. 100 . . voter utility or rating . . 0
----------------------------------------
2 Bush . Perot . . . . . . . . . Clinton
1 Perot . . . . . . . . . Bush . Clinton
2 Clinton . Perot . . . . . . . . . Bush
I'm aware of the problems with interpersonal comparison of utilities,
but have a hard time viewing the two cases as equivalent.
------------------------------
Message: 5
Date: Tue, 01 Feb 2005 00:12:44 -0800
From: Russ Paielli <[EMAIL PROTECTED]>
Subject: Re: [EM] Re: simulating an Approval campaign/election
To: [EMAIL PROTECTED]
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset=us-ascii; format=flowed
Rob LeGrand honky1998-at-yahoo.com |EMlist| wrote:
Russ Paielli wrote:
Here's what I modeled. I have three candidates only. I randomly
generate votes, with equal probabilities for all six possible
preference orders. The only control variable for each vote is
where the voter "draws the line." In this case, that amounts to
whether or not the voter approves the middle candidate of his
preference list. I initialized the middle-candidate state of each
vote randomly, with an expected mean of half approved and half
not.
Then I started an iterative simulation of polling cycles and
voter re-evaluation of his vote. I simply assumed that complete
and perfect polling data is available to every voter. Then I have
each voter re-evaluate his approval/disapproval of his middle
candidate based on Forest Simmons elegant strategy rule (special
case for three candidates only): if the voters first choice has
more votes than his third (last) choice, the middle candidate
does not get approved, but if the third choice has more votes
than the first choice, the middle candidate gets approved (if
they are equal I leave it unchanged).
You're simulating a DSV (Declared-Strategy Voting) election with
Approval. My current research is on just that topic, though I'm
also interested in using DSV with other point-count systems such as
plurality, Borda and several others. That Approval strategy is
identical to strategy A in the 3-candidate case.
Interesting. Do you mind if I ask why you are interested in
Declared-Strategy Voting as opposed to Undeclared-Strategy Voting?
<cut>
The first few runs I tried showed rapid convergence within a
cycle or two. Then I wrapped the whole thing in another loop to
simulate many separate elections. I found that most of them
converged within 2 or 3 iterations. However, roughly 1 in 10
fails to converge either to a stable vote count or a stable
winner.
1 in 10 agrees with Merrill's figure: 91.6% of random elections
with 3 candidates and 25 voters have a Condorcet winner. You used
more voters, but that would decrease the percentage only very
slightly. Actually, Approval DSV in batch mode using strategy A
doesn't always converge even when there's a Condorcet winner, but
the examples are quite contrived and require more than 3
candidates. Ballot-by-ballot mode, when the voter order is weakly
fair (no voter is shut out for more than 2n steps, say), always
finds an equilibrium eventually in my simulations. There's always
a path of changes that leads to an equilibrium, anyway. When no
Condorcet winner exists, strategy A can't lead to an equilibrium
because any poll leader can and will be toppled.
Does another strategy converge even if no Condorcet winner exists?
So the bottom line is that, even in the simplest, most idealized
case, Approval Voting can be unstable. In such cases, the
ultimate winner would essentially be a random function of when
the election happened to be held. A sort of random lottery. And
many voters would regret their decision.
Any voting system for which you can't say the same (like plurality)
is easily manipulated and leads to multiple equilibria, some of
which may not elect an existing Condorcet winner. If you find
I assume you mean that plurality can be manipulated by throwing in
spoilers (e.g., Nader or Perot).
And as for multiple equilibria, it seems to me that all but one of those
equilibria is practically inaccessable if it requires a third party to
switch places with one of the two dominant parties.
convergence more important than competitive elections and sincere
voting, you may prefer plurality to Approval. But I see
plurality's many equilibria as false ones that hide much about the
electorate's wishes. Approval only fails to converge when the
electorate's wishes are collectively irrational, in a sense, and in
that case Approval will eventually cycle only among the sincere
Schwartz set.
Note that all Condorcet-compliant ranked-ballot voting systems are
sometimes manipulable and nonconvergent when there's no Condorcet
winner. Some prefer Condorcet methods to Approval because they see
them as harder to manipulate and thus more stable, but I'd rather
voters know the rules of the game they're playing. Alex Small
wrote on the ApprovalVoting list:
Legitimacy should come from a transparent connection between the
decisions people make in the voting booth and the final outcome.
If it takes a game theorist to sketch out a flow chart and
explain why voting for A allowed B to win, how much respect will
the system command?
