Empathy List Archives

election-methods@mailman.electorama.com

Technical discussion of election methods

Re: [EM] (5) MJ better than IRV & MAM

steve bosworth

Wed, Jul 20, 2016 9:31 PM

Hi Kristofer,

Thank you for enabling me more fully to understand exactly how MAM is counted. For example, the link you sent me for Steve Seppley’s MAM counting tool has been very useful. With this tool, I have easily tested many other examples in an attempt to find a profile for which MAM elects a single-winner with a lower intensity of support from voters than the winner that would be elected by IRV. I did not find any such an example. For every example I tried, IRV and MAM elected the same winner. However, since IRV (unlike MAM) does not consider all the voters’ preferences until the majority winner is discovered, I assume there must be examples of the two methods electing different winners with different intensities of support. Still, I currently have no clear basis for continuing to suggest that IRV is more efficient at electing winners who have the highest available intensity of support from voters.

Do we agree that MAM has no disadvantage with respect to IRV except that MAM’s method of counting would be much more difficult for ordinary voters to understand? Also, do you agree that MJ (like MAM) has the advantage over IRV in electing a single-winner only after counting all the votes of each voter (i.e. the ‘grades’ that every voter has given to all of the candidates)? In addition, I see MJ’s method of counting these grades as being easier for ordinary citizens to understand than MAM’s method. Consequently, do you also prefer MJ to MAM? I also see MJ as more likely to prompt voters not to ‘rank’ the candidates but instead to ‘grade’ all of them honestly, i.e. to encourage more voters to grade or REJECT each candidate in the light of each of their own visions of what an EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, or POOR candidate looks like. Electing the candidate with the highest ‘majority-grade’ also seems to give the least incentive to citizens to vote strategically.

In this connection, below your say with regard to MJ that ‘it seems more that voters value expressing their true preference, and as long as the benefit to strategy is less than what they gain by expressing their preference, honesty wins.’

Of course, you say this only after listing a number objections that can be raised against MJ. Nevertheless, do you currently believe with me that these objections are less weighty than those that can also be raised against the practical use of any other single-winner method?

Finally, your questions and arguments have also driven me to accept that each these three methods respect the principle of "one citizen one vote".

From: Kristofer Munsterhjelm km_elmet@t-online.de
Sent: Saturday, July 16, 2016 3:43 PM
To: steve bosworth
Subject: Re: (5) MJ better than IRV & MAM

On 07/14/2016 06:11 PM, steve bosworth wrote:
[….}
K: Here's my detailed count (see attachment). See also
http://mam.hostei.com/default.php which explains the procedure for any
given ballot set.

-km

From: Kristofer Munsterhjelm km_elmet@t-online.de
Sent: Wednesday, June 29, 2016 11:19 AM
To: Kevin Venzke; steve bosworth; EM list
Subject: Re: [EM] The easiest method to 'tolerate'

On 06/29/2016 01:03 AM, Kevin Venzke wrote:

Hi Steve,

Majority Judgment is a variety of "median rating" methods which I see as
pretty similar. Woodall made one himself called Quota-Limited
Trickle-Down and in fact if you google "woodall qltd" you can find a
.pdf with a chart of some of the properties. The most noteworthy here
are the failures of Later-no-harm and Mono-add-top. (Both are failures
that IRV does not share.) For Later-no-harm: Suppose that candidate A is
elected. It's possible that there is a bloc of voters who rated B above
A, but A above zero, and that if these voters had lowered their A rating
to zero, then candidate B would win instead, which is an outcome this
bloc of voters would have preferred. They could criticize that the
method should be smart enough to not use their A ratings to elect A when
it would have been possible for them to elect B. If not a fairness
issue, it's at least an issue of the method requiring voters to keep
certain strategy in mind.

I'll also note that MJ fails:

Participation: Failure means that a voter might make the outcome worse
from his point of view by going to the polls. (Participation is
notoriously hard to pass)
All-equal ballots irrelevance: you can have a voter show up and give
every candidate the same rank, yet that changes the outcome. You'd
expect that to pull every candidate equally in the direction of the
grade that voter gave to every candidate, but that's not true.

