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

[Kristofer Munsterhjelm]

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 :-)