That's actually one reason why I like Approval Voting: Although
there are sometimes risky decisions to be made (do I approve my
second choice or only my first? Do I risk my least favorite
winning or risk hurting my favorite?), at least the cause and
effect is clear. We won't need a game theorist with a flow chart
to explain things to us the next morning.
I second that. Besides, Approval can make a sincerity guarantee
that no ranked-ballot system can: You should always vote the
maximum for your favorite candidate and the minimum for your least
favorite. If all you're given is poll information, you should
never vote for B and not for A when you prefer A to B; it never
pays to express a false pairwise preference. I still haven't found
another system that has that property of weak sincerity.
Anyway, the point is that I think Approval has the best combination
of manipulation-resistance, convergence and quality of winners, not
to mention simplicity. A little divergence is worth the better
equilibria.
That all seems reasonable to me, but let me outline my evolving view,
and you can let me know if you think I am on the right track.
You seem to have confirmed my hypothesis that, in the idealized case
(DSV batch mode), Approval voting almost always converges on the
Cordorcet winner if one exists, but rarely (never?) converges if one
does not exist.
If that is true, then it seems to me that Approval may be roughly
equivalent to Condorcet with random selection of the winner from the
Smith set. Do you agree with that? If so, has anyone shown that the
Condorcet winner based on a "good" Condorcet resolution method would at
least be favored in the random selection process?
That all applies to the idealized case, of course. Once you start adding
uncertainty and other "real-world" effects, things could change
dramatically.
--Russ
------------------------------
Message: 6
Date: Tue, 01 Feb 2005 13:18:23 +0100
From: Markus Schulze <[EMAIL PROTECTED]>
Subject: Re: MIKE OSSIPOFF vs The list (Re: [EM] I didn't choose to be
the topic
To: [EMAIL PROTECTED], [EMAIL PROTECTED]
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset=us-ascii
Dear Craig Carey,
instead of insulting those who don't agree with you,
you should rather try to convince them.
Example 1:
38 ABC
32 BCA
30 CBA
The IFPP winner is candidate A although a majority of the
voters strictly prefers candidate B and candidate C to
candidate A. This example demonstrates that IFPP violates
e.g. (1) majority for solid coalitions, (2) independence
of clones, (3) reversal symmetry, and (4) majority loser.
My method (aka Schwartz sequential dropping, cloneproof
Schwartz sequential dropping, beatpath method, beatpath
winner, path voting, path winner, strong immunity from
binary arguments) satisfies these criteria.
Example 2:
Suppose, in example 1, 5 CBA voters didn't go to the polls.
Then example 1 had looked as follows:
38 ABC
32 BCA
25 CBA
Now, the IFPP winner is candidate B. This example
demonstrates that IFPP violates mono-remove-bottom.
My method satisfies mono-remove-bottom in the
2-, 3- and 4-candidate case.
Example 3:
Situation 1:
10 ABCD
15 BACD
23 CABD
The quota is 12. A and D are eliminated in the first round,
then B beats C.
Situation 2:
10 ABCD
15 BACD
20 CABD
3 ACBD
D is eliminated in the first round. In the second round,
the quota is 16 so that A and B are eliminated and C wins.
This example demonstrates that IFPP violates monotonicity.
My method satisfies monotonicity.
Please convince me that IFPP was better than my method!
Markus Schulze
------------------------------
Message: 7
Date: Wed, 02 Feb 2005 02:08:58 +1300
From: Craig Carey <[EMAIL PROTECTED]>
Subject: Re: [EM] Craig: I did include ballot-counting code
To: election-methods-electorama.com@electorama.com
Message-ID: <[EMAIL PROTECTED]>
Content-Type: text/plain; charset="us-ascii"
MIKE has got me black-listed so, as with Mr Piaelli, I can only reply publicly
and I can never cut out the step when MIKE makes messages be diluted and
verbose by expressing false and untrue ideas.
In this matter you were simply in the wrong: it is a dull brainless piece
on how you hold a great desire to be sensitive to the public's desire to
"express rankings". What happened between 1992 (you were a CVD member) and
1997 (when believer in pairwise comparing) ?. At some point you got
attached to lies on what it was that voters want. They fill in ballot
papers with preference lists and hope for a correct set of winners.
Your programming idea, described with the words "express[ed] rankings"
is totally different from the voters' idea of:
(a) ballot paper counts as input, and
(b) sets of winners as output.
In 2000 you were a person who would never ever say (privately AND publicly)
that there was only "one" input to the method function returning a winner
set: the "collection of ballot papers".