See also, from a Range perspective: http://rangevoting.org/MedianVrange.html

RangeVoting.org - Balinski & Laraki's "majority judgment ...http://rangevoting.org/MedianVrange.html

rangevoting.org

On Balinski & Laraki's "majority judgment" median-based range-like voting scheme And comparison versus ordinary [i.e. average-based] range voting

The Mono-add-top issue works like this: Suppose that C is elected. It's
possible under median ratings methods that when some ballots rating a
different candidate "D" first (i.e. D is the first preference) are
removed from consideration, then a candidate D becomes the new winner.
In other words, when C wins, the D-first voters can criticize that they
were penalized for showing up to vote.

I should note that while IRV does not have these issues, probably most
of our proposed methods do, so they aren't necessarily deal-breakers.

Incidentally, Minmax (margins) passes Condorcet and mono-add-top. It's
not one of the methods I'd call advanced, though.

While median rating is more resistant to manipulation than Range, I
still view the manipulation potential as bad. For example, if you
"defensively" rate A as zero, in the Later-no-harm example above, out of
a quite reasonable fear that you need to do this to help B win instead
of A, this is the type of thing meant by manipulation. It is less likely
to have an effect than in Range, but you will still have the incentive
to do it.

There are two ways to consider strategic incentive. Suppose you have a
method whose benefit (additional utility) to a particular voter X is
something like:

http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+from+0+to+0.5

where the x axis is the size of the strategizing coalition X is part of,
when everybody not in the coalition votes honestly.

It's clear that no matter the size of X's group, X has an incentive to
strategize. A rational voter will clearly always strategize.

Now suppose the utility given to X is more like:

http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29++%28-SquareWave[1.2sqrt%28x%29]+%2B+1%29%2F2+from+0+to+0.5http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+*+%28-SquareWave%5b1.2*sqrt%28x%29%5d+%2B+1%29%2F2+from+0+to+0.5

i.e. there's a hard threshold before which strategy has absolutely no
effect, positive or negative.

A rational voter would still always strategize because there's no actual
harm to doing so, and if enough voters aligned with his candidate think
the way he does, he'll benefit. So it's a chance of getting something
better with no risk, and a rational voter would take that.

However, it seems unintuitive to me that a real voter would do so.
Instead, it seems more that voters value expressing their true
preference, and as long as the benefit to strategy is less than what
they gain by expressing their preference, honesty wins.

Your definition for "one citizen one vote" is difficult for me because
it seems focused on how the winner is found. For example you say
preferences should be counted equally "as long as possible, until"
something happens, which seems to assume that an election method
algorithm is something that unfolds over time. Normally I view an
election method as defined by its results, and there need not be a
single set of steps which finds the result. I wonder what would be an
example of a method that violates "one citizen one vote," and if there
might be another way of describing what is problematic about it.

S: I now accept that these three methods respect the principle of "one citizen one vote".

[….]

