) against which c0
scores the smallest oppositio
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