After 4 years of thinking about whether voters in an IRV election only
create a collection of IRV ballot papers, what you have got for us is the
total lie, "no", since they instead produced "express[ed] rankings".
Below you say that Russ probably argued that Americans don't actually
draw antisymmetric matrices onto their ballot papers. We knew that.
Making false claims that a public wants to have a collective preference
is done to protect one of your beliefs. A public does not "express rankings"
but instead the falsity of the claim is a stupid strict designed to
conceal a wrong belief you have.
The public fills in preference lists. What your Python code did was designed
to do was to trash the public into doing something it never did, sought, or
has a reason for: create a pretext and deceptive cover story for you. What
do you want: to believe the lie which is that Condorcet's original thought
was correct and that there seem to be Comdorcet cycles (those difficult
to resolve things).
The reason the input stage code was missing, is to help you get attached.
E.g. some concrete to keep you at the bottom of the water off the edge of
the wharf, and eventually you would be cataloguing the fish and boots.
At 2005-02-01 04:03 +0000 Tuesday, MIKE OSSIPOFF wrote:
Craig Carey said:
What the blazes ?: OSSIPOFF's Python code couldn't even accept ballot paper
counts as input. That is what I saw at the Piaelli website.
I reply:
Very good point. I agree that it didn't make sense for the Python listing
to not have code for receiving and counting rankings. The Python code that
I'd written, and Russ had it in its final debugged version, received and
counted the raw input to get the pairwise vote totals.
I wanted the program to be usable by anyone who wanted to copy it, and I
wanted it to be complete and self-contained. So I included code to receive
the rankings from a keyboard, and, from those rankings, to determine the
pairwise vote totals, and use those to determine the winner.
Russ passionately insisted no one would want to enter rankings from the
kekyboard. One could ask, then, if he thought that people would rather
determine the pairwise vote totals without any assistance from a computer
program.
Sure, for a user who writes programs, that user can write his own
ranking-receiving and counting program. But I wanted the program to be
accessible to people who weren't inclined to write their own input code. No
such luck. Russ left out the keyboard input and count code, leaving a
program that had the pairwise vote totals as its inputs--inputs to be
obtained by the user however s/he manages to.
Of course someone who wants to write their own input code could disregard
the keyboard-input code.
By the way, the code to receive the rankings from a keyboard and count
them to find the pairwise vote totals was considerably longer than the part
that uses those pairwise vote totals for the BeatpathWinner algorithm.
That's because, for practical use, it's necessary to give the user a way to
correct any keyboard-input errors that s/he makes, and to indicate when s/he
has completed each ranking, and when s/he has entered all the rankings. That
makes the code considerably longer.
That is so seemingly dumb, but it is really there to help OSSIPOFF prop up
some belief. Also the keyboard errors argument seems to be a lie. Though
OSSIPOFF can't stop a wide range of blunders, it is to be expected that the
public can't start making errors.
The best solution is for Piaelli to close MIKE's webpage.
We are talking about the format of the input data. I have considered the
problem and I conclude that computer programmers who develop algorithms,
will prefer this input:
Table A
----------------------------------
(1, (1, 0, 0, 0)) % = 1*(A)
(2, (1, 2, 0, 0)) % = 2*(AB)
(3, (2, 1, 0, 0)) % = 3*(BA)
(-4, (3, 2, 1, 0)) % = -4*(CBA)
----------------------------------
In instead the algorithm gets IRV ballot counts in a tree stuctured form,
then the algorithm can be much harder to understand.
OSSIPOFF;s 3rd option, of telling users to sum some of their STV papers,
is the same as requiring that input data be multiplied by a matrix.
For the input to be standardized, then every one else's algorithm has
to start off by multiplying by the inverse of MIKE OSSIPOFF's matrix.
The motive for creating the matrix seems to be so muddy and dark, that MIKE
is only prepared to withhold the motive and mislead about the motive, when
saying that the public will make mistakes.
Incredibly, MIKE has no words defining the matrix, and no words saying if it
can be inverted.
He has only got ONE program: surely it might as well set a good example,
for other programmers to follow.
Voters don't create cycles with their voter. They don't have preferences
to express, i.e. clues on what the method should do when their vote is
mixed with other votes. MIKE made a false claim saying voters expressed
preferences.
The title of this message
"Re: [EM] Craig: I did include ballot-counting code"
is totally untrue, as I recall, since MIKE never had code to count the
first column of numbers that is in Table A.
------------------------------
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