Hi Kristofer, Thank you for enabling me more fully to understand exactly how MAM is counted. For example, the link you sent me for Steve Seppley’s MAM counting tool has been very useful. With this tool, I have easily tested many other examples in an attempt to find a profile for which MAM elects a single-winner with a lower intensity of support from voters than the winner that would be elected by IRV. I did not find any such an example. For every example I tried, IRV and MAM elected the same winner. However, since IRV (unlike MAM) does not consider all the voters’ preferences until the majority winner is discovered, I assume there must be examples of the two methods electing different winners with different intensities of support. Still, I currently have no clear basis for continuing to suggest that IRV is more efficient at electing winners who have the highest available intensity of support from voters. Do we agree that MAM has no disadvantage with respect to IRV except that MAM’s method of counting would be much more difficult for ordinary voters to understand? Also, do you agree that MJ (like MAM) has the advantage over IRV in electing a single-winner only after counting all the votes of each voter (i.e. the ‘grades’ that every voter has given to all of the candidates)? In addition, I see MJ’s method of counting these grades as being easier for ordinary citizens to understand than MAM’s method. Consequently, do you also prefer MJ to MAM? I also see MJ as more likely to prompt voters not to ‘rank’ the candidates but instead to ‘grade’ all of them honestly, i.e. to encourage more voters to grade or REJECT each candidate in the light of each of their own visions of what an EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, or POOR candidate looks like. Electing the candidate with the highest ‘majority-grade’ also seems to give the least incentive to citizens to vote strategically. In this connection, below your say with regard to MJ that ‘it seems more that voters value expressing their true preference, and as long as the benefit to strategy is less than what they gain by expressing their preference, honesty wins.’ Of course, you say this only after listing a number objections that can be raised against MJ. Nevertheless, do you currently believe with me that these objections are less weighty than those that can also be raised against the practical use of any other single-winner method? Finally, your questions and arguments have also driven me to accept that each these three methods respect the principle of "one citizen one vote". ________________________________ From: Kristofer Munsterhjelm <km_elmet@t-online.de> Sent: Saturday, July 16, 2016 3:43 PM To: steve bosworth Subject: Re: (5) MJ better than IRV & MAM On 07/14/2016 06:11 PM, steve bosworth wrote: [….} K: Here's my detailed count (see attachment). See also http://mam.hostei.com/default.php which explains the procedure for any given ballot set. -km ________________________________ From: Kristofer Munsterhjelm <km_elmet@t-online.de> Sent: Wednesday, June 29, 2016 11:19 AM To: Kevin Venzke; steve bosworth; EM list Subject: Re: [EM] The easiest method to 'tolerate' On 06/29/2016 01:03 AM, Kevin Venzke wrote: > Hi Steve, > > Majority Judgment is a variety of "median rating" methods which I see as > pretty similar. Woodall made one himself called Quota-Limited > Trickle-Down and in fact if you google "woodall qltd" you can find a > .pdf with a chart of some of the properties. The most noteworthy here > are the failures of Later-no-harm and Mono-add-top. (Both are failures > that IRV does not share.) For Later-no-harm: Suppose that candidate A is > elected. It's possible that there is a bloc of voters who rated B above > A, but A above zero, and that if these voters had lowered their A rating > to zero, then candidate B would win instead, which is an outcome this > bloc of voters would have preferred. They could criticize that the > method should be smart enough to not use their A ratings to elect A when > it would have been possible for them to elect B. If not a fairness > issue, it's at least an issue of the method requiring voters to keep > certain strategy in mind. I'll also note that MJ fails: - Participation: Failure means that a voter might make the outcome worse from his point of view by going to the polls. (Participation is notoriously hard to pass) - All-equal ballots irrelevance: you can have a voter show up and give every candidate the same rank, yet that changes the outcome. You'd expect that to pull every candidate equally in the direction of the grade that voter gave to every candidate, but that's not true. See also, from a Range perspective: http://rangevoting.org/MedianVrange.html RangeVoting.org - Balinski & Laraki's "majority judgment ...<http://rangevoting.org/MedianVrange.html> rangevoting.org On Balinski & Laraki's "majority judgment" median-based range-like voting scheme And comparison versus ordinary [i.e. average-based] range voting > The Mono-add-top issue works like this: Suppose that C is elected. It's > possible under median ratings methods that when some ballots rating a > different candidate "D" first (i.e. D is the first preference) are > removed from consideration, then a candidate D becomes the new winner. > In other words, when C wins, the D-first voters can criticize that they > were penalized for showing up to vote. > > I should note that while IRV does not have these issues, probably *most* > of our proposed methods do, so they aren't necessarily deal-breakers. Incidentally, Minmax (margins) passes Condorcet and mono-add-top. It's not one of the methods I'd call advanced, though. > While median rating is more resistant to manipulation than Range, I > still view the manipulation potential as bad. For example, if you > "defensively" rate A as zero, in the Later-no-harm example above, out of > a quite reasonable fear that you need to do this to help B win instead > of A, this is the type of thing meant by manipulation. It is less likely > to have an effect than in Range, but you will still have the incentive > to do it. There are two ways to consider strategic incentive. Suppose you have a method whose benefit (additional utility) to a particular voter X is something like: http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+from+0+to+0.5 where the x axis is the size of the strategizing coalition X is part of, when everybody not in the coalition votes honestly. It's clear that no matter the size of X's group, X has an incentive to strategize. A rational voter will clearly always strategize. Now suppose the utility given to X is more like: http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+*+%28-SquareWave[1.2*sqrt%28x%29]+%2B+1%29%2F2+from+0+to+0.5<http://www.wolframalpha.com/input/?i=ln%2820x%2B1%29+*+%28-SquareWave%5b1.2*sqrt%28x%29%5d+%2B+1%29%2F2+from+0+to+0.5> i.e. there's a hard threshold before which strategy has absolutely no effect, positive or negative. A rational voter would still always strategize because there's no actual harm to doing so, and if enough voters aligned with his candidate think the way he does, he'll benefit. So it's a chance of getting something better with no risk, and a rational voter would take that. However, it seems unintuitive to me that a real voter would do so. Instead, it seems more that voters value expressing their true preference, and as long as the benefit to strategy is less than what they gain by expressing their preference, honesty wins. > Your definition for "one citizen one vote" is difficult for me because > it seems focused on how the winner is found. For example you say > preferences should be counted equally "as long as possible, until" > something happens, which seems to assume that an election method > algorithm is something that unfolds over time. Normally I view an > election method as defined by its results, and there need not be a > single set of steps which finds the result. I wonder what would be an > example of a method that violates "one citizen one vote," and if there > might be another way of describing what is problematic about it. S: I now accept that these three methods respect the principle of "one citizen one vote". [….]

