[EM] (7) MJ better than IRV & MAM

steve bosworth stevebosworth at hotmail.com
Mon Aug 8 15:05:18 PDT 2016

Hi Kristofer and everyone,


From: Kristofer Munsterhjelm <km_elmet at t-online.de>
Sent: Saturday, August 6, 2016 3:16 PM
To: steve bosworth; election-methods at lists.electorama.com
Subject: Re: (5) MJ better than IRV & MAM

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

S: > 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.


K: 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.

S: > 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.

K: 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.

S: > Consequently, do you also prefer MJ to MAM?

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

S:  I think I may understand you here but to be sure, where did you previously describe ‘scenarios 2 & 3?

S: > 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
> candidate looks like.

K:  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).

S:  Do you see MAM as ‘independent Condorcet’?  Is the Condorcet method you have in mind better than MAM?

K:  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.

S:  By ‘full information’, are you thinking of the seemingly impractical possibility of a strategic voter knowing in advance how all the other voters are planning to vote?

K:  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.

S: > 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.’

S: 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.

S:  Isn’t the ‘sum of ratings’ more manipulatable than majory-grades?

K:  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.

S: But he would not also be able to help elect the EXCELLENT candidate any more than the ACCEPTABLE candidate.

K: 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.

S: > 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?

K: I don't see mono-add-top or participation failures as being very
important. All-equal ballots irrelevance (IIB) is somewhat more

S: Please explain: ‘All-equal ballots irrelevance (IIB)’

K: …. but in the greater view of things, I think I can agree
with what you're saying.

K: 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.

S:  I would rather say MJ would still retain the advantage of allowing each voter clearly to express her evaluations of each candidate, as well denying success to half of any such ranking manipulations.

K:  If that happens, Condorcet methods are better.

S:  Given the above advantages of MJ which you acknowledge (e.g. its count being somewhat simpler for ordinary citizens to understand), and the fact that it, not Condorcet, escapes Arrow’s paradoxes. I would like to understand why you say ‘Condorcet methods are better’.  Are not the rankings attached to Condorcet doubly subject to manipulation when compared to those that might be imported by some citizens using MJ to rank rather than grade?


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