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

[steve bosworth]

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 at 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 at 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".


[….]



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