Kristofer Munsterhjelm

Sat, Aug 6, 2016 3:16 PM

On 07/20/2016 11:31 PM, steve bosworth wrote:

Hi Kristofer,

Thank you for enabling me more fully to understand exactly how MAM is
counted. For example, the link you sent me for Steve Seppley’s MAM
counting tool has been very useful. With this tool, I have easily
tested many other examples in an attempt to find a profile for which MAM
elects a single-winner with a lower intensity of support from voters
than the winner that would be elected by IRV. I did not find any such
an example. For every example I tried, IRV and MAM elected the same
winner. However, since IRV (unlike MAM) does not consider all the
voters’ preferences until the majority winner is discovered, I assume
there must be examples of the two methods electing different winners
with different intensities of support. Still, I currently have no clear
basis for continuing to suggest that IRV is more efficient at electing
winners who have the highest available intensity of support from voters.

I have given a few examples where MAM elects a winner with greater
intensity of support (as you put it) than IRV does.

The classical example is IRV's center squeeze. Say there's a very
polarized electorate that either prefers candidate L or candidate R.
Furthermore, say there's a center candidate who everybody can accept:
he's everybody's second or first choice. Then IRV fails to look past the
first preferences and so its first decision is to eliminate this center
candidate, like this:

48: L>C>R
32: R>C>L
20: C>R>L

Plurality elects L, IRV elects R, and every Condorcet method as well as
Bucklin/MJ elects C.

L's intensity is: (10 * 48 + 8 * 52)/100 = 8.96
C's intensity is: (9 * 48 + 9 * 32 + 10 * 20)/100 = 9.2
R's intensity is: (8 * 48 + 10 * 32 + 9 * 20)/100 = 8.84.

A similar MJ example is:

48: L Excellent, C Good, R Poor
32: R Excellent, C Good, R Poor
20: C Excellent, R Good, L Poor

The phenomenon is pretty general, and something similar to it happened
in Burlington: Montroll was the Condorcet winner, but got eliminated
early because IRV couldn't see past first preferences.

Here's the 2009 Burlington election with only three candidates remaining:

1332: M>K>W
767: M>W>K
455: M
2043: K>M>W
371: K>W>M
568: K
1513: W>M>K
495: W>K>M
1289: W

Intensity of preference counts (assume everyone not ranked is ranked
equal last):

M: (133210 + 76710 + 455*10 + 2043 * 9 + 371 * 8 + 568 * 9 + 1513 * 9

495 * 8 + 1289 * 9)/8833 = 9.19
K: (13329+7678+4559+204310+37110+56810+15138+4959+12899)/8833 =
9.08
W: (13328+7679+4559+20438+3719+5689+151310+49510+128910)/8833 =
8.99

Another way to see it is that the center/left wing was stronger than the
right wing in Burlington; and that Plurality got both the wing and the
winner wrong, IRV got the wing right but the winner wrong, and Condorcet
would have got both right.

I still don't think your intensity of support measure is very good,
however. I could show how it leads to paradoxical results. For instance,
it doesn't agree with majority rule (you can have a majority rank X
first, yet X doesn't get the highest rating); and cloning can make any
candidate highly rated.

Do we agree that MAM has no disadvantage with respect to IRV except that
MAM’s method of counting would be much more difficult for ordinary
voters to understand?

MAM is more susceptible to voter strategy than IRV is, so if strategy is
rampant, IRV may be a better choice. But in such a setting, I'd rather
use a Condorcet-IRV hybrid to get Condorcet efficiency, e.g. the method
Warren calls WBS-IRV: http://www.rangevoting.org/TidemanRev.html#WBSIRV
I have also been somewhat trying, by brute force, to find a Condorcet
method that resists strategy well. My program found some three-candidate
methods, but I haven't tried extending them to more than three candidates.

So, to refine the claim: when compared to MAM, IRV has no advantage that
I consider important (beyond what you have mentioned). I don't think MAM
itself is all that difficult to explain, but I concede that I'm not a
typical person as far as voting methods go.

Also, do you agree that MJ (like MAM) has the advantage over IRV in
electing a single-winner only after counting all
the votes of each voter (i.e. the ‘grades’ that every voter has given
to all of the candidates)? In addition, I see MJ’s method of
counting these grades as being easier for ordinary citizens to
understand than MAM’s method.

Yes, MJ takes more information into account than IRV does, and its
decision is less chaotic, i.e. it makes better use of the information it
does take into account.

Consequently, do you also prefer MJ to MAM?

In a scenario-2 situation, yes. In a scenario-3 situation, no.

I also see
MJ as more likely to prompt voters not to ‘rank’ the candidates but
instead to ‘grade’ all of them honestly, i.e. to encourage more voters
to grade or REJECT each candidate in the light of each of their own
visions of what an EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, or POOR
candidate looks like.

What you're saying here is in essence that you think scenario 2 is more
likely to reflect the real world than scenario 3: that voters, if given
the opportunity to grade to a common standard, will do so. I suppose I
lean in that direction, but others (e.g. Kevin Venzke) disagree.

If someone were to ask me "MJ or Condorcet?", I'd say "either is fine"
(assuming clone independent Condorcet etc). In the light of full
information, one might very well be better than the other, but as it is,
I don't know which direction it'd go.

B&L's data supports what you're saying. If they hadn't gathered that
data, I would have preferred Condorcet more strongly of the two.

Electing the candidate with the highest ‘majority-grade’ also seems
to give the least incentive to citizens to vote strategically.

In this connection, below your say with regard to MJ that ‘it seems more
that voters value expressing their true preference, and as long as the
benefit to strategy is less than what they gain by expressing their
preference, honesty wins.’

Yes. There's a class of rating/grading methods that go like this:

Each voter gives information about each candidate (e.g. ratings,
grades). The information is so that if a candidate joins, that doesn't
need to change the information about any other candidate.
The method works by calculating a score f(X) for each candidate X,
where the function only uses the information on that candidate alone.
If a voter increases his grade or rating of some candidate X, f(X)
will never decrease.
The candidate with the greatest f() score wins.

In MJ, f returns the majority grade (possibly with some tiebreakers). In
Range, f returns the sum of ratings.

These methods all have the property that if a voter can cleanly separate
the candidates into two categories "I like these" and "I don't like
these", then he'll never be worse off by rating the former at maximum
and the latter at minimum.

Of those methods, I think MJ is the most resistant to strategy (for the
reasons stated in the MJ paper, or because the statistical breakdown
point of the median is 0.5 which is the greatest possible). One result
of this is that it's possible for voters who don't cleanly divide the
candidates into two groups to vote without worrying too much about
whether they are throwing their vote away.

Of course, you say this only after listing a number objections that can
be raised against MJ. Nevertheless, do you currently believe with me
that these objections are less weighty than those that can also be
raised against the practical use of any other single-winner method?

I don't see mono-add-top or participation failures as being very
important. All-equal ballots irrelevance (IIB) is somewhat more
counterintuitive, but in the greater view of things, I think I can agree
with what you're saying.

However, again, I'd like to mention that this holds in a scenario-2
situation. If the voters start to use the grades as rankings (i.e. a
voter rating his first preference VERY GOOD, his second GOOD, his third
best ACCEPTABLE, and so on, even if he thinks every candidate is
mediocre), then much of the benefit of MJ is lost. If that happens,
Condorcet methods are better.

Finally, your questions and arguments have also driven me to accept
that each these three methods respect the principle of "one citizen one
vote".

"One citizen one vote" seems to be a very fuzzy concept. But it is good
that the methods respect that principle in your eyes :-)

On 07/20/2016 11:31 PM, steve bosworth wrote: > Hi Kristofer, > > Thank you for enabling me more fully to understand exactly how MAM is > counted. For example, the link you sent me for Steve Seppley’s MAM > counting tool has been very useful. With this tool, I have easily > tested many other examples in an attempt to find a profile for which MAM > elects a single-winner with a lower intensity of support from voters > than the winner that would be elected by IRV. I did not find any such > an example. For every example I tried, IRV and MAM elected the same > winner. However, since IRV (unlike MAM) does not consider all the > voters’ preferences until the majority winner is discovered, I assume > there must be examples of the two methods electing different winners > with different intensities of support. Still, I currently have no clear > basis for continuing to suggest that IRV is more efficient at electing > winners who have the highest available intensity of support from voters. I have given a few examples where MAM elects a winner with greater intensity of support (as you put it) than IRV does. The classical example is IRV's center squeeze. Say there's a very polarized electorate that either prefers candidate L or candidate R. Furthermore, say there's a center candidate who everybody can accept: he's everybody's second or first choice. Then IRV fails to look past the first preferences and so its first decision is to eliminate this center candidate, like this: 48: L>C>R 32: R>C>L 20: C>R>L Plurality elects L, IRV elects R, and every Condorcet method as well as Bucklin/MJ elects C. L's intensity is: (10 * 48 + 8 * 52)/100 = 8.96 C's intensity is: (9 * 48 + 9 * 32 + 10 * 20)/100 = 9.2 R's intensity is: (8 * 48 + 10 * 32 + 9 * 20)/100 = 8.84. A similar MJ example is: 48: L Excellent, C Good, R Poor 32: R Excellent, C Good, R Poor 20: C Excellent, R Good, L Poor The phenomenon is pretty general, and something similar to it happened in Burlington: Montroll was the Condorcet winner, but got eliminated early because IRV couldn't see past first preferences. Here's the 2009 Burlington election with only three candidates remaining: 1332: M>K>W 767: M>W>K 455: M 2043: K>M>W 371: K>W>M 568: K 1513: W>M>K 495: W>K>M 1289: W Intensity of preference counts (assume everyone not ranked is ranked equal last): M: (1332*10 + 767*10 + 455*10 + 2043 * 9 + 371 * 8 + 568 * 9 + 1513 * 9 + 495 * 8 + 1289 * 9)/8833 = 9.19 K: (1332*9+767*8+455*9+2043*10+371*10+568*10+1513*8+495*9+1289*9)/8833 = 9.08 W: (1332*8+767*9+455*9+2043*8+371*9+568*9+1513*10+495*10+1289*10)/8833 = 8.99 Another way to see it is that the center/left wing was stronger than the right wing in Burlington; and that Plurality got both the wing and the winner wrong, IRV got the wing right but the winner wrong, and Condorcet would have got both right. I still don't think your intensity of support measure is very good, however. I could show how it leads to paradoxical results. For instance, it doesn't agree with majority rule (you can have a majority rank X first, yet X doesn't get the highest rating); and cloning can make any candidate highly rated. > Do we agree that MAM has no disadvantage with respect to IRV except that > MAM’s method of counting would be much more difficult for ordinary > voters to understand? MAM is more susceptible to voter strategy than IRV is, so if strategy is rampant, IRV may be a better choice. But in such a setting, I'd rather use a Condorcet-IRV hybrid to get Condorcet efficiency, e.g. the method Warren calls WBS-IRV: http://www.rangevoting.org/TidemanRev.html#WBSIRV I have also been somewhat trying, by brute force, to find a Condorcet method that resists strategy well. My program found some three-candidate methods, but I haven't tried extending them to more than three candidates. So, to refine the claim: when compared to MAM, IRV has no advantage that I consider important (beyond what you have mentioned). I don't think MAM itself is all that difficult to explain, but I concede that I'm not a typical person as far as voting methods go. > Also, do you agree that MJ (like MAM) has the advantage over IRV in > electing a single-winner only after counting all > the votes of each voter (i.e. the ‘grades’ that every voter has given > to all of the candidates)? In addition, I see MJ’s method of > counting these grades as being easier for ordinary citizens to > understand than MAM’s method. Yes, MJ takes more information into account than IRV does, and its decision is less chaotic, i.e. it makes better use of the information it does take into account. > Consequently, do you also prefer MJ to MAM? In a scenario-2 situation, yes. In a scenario-3 situation, no. > I also see > MJ as more likely to prompt voters not to ‘rank’ the candidates but > instead to ‘grade’ all of them honestly, i.e. to encourage more voters > to grade or REJECT each candidate in the light of each of their own > visions of what an EXCELLENT, VERY GOOD, GOOD, ACCEPTABLE, or POOR > candidate looks like. What you're saying here is in essence that you think scenario 2 is more likely to reflect the real world than scenario 3: that voters, if given the opportunity to grade to a common standard, will do so. I suppose I lean in that direction, but others (e.g. Kevin Venzke) disagree. If someone were to ask me "MJ or Condorcet?", I'd say "either is fine" (assuming clone independent Condorcet etc). In the light of full information, one might very well be better than the other, but as it is, I don't know which direction it'd go. B&L's data supports what you're saying. If they hadn't gathered that data, I would have preferred Condorcet more strongly of the two. > Electing the candidate with the highest ‘majority-grade’ also seems > to give the least incentive to citizens to vote strategically. > In this connection, below your say with regard to MJ that ‘it seems more > that voters value expressing their true preference, and as long as the > benefit to strategy is less than what they gain by expressing their > preference, honesty wins.’ Yes. There's a class of rating/grading methods that go like this: - Each voter gives information about each candidate (e.g. ratings, grades). The information is so that if a candidate joins, that doesn't need to change the information about any other candidate. - The method works by calculating a score f(X) for each candidate X, where the function only uses the information on that candidate alone. - If a voter increases his grade or rating of some candidate X, f(X) will never decrease. - The candidate with the greatest f() score wins. In MJ, f returns the majority grade (possibly with some tiebreakers). In Range, f returns the sum of ratings. These methods all have the property that if a voter can cleanly separate the candidates into two categories "I like these" and "I don't like these", then he'll never be worse off by rating the former at maximum and the latter at minimum. Of those methods, I think MJ is the most resistant to strategy (for the reasons stated in the MJ paper, or because the statistical breakdown point of the median is 0.5 which is the greatest possible). One result of this is that it's possible for voters who don't cleanly divide the candidates into two groups to vote without worrying too much about whether they are throwing their vote away. > Of course, you say this only after listing a number objections that can > be raised against MJ. Nevertheless, do you currently believe with me > that these objections are less weighty than those that can also be > raised against the practical use of any other single-winner method? I don't see mono-add-top or participation failures as being very important. All-equal ballots irrelevance (IIB) is somewhat more counterintuitive, but in the greater view of things, I think I can agree with what you're saying. However, again, I'd like to mention that this holds in a scenario-2 situation. If the voters start to use the grades as rankings (i.e. a voter rating his first preference VERY GOOD, his second GOOD, his third best ACCEPTABLE, and so on, even if he thinks every candidate is mediocre), then much of the benefit of MJ is lost. If that happens, Condorcet methods are better. > Finally, your questions and arguments have also driven me to accept > that each these three methods respect the principle of "one citizen one > vote". "One citizen one vote" seems to be a very fuzzy concept. But it is good that the methods respect that principle in your eyes :-)